Search

The single-valued neutrosophic hesitant fuzzy set (SV-NHFS) is a hybrid structure of the single-valued neutrosophic set and the hesitant fuzzy set that is designed for some incomplete, uncertain, and inconsistent situations in which each element has a few different values designed by the truth membership hesitant function, indeterminacy membership hesitant function, and falsity membership hesitant function. A strategic decision-making technique can help the decision-maker accomplish and analyze the information in an effcient manner. However, in our real lives, uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm in the SV-NHFS environment. In this paper, we first presented the basic operational laws for SV-NHF information under Einstein's t-norm and tconorm. Furthermore, important properties of Einstein operators, including the Einstein sum, product, and scalar multiplication, are done under SV-NHFSs. Then, we proposed a list of novel aggregation operators' names: Single-valued neutrosophic hesitant fuzzy Einstein weighted averaging, weighted geometric, order weighted averaging, and order weighted geometric aggregation operators. Finally, we discuss a multi-attribute decision-making (MADM) algorithm based on the proposed operators to address the problems in the SV-NHF environment. A numerical example is given to illustrate the work and compare the results with the results of the existing studies. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of Pythagorean fuzzy valued neutrosophic set (PFVNS) and Pythagorean fuzzy valued neutrosophic (PFVNV) constructