4,349 results on '"fuzzy numbers"'
Search Results
2. The simplest fuzzy variational formulation and its generalization.
- Author
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Hatif, Sinan and Fadhel, Fadhel S.
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LAGRANGE equations , *GENERALIZATION , *FUZZY numbers - Abstract
In the present paper, we employ the first variation method to derive the fuzzy necessary condition, as a Euler-Lagrange equation for extremizing both the simplest and the generalized fuzzy variational problems. The latter class of problems includes those with higher derivatives, subject to the generalized Hukuhara differentiability. To illustrate the validity of the newly obtained Euler-Lagrange equation, two examples are considered in which the first example is considered with trapezoidal fuzzy numbers as the endpoints conditions while the second example is considered with triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]
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- 2024
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3. The convex fuzzy metric space.
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Kider, Jehad R.
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METRIC spaces , *BINARY operations , *FUZZY numbers , *CONTINUOUS functions - Abstract
Here our goal is to present another type of fuzzy metric space known as convex fuzzy metric space which does not depends on the binary operations t-norm and t-conorm then some examples are introduced to show the existences of such space. After that important concepts and properties of this space is introduced with proves here we proved that the convex fuzzy metric is a fuzzy continuous function. To construct more convex fuzzy metric spaces here we proved that the cross product of finite number of convex fuzzy metric space is again a convex fuzzy metric space. [ABSTRACT FROM AUTHOR]
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- 2024
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4. Generalized hendecagonal fuzzy number.
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Premalatha, M., Jeeva, A., Selvaraj, A., and Karthik, S.
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FUZZY numbers , *MEMBERSHIP functions (Fuzzy logic) , *FUZZY sets , *RESEARCH personnel , *DECISION making , *SOFT sets - Abstract
In the process of decision making, ranking vague figures is essential. Researchers in the field of decision-making analysis have used a wide variety of fuzzy numbers, such as triangular fuzzy numbers, trapezoidal fuzzy numbers, pentagonal fuzzy numbers, hexagonal fuzzy numbers, heptagonal fuzzy numbers, and so on, in order to find solutions to problems that occur in the real world that take place in an uncertain environment. For linear symmetric, asymmetric, and non-linear symmetric, the generalised definition of asymmetric is provided here. This research investigates hendecagonal fuzzy numbers, and it establishes membership functions and alpha cuts. [ABSTRACT FROM AUTHOR]
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- 2024
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5. New algorithmic approach for solving transportation problem in fuzzy environment with trapezoidal fuzzy numbers.
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Pooja, M., Thangapandi, C., and Srinivasan, R.
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FUZZY numbers , *PROBLEM solving - Abstract
In this paper, we have proposed a new algorithm to find optimal solutions to fuzzy transportation problems. Here, defuzzified the trapezoidal fuzzy numbers by implementing the ranking methodology. This article gives methodology that brings down the optimal solution. The numerical example illustrates the validity of our proposed method. [ABSTRACT FROM AUTHOR]
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- 2024
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6. Benefit of warm-up period, maintenance, reworking, and fuzzy learning in a cleaner production system.
- Author
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Bhatnagar, Pankaj, Sami, Saif, Kumar, Satish, and Yadav, Dharmendra
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GREEN business , *WARMUP , *CARBON emissions , *FUZZY numbers , *MANUFACTURING processes , *ENERGY consumption - Abstract
In any manufacturing process, lots of challenges are faced by the manufacturer, and how these challenges are considered and resolved in a profitable way is also a challenge for researchers. This study investigates a cleaner production inventory model, considering the warm-up period and maintenance of machines. Imperfect production is considered in the warm-up period and normal period. In order to reduce the waste in society, after screening, reworking of faulty goods is performed. Environmental concerns are also considered in the form of associated costs due to energy consumption and carbon emissions in this model. The proposed production model is fuzzified considering triangular fuzzy numbers, and later on, learning in fuzziness is also considered. The impact of promotional efforts is also incorporated into the model to take competitive advantage in the market. Numerical examples are presented for different cases, and managerial insights are provided to illustrate the model. Results indicate that fuzzy models give optimal results in terms of finance, while fuzzy learning models give a real picture of the financial status. [ABSTRACT FROM AUTHOR]
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- 2024
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7. A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework based on a novel cross-entropy measure.
- Author
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Peng, Juan Juan, Chen, Xin Ge, Tan, Hao, Sun, Jing Yi, Long, Qing Qi, and Jiang, Luo Luo
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FUZZY numbers , *FUZZY measure theory , *MILITARY supplies , *RATIO analysis , *PICTURES - Abstract
Multi-criteria decision-making (MCDM) entails a heterogeneous decision-making problem, which poses challenges for decision-makers (DMs) in generating an optimal solution. To address this, we have proposed a heterogeneous evaluation framework. First, a novel picture fuzzy cross-entropy measure was defined with the simultaneous consideration of uncertainty and hesitancy of picture fuzzy information, overcoming the shortcomings of the existing cross-entropy measure in relation to its validity and properties. Next, an optimisation-model for determining the objective weights of criteria was constructed based on the proposed closeness measurement and the step-wise weight assessment ratio analysis (SWARA) method. This model was constituted from both objective and subjective perspectives under the circumstance of completely unknown criterion information. Additionally, the conventional Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method was extended to the picture fuzzy environment, and a normalisation method was developed to transform heterogeneous judgments, including linguistic terms, interval numbers, and picture fuzzy numbers, into a unified representation form. A heterogeneous picture fuzzy SWARA-MARCOS evaluation framework was then established and used to solve a military equipment supplier selection problem. The results demonstrated the validity and feasibility of the proposed evaluation framework, while sensitivity, comparative, and complexity analyses demonstrated the robustness and superiority of it. [ABSTRACT FROM AUTHOR]
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- 2024
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8. A risk‐based fuzzy arithmetic model to determine safety integrity levels considering individual and societal risks.
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Cheraghi, Morteza, Reniers, Genserik, Eslami Baladeh, Aliakbar, Khakzad, Nima, and Taghipour, Sharareh
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FUZZY numbers , *FUZZY arithmetic , *SAFETY - Abstract
Risk‐based techniques such as risk graph and Layer of Protection Analysis (LOPA) are used to determine the Safety Integrity Level (SIL) of safety instrumented functions to ensure that risk is reduced to a tolerable level. However, these techniques have some drawbacks. For instance, they need absolute and precise numbers to evaluate SIL parameters, which are rarely available or are highly uncertain. In addition, they are incapable of considering individual and societal risks simultaneously. Moreover, risk tolerance criteria are likely to be used incorrectly in the LOPA technique, and risk graph is difficult to calibrate. In the current paper, a novel comprehensive fuzzy arithmetic model has been developed to determine the required SILs in process industries. The fuzzy required Risk Reduction Factor (RRF) is calculated for both individual and societal risks. Fuzzy numbers are developed from crisp intervals, based on the expected interval of the fuzzy numbers. Expert fuzzy‐scaled elicitation has been applied to obtain the SIL parameters. In the proposed model, the overall risk tolerance criterion and apportionment factor are defined as SIL parameters for both individual and societal risks to ensure that the applied risk criteria are compliant with the requirements of the system. In addition, an approach is introduced for determining the required SIL based on the fuzzy required RRF. The proposed methodology was demonstrated to alleviate the limitations, and thus, can be considered as a more precise alternative to the conventional methods. [ABSTRACT FROM AUTHOR]
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- 2024
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9. On Maximum Guaranteed Payoff in a Fuzzy Matrix Decision-Making Problem with a Fuzzy Set of States.
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Bekesiene, Svajone and Mashchenko, Serhii
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FUZZY sets , *SOFT sets , *FUZZY numbers , *MEMBERSHIP functions (Fuzzy logic) , *DECISION making - Abstract
The current study delves into a fuzzy matrix decision-making problem involving fuzzy sets of states. It establishes that a maximum guaranteed payoff constitutes a type-2 fuzzy set defined on the real line. Additionally, it provides the associated type-2 membership function. Moreover, the paper illustrates that the maximum guaranteed payoff type-2 fuzzy set of the decision-making problem can be broken down, based on the secondary membership grades, into a finite collection of fuzzy numbers. Each of these fuzzy numbers represents the maximum guaranteed payoff of the corresponding decision-making problem with a crisp set of states. This set corresponds to a specific cut of the original fuzzy set of states. Some properties of the maximum guaranteed payoff type-2 fuzzy set are investigated, and illustrative examples are provided. Since the problem formulation is symmetrical with respect to alternatives and states of nature, the results obtained can be used in the case of a fuzzy set of alternatives. [ABSTRACT FROM AUTHOR]
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- 2024
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10. Information aggregation based group decision making under Fermatean fuzzy environment for spent lithium-ion battery recycling techniques evaluation.
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Debbarma, Saima, Chakraborty, Sayanta, and Saha, Apu Kumar
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GROUP decision making , *LITHIUM-ion batteries , *ELECTRIC vehicle industry , *ELECTROLYTIC reduction , *FUZZY measure theory , *FUZZY numbers - Abstract
The increasing production of electric vehicles (EVs) has boosted the demand for recycling spent lithium-ion batteries (LiBs), as recycling preserves many valuable and useful materials such as cobalt, iron, nickel, and so on, and can lead to sustainable environmental development and public health safety by reducing waste volume. Mining and processing these minerals are both financially and environmentally costly, thus reclaiming and reusing them is prudent, as they can be damaging to the environment if not recycled. To ensure environmental sustainability, it is vital to select the best recycling procedure for wasted LiBs. However, uncertainty and vagueness are associated with the selection of recycling alternatives in real-life scenarios, so the current study aims to develop a multi-criteria group decision-making (MCGDM) model under the Fermatean fuzzy environment (FFE) to identify the optimal spent LiB recycling (LiBR) technique using the FF weighted power average operator (FFWPAO). The notion of Methods based on the Removal Effects of criteria (MEREC) has been extended under FFE with the aid of FFWPAO to identify the importance of influential parameters involved in spent LiB recycling (LiBR) process selection. A new Fermatean fuzzy distance measure (DsM) has been developed, and its significance has been demonstrated using theoretical explanation. Furthermore, a weighted DsM (WDsM), and a novel FFWDsM-based ranking approach have been proposed under FFE to evaluate LiBR processes. Furthermore, to address the constraints of the current Fermatean fuzzy score function (FFSF), an improved FFSF (IFFSF) has been presented that may rank any sort of Fermatean fuzzy numbers (FFNs), regardless of membership or non-membership grades.The envisioned integrated method's homogeneity and dependability have been evaluated by comparisons. The proposed approach has indicated "amalgamation of mechanical shredding (MS), electrolyte extraction (EE), electrode dissolution (ED), and cobalt electrochemical reduction (CECR)" as the best option for recycling spent LiBs. • An improved Fermatean fuzzy (FF) score function is introduced to rank FF numbers. • Novel FF distance measure and weighted distance measure (DM) are introduced. • FFWPAO based MEREC and novel FFWDM based ranking methods are developed and integrated. • Spent LiB recycling technology selection problem has been modelled and solved. • The proposed technique is validated through comparative and sensitivity analyses. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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11. A Novel Method for Solving the Time-Dependent Shortest Path Problem under Bipolar Neutrosophic Fuzzy Arc Values.
- Author
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K., Vidhya, A., Saraswathi, and Said, Broumi
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FUZZY numbers , *WEATHER , *FUZZY graphs , *ALGORITHMS , *COMPARATIVE studies - Abstract
The Shortest path problem is highly relevant in our daily lives, addressing uncertainties like traffic conditions and weather variations. To handle such uncertainties, we utilize Fuzzy Numbers. This paper focuses on Bipolar Neutrosophic Fuzzy Numbers, which have dual positive and negative aspects. They provide a robust framework for representing arc (node/edge) weights, signifying uncertain travel times between nodes. Importantly, these weights can change over time in bipolar neutrosophic fuzzy graphs. Our study introduces an extended Bellman-Ford Algorithm for identifying optimal paths and minimum times with time-dependent Bipolar Neutrosophic Fuzzy arc weights. We demonstrate its effectiveness through a step-by-step numerical example and conduct a comparative analysis to evaluate its efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2024
12. A Novel Fuzzy Cumulative Sum Control Chart with an α-Level Cut Based on Trapezoidal Fuzzy Numbers for a Real Case Application.
- Author
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Özdemir, Akın, Uçurum, Metin, and Serencam, Hüseyin
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QUALITY control charts , *STATISTICAL process control , *FUZZY numbers , *CALCITE , *PROCESS capability , *MANUFACTURING processes , *FUZZY measure theory - Abstract
Statistical process control (SPC) is widely used to monitor production processes in many industries under certain conditions. When dealing with a quality characteristic for uncertainty, fuzzy numbers are used in the context of the statistical process control (SPC) to monitor a fuzzy production process. The aim of this paper is fourfold. One, a fuzzy X ¯ - R control chart with an α-level cut is used based on trapezoidal fuzzy numbers (TFNs) for detecting the large shifts in the fuzzy process mean. Second, a fuzzy cumulative sum (FCUSUM) control with an α-level cut based on TFNs is firstly developed for detecting the small shifts in the fuzzy process mean. Third, the fuzzy process capability indices (FPCIs) are presented to measure the fuzzy process performance. Finally, an ultra-fine calcite production process is controlled with both the fuzzy X ¯ - R control chart and the proposed FCUSUM control chart. The results of the fuzzy X ¯ - R control charts show that the fuzzy production process is in control, and large shifts in the fuzzy process mean were detected. On the other hand, the results of the FCUSUM charts show that the fuzzy production process is out of control, and small shifts in the fuzzy process mean were detected. FPCIs are also conducted, and the results of fuzzy Cpk indices show that the ultra-fine calcite production process is not capable of meeting specification limits. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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13. PyMissingAHP: An Evolutionary Algorithm for Filling Missing Values in Incomplete Pairwise Comparisons Matrices with Real or Fuzzy Numbers via Mono and Multiobjective Approaches.
- Author
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Heymann, Mozart Caetano, Pereira, Valdecy, and Caiado, Rodrigo Goyannes Gusmão
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EVOLUTIONARY algorithms , *ANALYTIC hierarchy process , *FUZZY numbers , *GENETIC algorithms , *FUZZY sets , *FUZZY algorithms , *MATRICES (Mathematics) - Abstract
The Analytic Hierarchy Process (AHP) is a multi-criteria decision-making method that relies on constructing a pairwise comparison matrix (PCM) based on decision-makers' (DMs) judgments regarding alternatives and criteria. The objective is to obtain weights and ultimately rank and select alternatives. However, in some cases, DMs may not provide judgments due to a lack of experience, knowledge, or reluctance to express opinions on the subject, resulting in missing pairs in the PCM. Existing techniques for filling these missing pairs have inherent limitations. This paper demonstrates the application of the pymissingAHP algorithm, implemented in Python and available at https://bit.ly/3UFdqSZ, to address missing pairs using mono and multiobjective approaches. The pymissingAHP algorithm employs a Genetic Algorithm (GA) featuring a specialized encoding to address this issue. Our approach can handle mono or multiple objective scenarios, which involve minimizing the consistency index and maintaining the ranking of weights as defined by experts. Additionally, the algorithm accommodates fuzzy numbers within the AHP framework (FAHP). PCMs containing numerous missing values may yield multiple solutions and not accurately reflect experts' opinions. Although our approach can solve entirely depleted PCMs, obtaining as many comparisons as possible is recommended to ensure a faithful representation of expert opinions for the decision-makers. The pymissingAHP algorithm provides a significant advantage: the capacity to seek solutions that address single or multiple objectives, utilizing continuous or discrete values, and additionally, the ability to solve FAHP problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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14. A fuzzy computing approach to aggregate expert opinions using parabolic and exparabolic approximation procedures for solving multi-criteria group decision-making problems.
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Ic, Yusuf Tansel
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GROUP decision making , *FUZZY decision making , *FUZZY sets , *TOPSIS method , *FUZZY numbers , *PROBLEM solving - Abstract
Triangular fuzzy numbers (TFNs) are widely used for selection problems to determine expert opinions using linguistic expressions. Some aggregation procedures are developed to determine expert opinions more accurately. However, there is a need for a simple and more useful procedure to solve the selection problems more suitably. For this purpose, our study offers a triangular, exparabolic, and parabolic area calculation-based approximation approach for TFNs to aggregate the possible hedges (very and more or less) for TFNs. Hence, this aggregation procedure provides a tuning opportunity for classical TFN expressions to capture possible tuning processes to reflect the hesitancies of experts. The technique for order preferences by similarity to ideal solution (TOPSIS) method is applied in the two studies from extant literature, and suitable alternatives are determined as a result of the ranking process. Finally, a comparative analysis is presented to illustrate the efficiency of the proposed procedure. The conventional TOPSIS model's ranking scores are very close for exemplified examples (i.e., 0.5308, 0.4510, 0.4550 and 0.5304, 0.4626, 0.4940), but the proposed model's result has fluctuated for the same examples (i.e., 0.346, 0,669, 0,567 and 0.208, 0.991, 0.148). So, the main advantage of the proposed aggregation procedure is the alternative ranking scores separation capability analyzed with their linguistic diversification. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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15. Type-2 Fuzzy Metric Spaces.
- Author
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Samanta, Upasana
- Abstract
In this paper, an attempt is made to define a Type-2 fuzzy metric on a nonempty set X by allowing it to take fuzzy numbers as values of distance of a pair of points under a membership grade which is also a fuzzy number. Its type-1 counterpart is a fuzzy metric mostly similar to those defined by Kramosil and Michalek10 and also by George and Veeramani.6 It is shown that the topology induced by this fuzzy metric is Hausdorff in nature. In this type of fuzzy metric space, Banach’s fixed point theorem and Edelstein’s fixed point theorems are extended. Finally decomposition theorems for this fuzzy metric are proved from which a justification of type-2 behavior of this fuzzy metric can also be interpreted. [ABSTRACT FROM AUTHOR]
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- 2024
- Full Text
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16. Disturbing Fuzzy Multi-Attribute Decision-Making Method with If Weight Information Is Disturbing Fuzzy Number.
- Author
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Li, Li and Yang, Jin
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FUZZY numbers , *FUZZY sets , *FUZZY integrals , *DECISION making , *REAL numbers - Abstract
Fuzzy multi-attribute decision-making is a hot research topic in which weight information is one of the conditions for forming a complete decision-making model, and it is also an important factor affecting the decision result. In most fuzzy multi-attribute decision-making problems, the weight information is often given in the form of real numbers. However, in real life, the weight information may not be suitable for specific numerical representation, or we cannot accurately determine the weight information. Therefore, it is very important to use fuzzy numbers to represent weight information. In this paper, we study the problem of disturbing fuzzy multi-attribute decision-making in which the attribute weight, decision-maker weight, and attribute information are given in the form of disturbing fuzzy numbers. Firstly, a new disturbing fuzzy integration operator, namely the disturbing fuzzy ring and multiplication aggregation (DFRMA) operator, is proposed, and its characteristics of closure, monotonicity, and boundary are studied. Then, the general steps of the disturbing fuzzy multi-attribute decision method based on the disturbing fuzzy ring and multiplication aggregation (DFRMA) operator are given, which include the single decision step and group decision step. Finally, an example is given to illustrate the practicability and effectiveness of the method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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17. An integrated design concept evaluation model based on interval valued picture fuzzy set and improved GRP method.
- Author
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Ma, Qing, Chen, Zhe, Tan, Yuhang, and Wei, Jianing
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FUZZY sets , *ANALYTIC hierarchy process , *INDUSTRIAL design , *QUALITY function deployment , *CONCEPTUAL design , *FUZZY numbers , *AMBIGUITY - Abstract
The objective of this research is to enhance the precision and efficiency of design concept assessments during the initial stages of new product creation. Design concept evaluation, which occurs at the end of the conceptual design phase, is a critical step in product development. The outcome of this evaluation significantly impacts the product's eventual success, as flawed design concepts are difficult to remedy in later stages. However, the evaluation of new product concepts is a procedure that encompasses elements of subjectivity and ambiguity. In order to deal with the problem, a novel decision-making method for choosing more logical new product concepts is introduced. Basically, the evaluation process is outlined in three main phases: the construction of evaluation index system for design concept alternatives, the calculation of weights for evaluation criteria and decision-makers, the selection of the best design concept alternatives. These stages are composed of a hybrid method based on kano model, multiplicative analytic hierarchy process (AHP) method, the entropy of IVPFS and improved grey relational projection (GRP) under interval-valued picture fuzzy set (IVPFS). The novel approach integrates the strength of interval-valued picture fuzzy number in handling vagueness, the advantage of multiplicative AHP and the merit of improved GRP method in modelling multi-criteria decision-making. In final, the effectiveness of the proposed model is validated through comparisons with other models. The potential applications of this study include but are not limited to product development, industrial design, and innovation management, providing decision-makers with a more accurate and comprehensive design concept evaluation tool. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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18. Clustering analysis for Pythagorean fuzzy sets and its application in multiple attribute decision making.
- Author
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Yang, Lei, Li, Deqing, Zeng, Wenyi, Ma, Rong, Xu, Zeshui, and Yu, Xianchuan
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FUZZY sets , *DECISION making , *CLUSTER analysis (Statistics) , *FUZZY algorithms , *IMAGE recognition (Computer vision) , *FUZZY numbers - Abstract
Pythagorean fuzzy sets, as a generalization of intuitionistic fuzzy sets, have a wide range of applications in many fields including image recognition, data mining, decision making, etc. However, there is little research on clustering algorithms of Pythagorean fuzzy sets. In this paper, a novel clustering idea under Pythagorean fuzzy environment is presented. Firstly, the concept of feature vector of Pythagorean fuzzy number (PFN) is presented by taking into account five parameters of PFN, and some new methods to compute the similarity measure of PFNs by applying the feature vector are proposed. Furthermore, a fuzzy similarity matrix by utilizing similarity measure of PFNs is established. Later, the fuzzy similarity matrix is transformed into a fuzzy equivalent matrix which is utilized to establish a novel Pythagorean fuzzy clustering algorithm. Based on the proposed clustering algorithm, a novel multiple attribute decision making (MADM) method under Pythagorean fuzzy environment is presented. To illustrate the effectiveness and feasibility of the proposed technique, an application example is offered. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
19. An improved loci method for outlier detection in fuzzy datasets based on fractional distance metric and outlierness degree.
- Author
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Hajiloei, Mehdi, Jahromi, Alireza Fakharzadeh, and Zolmani, Somayeh
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OUTLIER detection , *FUZZY numbers , *EUCLIDEAN distance , *FUZZY algorithms - Abstract
Density based methods are significant approaches in outlier detection for high dimensional datasets and Local correlation integral (LOCI) is one of the best of them. To extend LOCI for fuzzy datasets, we should employ suitable metrics to measure the distance between two fuzzy numbers. Euclidean distance measure is a classic one in metric learning, but to overcome curse of dimensionality, we apply fractional distance metric too. Then, after introducing the FLOCI outlier detection algorithm for identifying the fuzzy outliers, we study the efficiency of the proposed method by doing some numerical experiments, in which the obtained results were completely successfull. We also compared the results with Fuzzy versions of Distance based ABOD and SOD methods to prove robustness of this approache. More than the above, one of the main advantages of the new approach is the determination of outlierness factor for each data which is not presented in classical LOCI method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
20. Solving a Multimodal Routing Problem with Pickup and Delivery Time Windows under LR Triangular Fuzzy Capacity Constraints.
- Author
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Ge, Jie and Sun, Yan
- Subjects
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CONTAINERIZATION , *FUZZY numbers , *BUDGET , *MATHEMATICAL reformulation , *MULTIMODAL user interfaces , *PROBLEM solving - Abstract
This study models a container routing problem using multimodal transportation to improve its economy, timeliness, and reliability. Pickup and delivery time windows are simultaneously formulated in optimization to provide the shipper and the receiver with time-efficient services, in which early pickup and delayed delivery can be avoided, and nonlinear storage periods at the origin and the destination can be minimized. Furthermore, the capacity uncertainty of the multimodal network is incorporated into the advanced routing to enhance its reliability in practical transportation. The LR triangular fuzzy number is adopted to model the capacity uncertainty, in which its spread ratio is defined to measure the uncertainty level of the fuzzy capacity. Due to the nonlinearity introduced by the time windows and the fuzziness from the network capacity, this study establishes a fuzzy nonlinear optimization model for optimization problem. A chance-constrained linear reformulation equivalent to the proposed model is then generated based on the credibility measure, which makes the global optimum solution attainable by using Lingo software. A numerical case verification demonstrates that the proposed model can effectively solve the problem. The case analysis points out that the formulation of pickup and delivery time windows can improve the timeliness of the entire transportation process and help to achieve on-time transportation. Furthermore, improving the confidence level and the uncertainty level increases the total costs of the optimal route. Therefore, the shipper and the receiver must prepare more transportation budget to improve reliability and address the increasing uncertainty level. Further analysis draws some insights to help the shipper, receiver, and multimodal transport operator to organize a reliable and cost-efficient multimodal transportation under capacity uncertainty through confidence level balance and transportation service and transfer service selection. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
21. A Novel Data-Envelopment Analysis Interval-Valued Fuzzy-Rough-Number Multi-Criteria Decision-Making (DEA-IFRN MCDM) Model for Determining the Efficiency of Road Sections Based on Headway Analysis.
- Author
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Andjelković, Dejan, Stojić, Gordan, Nikolić, Nikola, Das, Dillip Kumar, Subotić, Marko, and Stević, Željko
- Subjects
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DATA envelopment analysis , *MULTIPLE criteria decision making , *INFRASTRUCTURE (Economics) , *DECISION making , *FUZZY numbers - Abstract
The capacity of transport infrastructure is one of the very important tasks in transport engineering, which depends mostly on the geometric characteristics of road and headway analysis. In this paper, we have considered 14 road sections and determined their efficiency based on headway analysis. We have developed a novel interval fuzzy-rough-number decision-making model consisting of DEA (data envelopment analysis), IFRN SWARA (interval-valued fuzzy-rough-number stepwise weight-assessment-ratio analysis), and IFRN WASPAS (interval-valued fuzzy-rough-number weighted-aggregate sum–product assessment) methods. The main contribution of this study is a new extension of WASPAS method with interval fuzzy rough numbers. Firstly, the DEA model was applied to determine the efficiency of 14 road sections according to seven input–output parameters. Seven out of the fourteen alternatives showed full efficiency and were implemented further in the model. After that, the IFRN SWARA method was used for the calculation of the final weights, while IFRN WASPAS was applied for ranking seven of the road sections. The results show that two sections are very similar and have almost equal efficiency, while the other results are very stable. According to the results obtained, the best-ranked is a measuring segment of the Ivanjska–Šargovac section, with a road gradient = −5.5%, which has low deviating values of headways according to the measurement classes from PC-PC to AT-PC, which shows balanced and continuous traffic flow. Finally, verification tests such as changing the criteria weights, comparative analysis, changing the λ parameter, and reverse rank analysis have been performed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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22. The Inverse and General Inverse of Trapezoidal Fuzzy Numbers with Modified Elementary Row Operations.
- Author
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Mashadi, Safitri, Yuliana, Sukono, Prihanto, Igif Gimin, Johansyah, Muhamad Deni, and Saputra, Moch Panji Agung
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FUZZY numbers , *REAL numbers , *NUMBER systems , *ADDITION (Mathematics) , *LINEAR systems , *RESEARCH personnel - Abstract
Trapezoidal positive/negative fuzzy numbers have no single definition; instead, various authors define them in relation to different concepts. This means that arithmetic operations for trapezoidal fuzzy numbers also differ. For the operations of addition, subtraction, and scalar multiplication, there are not many differences; for multiplication, however, there are many differences. In general, multiplication is divided into various cases. For the inverse operation, there is not much to define; in general, for any trapezoidal fuzzy number u ~ , u ~ ⊗ 1 u ~ = i ~ = (1 , 1 , 0 , 0) does not necessarily apply. As a result of the different arithmetic operations for multiplication and division employed by various authors, several researchers have tackled the same problem and reached different solutions, meaning that the application will also produce different results. To date, many authors have proposed various alternatives for the algebra of the trapezoidal fuzzy number. In this paper, using the parametric form approach to trapezoidal fuzzy numbers, an alternative to multiplication with only one formula is constructed for various cases. Furthermore, based on the definition of multiplication for any trapezoidal fuzzy number, u ~ is constructed 1 u ~ so that u ~ ⊗ 1 u ~ = i ~ = (1 , 1 , 0 , 0) . Based on these conditions, we show that various properties that apply to real numbers also apply to any trapezoidal fuzzy number. Furthermore, we modify the elementary row operational steps for the trapezoidal fuzzy number matrix, which can be used to determine the inverse of a trapezoidal fuzzy number matrix with the order m × m . We also give the steps and examples necessary to determine the general inverse for a trapezoidal fuzzy number matrix of the order m × n with m ≠ n . This ability to easily determine the inverse and general inverse of a trapezoidal fuzzy number matrix has a number of applications, such as solving fully trapezoidal fuzzy number linear systems and fuzzy transportation problems, especially in applications in fields outside of mathematics; for example, the application of triangular fuzzy numbers in medical problems is a topic currently receiving a significant amount of attention. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Research on Virtual Enterprise Partner Selection Based on Fuzzy Number Ranking Score with Distance-area Index.
- Author
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Junfeng Zhao, Zhiyan Chen, Xue Deng, Yechun Yu, Dayong Ye, and Fengting Geng
- Subjects
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BUSINESS partnerships , *ANALYTIC hierarchy process , *FUZZY numbers - Abstract
It is very crucial for virtual enterprises to select the suitable partners when facing unprecedented opportunities and challenges. Most research in this area relies on the Analytic Hierarchy Process method. However, an alternative and potentially more effective approach is proposed by using the fuzzy number ranking score model to assess virtual enterprise partners, yet there has been limited investigation in this direction. In our paper, we establish evaluation criteria for selecting partners for virtual enterprises, including capability, efficiency, cost, risk, goal congruence, and trust level. Subsequently, we develop a ranking score model based on distance-index and area-index for these six criteria in the fuzzy environment. Additionally, the score function is calculated to rank potential virtual enterprise partners by considering defuzzification value, dispersion degree, and positive-negative area indices. Furthermore, the empirical analysis verifies the effectiveness of this method to solve the problem of partner selection in virtual enterprises. The results will help decision makers to make the right selections and decisions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
24. Trajectory Control of Mars Rover Based on Fuzzy Control Theory.
- Author
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Caiying Yang, Yuesheng Ye, Qingnan Huang, Ziying Zeng, and Hongyang Zhang
- Subjects
- *
MARS rovers , *LYAPUNOV stability , *TIME-varying systems , *FUZZY numbers , *SYSTEMS design - Abstract
A variable-parameter fuzzy model for the Mars Rover is designed to account for time-varying systems and sector nonlinearities. This model addresses the limitations of the traditional T-S fuzzy model by increasing the number of fuzzy rules, which allows for a more accurate representation of the Mars Rovers dynamics. Furthermore, the model reduces complexity through linearization, making it more practical for control system design. Gain-scheduling controllers for the Mars Rover is designed based on the second-order Lyapunov stability theorem. This approach ensures that the controller provides stable and reliable performance for the Rover under varying operating conditions. We will demonstrate the effectiveness of our work by simulation, showcasing the superiority over traditional methods. This variable-parameter fuzzy model has the potential to enhance the performance and reliability of the Mars Rover in real-world applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
25. Solution of interval two-points fuzzy boundary value problems using the shooting method.
- Author
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Hasan, Hussein R. and Fadhel, Fadhel S.
- Subjects
- *
BOUNDARY value problems , *FUZZY numbers , *ORDINARY differential equations , *TRAPEZOIDS - Abstract
The main objective of this paper is to introduce interval two-points fuzzy boundary value problems, in which the fuzziness course when the coefficients of the governing ordinary differential equation and/or the boundary conditions includes fuzzy numbers of either triangular or trapezoidal types. Such equations will be solved by introducing the concept of α – level sets, α ∈ [0,1] to treat the fuzzy ordinary differential equation into two nonfuzzy ordinary differential equations, which are corresponds to the lower and upper solutions of the interval fuzzy solution. The shooting method is applied to solve the resultant equations in both cases, linear and nonlinear. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
26. Optimal fuzzy solution for fully fuzzy quadratic fractional programming problems with decagonal membership function and ranking function technique.
- Author
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Hasan, Israa H. and Kanani, Iden H. Al
- Subjects
- *
FRACTIONAL programming , *QUADRATIC programming , *FUZZY numbers , *MEMBERSHIP functions (Fuzzy logic) , *SIMPLEX algorithm , *ARITHMETIC functions , *NONLINEAR functions - Abstract
The fuzziness approach is useful when finding a solution to a programming problem with some element of uncertainty. Using standard programming techniques, an optimal value for coefficients may be difficult to compute. The quality of fuzziness makes the programming method especially useful in situations where the coefficients are fuzzy-shaped representations of real-world occurrences and cannot be determined accurately. There have been many attempts in recent years to solve the problem of fractional programming. But not be bounded that many papers or studies have been written about the fuzzy quadratic fractional programming problem. This paper first introduces a development method for solving quadratic fractional programming (QFP) problems depending on separating the quadratic objective function. Secondly, to solve a fully fuzzy quadratic fractional programming (FFQFP) problem in which all the variables and parameters of the problem are decagonal fuzzy numbers, we proposed a new nonlinear membership function of decagonal fuzzy numbers with a new ranking function technique to obtain the optimal fuzzy solution to the (FFQFP) problem as well as, development of the algorithm simplex method, in which the new data of tableau are made available with both to help of the new ranking function and the arithmetic's decagonal operations to find the optimal decagonal fuzzy solution. Finally, the applied part of this paper includes an example that shows the steps to finding a fuzzy optimal solution to the presented problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
27. Novel Archimedean copula aggregation operator of fuzzy credibility numbers in multiple attribute decision making.
- Author
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Giakoumakis, Stylianos, Konguetsof, Avrilia, and Papadopoulos, Basil
- Subjects
- *
DECISION making , *FUZZY numbers , *AGGREGATION operators , *MULTIPLE comparisons (Statistics) , *ARITHMETIC - Abstract
In this paper, we develop a new computational model of Fuzzy Credibility Numbers (FCNs) with the usage of Archimedean Copulas. This process is achieved through the extension of the existing operations of FCNs. Following this extension procedure, the introduction of Archimedean Copula Weighted Arithmetic Averaging Aggregation Operator (ACWAAAO) for FCNs is achieved. Finally, a case study and comparison of the Multiple Attribute Decision Making (MADM) results is conducted. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Estimation of postseismic structural damage with the use of multiple linear regression and fuzzy linear regression methods.
- Author
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Gkountakou, Fani, Elenas, Anaxagoras, and Papadopoulos, Basil
- Subjects
- *
ACCELEROGRAMS , *FUZZY numbers , *EARTHQUAKES , *CIVIL engineers , *EFFECT of earthquakes on buildings , *CIVIL engineering , *BUILDING failures , *EARTHQUAKE damage - Abstract
Seismic analysis is recognized as the most important factor in the design of structures that ensures the protection of the building after the occurrence of an earthquake. Therefore, the evaluation of the postseismic structural damage is essential for determining the structural damage status of the building. In this study, the Multiple Linear Regression (MLR) method and Fuzzy Linear Regression (FLR) with triangular fuzzy numbers were applied to estimate the damage indices of an eight-story steel structure with the use of 65 accelerograms and 20 seismic parameters. A blind prediction approach was also implemented by applying a series of 10 different accelerograms in order to evaluate the accuracy of the methods. The results demonstrated that the FLR method revealed the smallest deviations from the observed output in contrast to the other method. Therefore, it can be used as a valid approach in the field of civil engineering. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Transformation and generalization of fuzzy implication using disjunction.
- Author
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Daniilidou, Athina, Konguetsof, Avrilia, Souliotis, Georgios, and Papadopoulos, Basil
- Subjects
- *
FUZZY numbers , *GENERALIZATION , *AXIOMS , *FUZZY sets , *HUMIDITY - Abstract
In this paper a family of fuzzy implications is derived using the operation of disjunction repeatedly and a new methodology of generating fuzzy implications is proposed. The set of the related fuzzy implication axioms was considered in order to check, which of them are satisfied. A relation is found and proven seeking the optimum number of repetitions according to the desired truth value of the implications. Finally, a large number of fuzzy implications was applied and compared using the data from temperature and humidity in a certain period of time. The proposed general formulae are verified by the computed results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Comparison of intuitionistic fuzzy time series forecasting models using different interval partitioning methods in predicting Malaysian crude palm oil prices.
- Author
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Alam, Nik Muhammad Farhan Hakim Nik Badrul, Ramli, Nazirah, Nassir, Asyura Abd, Mohd, Ainun Hafizah, and Mohammed, Norhuda
- Subjects
- *
FORECASTING , *NATURE reserves , *FUZZY numbers , *FUZZY sets , *VEGETABLE oils - Abstract
An intuitionistic fuzzy time series forecasting (IFTSF) model is capable of handling the non-determinism in time series data. Partitioning the universe of discourse into several intervals is one of the preliminary steps in conducting the IFTSF. The effective interval length for the IFTSF needs to be determined to decrease the computing complexity and speed up the forecasting procedure. This research develops the IFTSF model using three different interval partitioning methods, namely the average-based (L1), the frequency-density-based (L2) and the redivide-randomly chosen length (L3). The data are fuzzified using triangular fuzzy numbers, and the intuitionistic fuzzy sets (IFS) are then built. The IFS is then defuzzified using the crispification formula, which preserves the nature of the IFS. The Malaysian crude palm oil prices data are used to illustrate the proposed model. The forecasting accuracy of each model is measured, and the results show that the redivide-randomly chosen length outperforms the other interval partitioning methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. B-spline curve modeling of Z-number triangular fuzzy data.
- Author
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Zakaria, Rozaimi, Wahab, Abd. Fatah, Ismail, Isfarita, and Zenian, Suzelawati
- Subjects
- *
FUZZY numbers , *DATA modeling , *CURVES - Abstract
Uncertainty data modeling become a major problem in visualizing and describing the properties of data. Furthermore, if the data have multiple attributes of uncertainty such as the combination between imprecision and reliability of the data. Therefore, the combination of the two issues of uncertainty data can be defined as the Z-number whereas this Z-number is a dual fuzzy number known as ordered pair. This study focuses on developing a curve model by using the Z-number data after been defined. The curve model will use the B-spline function as a tool for visualizing the data. Also, the numerical example will be given and visualized in B-spline curve form of Z-number triangular fuzzy data points (ZnTrFDPs). Therefore, this finding gives the advantage of modeling data that have multiple attributes of uncertainties. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. Application of fuzzy Z-Hesitant data information in fuzzy C-means clustering analysis.
- Author
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Jamal, Noor Jamalina Mohd, Khalif, Ku Muhammad Naim Ku, and Mohamad, Mohd Sham
- Subjects
- *
CLUSTER analysis (Statistics) , *FUZZY numbers , *FUZZY algorithms , *FUZZY sets - Abstract
This paper aims to offer a new fuzzy Z-Hesitant methodology as a novel approach to analyzing fuzzy data information. In a nutshell, Z-Hesitant is the combination of Z-numbers with Hesitant Fuzzy Sets in which Z-numbers represent an ordered pair of fuzzy numbers having a structure of restriction (A) and reliability (B). The restriction (A) represents the uncertainty of the evaluation, while the reliability (B) represents a measure of certainty towards the restriction (A). On the other hand, Hesitant Fuzzy Sets hold the definition that the membership degree with respect of an element is a set of a variety of possible values in the range of [0,1]. Here, the importance of both extensions is evident. Z-numbers have a more remarkable ability to describe human knowledge because it considers the level of certainty in their calculation. On top of that, Hesitant Fuzzy Sets are beneficial because each of the opinions is considered, resulting in a more reasonable decision. Moreover, when the data information is converted using fuzzy Z-Hesitant methodology, it can significantly hold a substantial amount of what Z-numbers and Hesitant Fuzzy Sets offer. In this approach, the Z-Hesitant is described as an ordered pair of fuzzy numbers whose restriction (A) as well as reliability (B) are hesitant fuzzy numbers, resulting in more than one possible membership degree. Furthermore, applying Z-Hesitant data information in fuzzy clustering analysis using the fuzzy c-means algorithm is used to better comprehend this information. The results indicate that the fuzzy c-means algorithm successfully clusters the fuzzy Z-Hesitant data information. The comparison with other types of fuzzy data information shows that fuzzy Z-Hesitant data information clustering is more compact in internal cluster validation analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Interpolation rational Bezier curve modeling through fuzzy intuitionistic alpha-cut for uncertainty data visualization.
- Author
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Jaman, Siti Nasyitah and Zakaria, Rozaimi
- Subjects
- *
DATA visualization , *INTERPOLATION , *NUMBER concept , *SET theory , *GEOMETRIC modeling , *FUZZY numbers , *CURVES - Abstract
In order to model uncertainty in data, the fuzzy intuitionistic alpha-cut modeling interpolation rational Bezier curve process will be examined in this paper. In defining the uncertainty data and then modeling it using a chosen curve function, the basic theories and definitions that will be used are fuzzy set theory, fuzzy intuitionistic, and curve functions under geometrical modeling. This study has three main processes, the first of which is the definition of the uncertainty data using the fuzzy number concept. The fuzzy intuitionistic definition will then be used to calculate the alpha value (also known as the alpha-cut) for both membership values and non-membership values. Following the definition of fuzzy intuitionistic into an alpha-cut value, the fuzzification process will be applied to the data set. Defuzzification will be used after the fuzzification process to produce single values data that are defined as crisp fuzzy data for modeling. Rational Bezier interpolation will be used for visualization of the modeling data for each process in order to make analyses and conclusions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. A two-phase service single server Morkovian queue under N-policy with a fuzzy environment.
- Author
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Prasad, B. V. S. N. Hari, Sama, Hanumantha Rao, Vemuri, Vasanta Kumar, and Kalapala, Satish Kumar
- Subjects
- *
NONLINEAR programming , *FUZZY numbers , *NONLINEAR equations , *UNITS of time - Abstract
In this paper a controllable two-phase service single server Morkovian queue under N-policy is examined. The queue parameters and cost elements are assumed as Fuzzy numbers. Parametric nonlinear programming problems are developed based on the a-cuts and Zadeh's extension principle to determine the bounds of the minimum estimated cost per unit time(MEC) at the possibility level a. By considering the system parameters and cost elements as trapezoidal fuzzy numbers, numerical values for the bounds to the optimal threshold N and the MEC are computed by solving the nonlinear programming problems through MATLAB. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Calculating Insurance Claim Reserves with an Intuitionistic Fuzzy Chain-Ladder Method.
- Author
-
Andrés-Sánchez, Jorge De
- Subjects
- *
INSURANCE reserves , *INSURANCE claims , *INSURANCE companies , *FUZZY numbers , *EPISTEMIC uncertainty , *ACTIVE aging - Abstract
Estimating loss reserves is a crucial activity for non-life insurance companies. It involves adjusting the expected evolution of claims over different periods of active policies and their fluctuations. The chain-ladder (CL) technique is recognized as one of the most effective methods for calculating claim reserves in this context. It has become a benchmark within the insurance sector for predicting loss reserves and has been adapted to estimate variability margins. This variability has been addressed through both stochastic and possibilistic analyses. This study adopts the latter approach, proposing the use of the CL framework combined with intuitionistic fuzzy numbers (IFNs). While modeling with fuzzy numbers (FNs) introduces only epistemic uncertainty, employing IFNs allows for the representation of bipolar data regarding the feasible and infeasible values of loss reserves. In short, this paper presents an extension of the chain-ladder technique that estimates the parameters governing claim development through intuitionistic fuzzy regression, such as symmetric triangular IFNs. Additionally, it compares the results obtained with this method with those derived from the stochastic chain ladder by England and Verrall. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. Optimizing the Economic Order Quantity Using Fuzzy Theory and Machine Learning Applied to a Pharmaceutical Framework.
- Author
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Kalaichelvan, Kalaiarasi, Ramalingam, Soundaria, Dhandapani, Prasantha Bharathi, Leiva, Víctor, and Castro, Cecilia
- Subjects
- *
MACHINE theory , *MACHINE learning , *INVENTORY control , *FUZZY numbers , *INVENTORY costs - Abstract
In this article, we present a novel methodology for inventory management in the pharmaceutical industry, considering the nature of its supply chain. Traditional inventory models often fail to capture the particularities of the pharmaceutical sector, characterized by limited storage space, product degradation, and trade credits. To address these particularities, using fuzzy logic, we propose models that are adaptable to real-world scenarios. The proposed models are designed to reduce total costs for both vendors and clients, a gap not explored in the existing literature. Our methodology employs pentagonal fuzzy number (PFN) arithmetic and Kuhn–Tucker optimization. Additionally, the integration of the naive Bayes (NB) classifier and the use of the Weka artificial intelligence suite increase the effectiveness of our model in complex decision-making environments. A key finding is the high classification accuracy of the model, with the NB classifier correctly categorizing approximately 95.9% of the scenarios, indicating an operational efficiency. This finding is complemented by the model capability to determine the optimal production quantity, considering cost factors related to manufacturing and transportation, which is essential in minimizing overall inventory costs. Our methodology, based on machine learning and fuzzy logic, enhances the inventory management in dynamic sectors like the pharmaceutical industry. While our focus is on a single-product scenario between suppliers and buyers, future research hopes to extend this focus to wider contexts, as epidemic conditions and other applications. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. A fuzzy interval optimization approach for p-hub median problem under uncertain information.
- Author
-
Wang, Yu, Zhu, Tao, Yuan, Kaibo, and Li, Xin
- Subjects
- *
TABU search algorithm , *GENETIC algorithms , *FUZZY numbers , *NETWORK hubs , *DATA integrity , *ROBUST optimization , *SEARCH algorithms - Abstract
Stochastic and robust optimization approaches often result in sub-optimal solutions for the uncertain p-hub median problem when continuous design parameters are discretized to form different environmental scenarios. To solve this problem, this paper proposes a triangular fuzzy number model for the Non-Strict Uncapacitated Multi-Allocation p-hub Median Problem. To enhance the quality and the speed of optimization, a novel optimization approach, combining the triangular fuzzy number evaluation index with the Genetic-Tabu Search algorithm, is proposed. During the iterations of the Genetic-Tabu Search algorithm for finding the optimal solution, the fitness of fuzzy hub schemes is calculated by considering the relative positional relationships of triangular fuzzy number membership functions. This approach directly addresses the triangular fuzzy number model and ensures the integrity of information in the p-hub problem as much as possible. It is verified by the classic Civil Aeronautics Board and several self-constructed data sets. The results indicate that, compared to the traditional Genetic Algorithm and Tabu Search algorithm, the Genetic-Tabu Search algorithm reduces average computation time by 49.05% and 40.93%, respectively. Compared to traditional random, robust, and real-number-based optimization approaches, the proposed optimization approach reduces the total cost in uncertain environments by 1.47%, 2.80%, and 8.85%, respectively. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
38. Nonlinear prediction of fuzzy regression model based on quantile loss function.
- Author
-
Arefi, Mohsen and Khammar, Amir Hamzeh
- Subjects
- *
QUANTILE regression , *REGRESSION analysis , *KERNEL functions , *GOODNESS-of-fit tests , *FUZZY numbers , *NONLINEAR functions - Abstract
In this paper, a new approach is presented to fit a fuzzy regression model with the fuzzy coefficients when the explanatory variables and the response variable are as fuzzy numbers. In this approach, a nonlinear function is introduced to predict the response variables based on the kernel function. To estimate the parameters of regression model, the objective function is calculated using the quantile loss function on fuzzy numbers. To evaluate the goodness of fit of the optimal quantile fuzzy regression models, two indices are introduced using the similarity measures. Based on the presented results, the proposed fuzzy regression models have the perfect performances on the original data and also in the presences of different types of outliers. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. A hybrid model for choosing the optimal stock portfolio under intuitionistic fuzzy sets.
- Author
-
Rasoulzadeh, M., Edalatpanah, S. A., Fallah, M., and Najafi, S. E.
- Subjects
- *
DATA envelopment analysis , *FUZZY sets , *PORTFOLIO management (Investments) , *PARETO analysis , *STOCKS (Finance) , *GENETIC algorithms , *FUZZY numbers - Abstract
In the dynamic world of financial investment, crafting an optimal stock portfolio that judiciously balances risk, return, and efficiency emerges as a critical challenge. Despite the wealth of research on financial portfolio optimization, prevailing methodologies predominantly emphasize either risk minimization or return maximization, often overlooking the imperative for a holistic strategy that simultaneously boosts efficiency and effectiveness. Addressing this gap in the literature, this study introduces an innovative four-objective model that intricately blends risk, return, and efficiency considerations for the strategic selection of stock portfolios. This model ingeniously integrates the foundational principles of Markowitz’s mean-variance analysis with the sophisticated network data envelopment analysis (NDEA) techniques, significantly refining the portfolio selection methodology. It further distinguishes itself by incorporating returns represented as trapezoidal intuitionistic fuzzy numbers, adeptly capturing the inherent uncertainties in financial returns. Additionally, the model employs the network data envelopment analysis’s cross-efficiency principle, providing a nuanced measure of company performance. To effectively navigate the complexities of this model, we deploy the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a multi-objective genetic algorithm, demonstrating the model’s capability to unearth optimal solutions efficiently. The comparative analysis highlights that the proposed model significantly outperforms the efficiency and effectiveness of existing models, marking a substantial advancement in portfolio optimization strategies. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. A novel similarity measure based on the center of nine-point circle of the isosceles triangular fuzzy numbers and their applications.
- Author
-
Cheng, H.
- Subjects
- *
CIRCLE , *FUZZY numbers , *CENTROID , *TRIANGLES - Abstract
A new similarity/distance measure based on the center of nine-point circle of the isosceles triangular fuzzy numbers is recommend in this paper. Extend the similarity/distance measure based on centroid, orthocenter, circumcenter, incenter and nine-point circle center of the isosceles triangles. It is proved that this general similarity/distance measure conforms to the properties of distance. Subsequently, some examples are presented to justify the superiority and validity of the proposed similarity/distance measure between IFSs based on the center of nine-point circle, which demonstrate that this measure overcomes the disadvantage of the existing similarity measures. The application of the proposed similarity measure to deal with pattern recognition problems is described, and the results are correlated with those reported in some prevailing studies. In addition, a clustering technique to classify objects based on the proposed similarity measure is discussed. Through a detailed comparative analysis of some existing measures, it is concluded that some of the existing measures fail to discriminate the results obtained under different circumstances, such as zero division or counter intuitive cases; in contrast, the proposed similarity measure successfully overcomes this weakness. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. A NEW ALGORITHM TO SOLVE MULTI-OBJECTIVE TRANSPORTATION PROBLEM WITH GENERALIZED TRAPEZOIDAL FUZZY NUMBERS.
- Author
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SHARMA, RAMAKANT and TYAGI, SOHAN LAL
- Subjects
- *
FUZZY numbers , *TRANSPORTATION problems (Programming) , *GENERALIZATION - Abstract
Transportation Problem is a specific type of linear programming problem (LPP). Today, in the real world, the decision maker handles the multi-objectives at the same time. Fuzzy Concepts are used in LPP to handle the uncertainty and vagueness of data. This paper presents a new algorithm to solve a special type of fuzzy transportation problem (FTP) with the generalized trapezoidal fuzzy numbers (GTpFN) in which the decision maker is not certain about the exact value of transportation charge and the availabilities and requirements are the real numbers. In this Proposed Algorithm first, the fuzzy multi-objective transportation problem (FMOTP) is converted into a Crisp multi-objective transportation problem (MOTP) by the Proposed ranking function, and then the Crisp MOTP is transformed into a single objective transportation problem using the sum of objective functions values. The proposed algorithm gives an efficient compromise solution of FMOTP. To elaborate the proposed algorithm, one numerical example is solved. [ABSTRACT FROM AUTHOR]
- Published
- 2024
42. PROJECT SELECTION REVISITED: CUSTOMIZED TYPE-2 FUZZY ORESTE APPROACH FOR PROJECT PRIORITIZATION.
- Author
-
Uluskan, Meryem and Beki, Büşra
- Subjects
- *
TOPSIS method , *INDUSTRIAL capacity , *PROJECT evaluation , *AUTOMOBILE industry , *FUZZY sets , *DECISION making , *FUZZY numbers - Abstract
In this study, a customized version of a less-preferred methodology in decision-making processes, i.e., the interval type-2 fuzzy ORESTE (IT2F-ORESTE), is proposed, and its effectiveness for selecting the most viable projects is demonstrated. The findings are evaluated against those of fuzzy TOPSIS, which is among the most preferred methods, to provide evidence that the proposed method achieves comparable and even superior results. To this end, multicriteria decision-making studies conducted between 2016 and 2021 were examined. Subsequently, 30 automotive manufacturing projects were evaluated over seven criteria using the fuzzy TOPSIS and customized IT2F-ORESTE methods. The results revealed that IT2FORESTE assigned the highest ranks to projects with high earning potential, low cost, low number of operations, and high production capacity, whereas fuzzy TOPSIS failed to select the best project. To the best of the authors' knowledge, this is the first study to utilize this new IT2F-ORESTE method in project evaluation within the automotive industry and demonstrate its superiority over that of conventional methods. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
43. Impact of Fear and Prey Refuge Parameters in a Fuzzy Prey–Predator Model with Group Defense.
- Author
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Das, Soumya, Biswas, Suvankar, and Das, Pritha
- Subjects
- *
HOPF bifurcations , *LIMIT cycles , *FUZZY numbers , *CHAOS theory , *DERIVATIVES (Mathematics) - Abstract
Prey–predator interactions are perhaps the most ordinarily noticed phenomena in the environment. In this article, we have proposed a three-species prey–predator model incorporating three important factors, namely, prey refuge, group defense, and the growth rate of two prey species which is reduced for the amount of fear of the predator species. All the biological parameters of our system have been presented as fuzzy numbers to make them more realistic. The system has been studied analytically and numerically in the fuzzy sense. Model analyses such as positivity, boundedness, and permanence of the system are investigated. Stability analysis at all equilibrium points of the system has been studied. Hopf bifurcation analysis around the positive interior equilibrium point has been discussed. All the numerical simulations of the system are presented with suitable tables and graphical diagrams by using MATHEMATICA and MATLAB. Numerically, we have seen that the fear effect and prey refuge parameter can stabilize the system from chaos to a stable region. The effect of fear and prey refuge on stability has been analyzed in the numerical section. Stable focus and limit cycle analysis are investigated in crisp as well as fuzzy environment. The system undergoes Hopf bifurcation at the positive equilibrium point when the fear parameter k and refuge parameter m cross the threshold value in crisp as well as fuzzy environment. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
44. Ranking Type-2 Intuitionistic Fuzzy Sets Based on Dice Similarity Measures.
- Author
-
Annapurna, N. and Sireesha, V.
- Subjects
- *
FUZZY sets , *SOFT sets , *FUZZY numbers - Abstract
Ranking fuzzy numbers is an important part of decision-making in a fuzzy domain. Similarity measures are one of the widely used methods for sorting fuzzy numbers. In this paper, a Dice similarity measure is proposed for type-2 intuitionistic fuzzy sets (T2IFSs) and the properties of similarity measure are verified. The ranking in the proposed method is accomplished by comparing the given set to the best possible set under consideration. The proposed measure is tested on a wide range of T2IFSs and the results are analyzed with existing ranking methods. The comparison shows that the proposed method outperforms some of the shortcomings of existing ranking techniques and is thus effective in ranking. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
45. Special Discrete Fuzzy Numbers on Countable Sets and Their Applications.
- Author
-
Qin, Na and Gong, Zengtai
- Subjects
- *
TRIANGULAR norms , *IMAGE fusion , *ADDITION (Mathematics) , *FUZZY numbers , *PROBLEM solving , *ARITHMETIC - Abstract
There are some drawbacks to arithmetic and logic operations of general discrete fuzzy numbers, which limit their application. For example, the result of the addition operation of general discrete fuzzy numbers defined by the Zadeh's extension principle may not satisfy the condition of becoming a discrete fuzzy number. In order to solve these problems, special discrete fuzzy numbers on countable sets are investigated in this paper. Since the representation theorem of fuzzy numbers is the basic tool of fuzzy analysis, two kinds of representation theorems of special discrete fuzzy numbers on countable sets are studied first. Then, the metrics of special discrete fuzzy numbers on countable sets are defined, and the relationship between these metrics and the uniform Hausdorff metric (i.e., supremum metric) of general fuzzy numbers is discussed. In addition, the triangular norm and triangular conorm operations (t-norm and t-conorm for short) of special discrete fuzzy numbers on countable sets are presented, and the properties of these two operators are proven. We also prove that these two operators satisfy the basic conditions for closure of operation and present some examples. Finally, the applications of special discrete fuzzy numbers on countable sets in image fusion and aggregation of subjective evaluation are proposed. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
46. Enhanced MADM framework for fuzzy comprehensive evaluation of attack ability of basketball defenders with the triangular fuzzy neutrosophic numbers.
- Author
-
Rao, Fengshuo, Chung, Sung-Pil, and Xing, Kailin
- Subjects
- *
FUZZY numbers , *BASKETBALL , *BASKETBALL players , *FUZZY sets - Abstract
With the continuous improvement of modern basketball technology, higher requirements have been put forward for the personal abilities of basketball players. As the core of an organization, the offensive ability of a defender largely determines the team's performance. Therefore, it is necessary to objectively evaluate the attacking ability of defenders. Traditional techniques cannot objectively reflect the true level of players due to their strong subjectivity. Therefore, establishing a scientific evaluation technique is particularly important. The fuzzy comprehensive evaluation of attack ability of basketball defenders is viewed as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic number cross-entropy (TFNN-CE) technique is designed with help of cross-entropy and triangular fuzzy neutrosophic sets (TFNSs). Furthermore, Then, TFNN-CE technique is addressed to solve the MADM. Finally, a numerical example for fuzzy comprehensive evaluation of attack ability of basketball defenders is given and some comparisons are conducted to r illustrate advantages of the designed technique. The main contribution of this paper is addressed: (1) The TFNN-CE technique is addressed under TFNSs; (2) the TFNN-CE technique is addressed for MADM under TFNSs; (2) the TFNN-CE technique for fuzzy comprehensive evaluation of attack ability of basketball defenders is addressed; (3) Through the several efficient comparisons, it is addressed that TFNN-CE technique is effective for fuzzy comprehensive evaluation of attack ability of basketball defenders. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
47. Enterprise technological innovation capability evaluation using a spherical fuzzy number based CSM-EDAS model.
- Author
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Wang, Kai and Bai, Yameng
- Subjects
- *
TECHNOLOGICAL innovations , *FUZZY numbers , *GROUP decision making , *SMALL business , *FUZZY sets , *INFORMATION economy - Abstract
With the rapid development of science and technology, the flow of information has become more convenient, and society has entered the era of knowledge economy. In this era, technological innovation capability is becoming increasingly important and has become an important weapon for enterprises to survive in fierce competition, especially for technology-based small and medium-sized enterprises. Nowadays, technology-based small and medium-sized enterprises have developed many technological innovation achievements through continuous technological innovation, and have created a large number of high-tech products and services. Technological innovation has been proven to effectively improve the core competitiveness and economic benefits of technology-based small and medium-sized enterprises. Therefore, evaluating the technological innovation capabilities of technology-based small and medium-sized enterprises has both theoretical and practical significance. The enterprise technological innovation capability evaluation from a low carbon perspective could be deemed as the multiple attribute group decision making (MAGDM) problem. Recently, the evaluation based on distance from average solution (EDAS) technique and cosine similarity measure (CSM) technique has been employed to manage MAGDM issues. The spherical fuzzy sets (SFSs) are used as an efficient tool for portraying uncertain information during the enterprise technological innovation capability evaluation from a low carbon perspective. In this paper, the spherical fuzzy number EDAS based on the CSM (SFN-CSM-EDAS) technique is cultivated to manage the MAGDM under SFSs. Finally, a numerical study for enterprise technological innovation capability evaluation from a low carbon perspective is supplied to validate the proposed technique. The main contributions of this paper are outlined: (1) the EDAS and CSM technique was extended to SFSs; (2) the CRITIC technique is used to derive weight based on CSM technique under SFSs. (3) the SFN-CSM-EDAS technique is founded to manage the MAGDM under SFSs; (4) a numerical case study for enterprise technological innovation capability evaluation from a low carbon perspective and some comparative analysis is supplied to validate the SFN-CSM-EDAS technique. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
48. A probability-exponential method of converting Z-numbers and its systematic applications in multi-attribute decision making.
- Author
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Sun, Hong and Zhang, Xianyong
- Subjects
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DECISION making , *FUZZY numbers , *FUZZY sets , *INITIAL value problems , *STATISTICAL hypothesis testing , *STATISTICS , *DISTRIBUTION (Probability theory) - Abstract
Z-numbers contain fuzzy restrictions, credibility measures, and probability distributions to effectively represent uncertain information. Converting Z-numbers to fuzzy numbers facilitates extensive applications (such as multi-attribute decision-making (MADM)), thus becoming valuable for research purposes. Regarding Z-number conversions, the original method never considers the association probability, while probabilistic strategies offer better informatization. Recently, a probability-driven conversion starts with a linear transformation of the centroid difference between the fuzzy restriction and probabilistic distribution. However, it has the invalidation weakness of edge information due to underlying non-normalization. To improve this probability-linear conversion, a Z-number conversion is proposed by using underlying probability-exponential descriptions, and this new method is further applied to MADM. At first, the current probability-linear conversion is analyzed based on the initial non-probabilistic conversion, and its intrinsic weakness and correctional improvement are revealed. Then, the novel probability-exponential conversion resorts to an exponential characterization of centroid difference between the restriction and distribution, and it gains information enrichment due to underlying normalization. The refined method preserves the inherent characteristics of Z-numbers more effectively, facilitating their application in subsequent engineering practices. This is especially pertinent in decision-making systems based on expert input and initial value problems. The proposed method for converting Z-numbers aims to minimize information loss in transitions between Z-numbers and classical fuzzy numbers. This approach will be further explored in future research. Furthermore, the probability-exponential conversion induces an ExpTODIM algorithm for MADM, called PE-ExpTODIM. Three Z-number conversions (i.e., the non-probabilistic, probability-linear, and probability-exponential types) and three decision algorithms (i.e., ExpTODIM, EDAS, MOORA) are combined to establish a 3 × 3 framework of Z-number-driven MADM. Finally, the systematical 9 algorithms are applied to the problem of site selection of carbon storage. They are validated by criss-cross contrast analyses and statistical significance tests. Thus, PE-ExpTODIM exhibits the desired optimization. The last technology of statistical testing is original, ingenious, and valuable for MADM. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
49. Intelligent decision support system for pulmonary tuberculosis detection using bipolar fuzzy utility matrix and bipolar Mamdani fuzzy inference system.
- Author
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Natarajan, Ezhilarasan and Augustin, Felix
- Subjects
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FUZZY logic , *TUBERCULOSIS , *FUZZY systems , *DECISION support systems , *FUZZY numbers , *FUZZY sets - Abstract
Tuberculosis (TB) stands as the second leading global infectious cause of death, following closely behind the impact of COVID-19. The standard approach to diagnose TB involves skin tests, but these tests can yield inaccurate results due to limited access to healthcare and insufficient diagnostic resources. To enhance diagnostic accuracy, this study introduces a novel approach employing a Bipolar Fuzzy Utility Matrix Inference System (BFUMIS) and a Bipolar Mamdani Fuzzy Inference System (BMFIS) to assess TB disease levels. By considering factors associated with the causation of TB, the study devises suitable membership functions for bipolar fuzzy sets (BFS) using both triangular and trapezoidal fuzzy numbers. Using a point factor scale, the study clusters the rules systematically and assesses the level of uncertainty within these grouped rules by utilizing bipolar triangular fuzzy numbers (BTFN). To handle the BTFN, this study proposes converting bipolar triangular fuzzy into bipolar crisp score (CBTFBCS) algorithm as a defuzzification method. The optimal bipolar fuzzy utility sets (BFUS) are determined from the bipolar fuzzy utility matrix to identify patients' TB disease levels. These sets play a pivotal role in characterizing the severity of TB disease levels in patients. Additionally, rigorous validation of the utility framework is accomplished through measures of bipolar fuzzy satisfactory factors and sensitivity analyses. Furthermore, the study introduces the BMFIS, which presents a novel perspective on the conventional fuzzy inference system. This innovative system integrates the Mamdani fuzzy inference system (MFIS) into a bipolar fuzzy context, enriching the diagnostic process with enhanced insights. To demonstrate the efficacy of the proposed methods, extensive validation is carried out using actual clinical data. The performance metrics used in this validation effectively demonstrate the superiority of the proposed approach. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
50. TODIM-PROMETHEE method for tourism landscape planning design scheme evaluation based on the virtual reality technology under spherical fuzzy sets.
- Author
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Tong, Mingjia
- Subjects
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LANDSCAPE design , *FUZZY sets , *VIRTUAL reality , *GROUP decision making , *TOURISM , *FUZZY numbers - Abstract
How to explore the potential value of landscape, realize the organic combination of tourism landscape, enrich landscape elements and enhance tourism experience has become an important topic of tourism landscape planning and design, which is also a practical problem that needs to be solved urgently in the process of tourism landscape development and planning in different regions of China. The tourism landscape planning design scheme evaluation based on the virtual reality technology a typical multi-attribute group decision-making (MAGDM) problem. With the complexity of economic activities, uncertain information has an increasing impact on production activities. However, due to the ambiguity and uncertainty of human cognition, the factors affecting the risk of things cannot be accurately expressed. Therefore, selecting spherical fuzzy sets (SFSs) can make the expression of information more accurate and complete. On basis of the TODIM method and the PROMETHEE method, in this study, spherical fuzzy number TOMIM-PROMETHEE (SFN-TOMIM-PROMETHEE) method is implemented to solve the MAGDM problem under SFSs. Furthermore, CRITIC method under SFSs is implemented to determine relative weights. Then a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology is selected to illustrate the effectiveness and practicality of the method. Finally, the comparative analysis shows that the SFN-TOMIM-PROMETHEE method under SFSs is an effective method to deal with MAGDM problems. The main contribution of this paper is managed: (1) the TODIM and PROMETHEE technique was extended to SFSs; (2) CRITIC technique is employed to manage the weight values under SFSs. (3) the SFN-TOMIM-PROMETHEE technique is founded to manage the MAGDM under IVPFSs; (4) a numerical example for tourism landscape planning design scheme evaluation based on the virtual reality technology and comparison analysis are constructed to verify the feasibility and effectiveness of the SFN-TOMIM-PROMETHEE technique. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
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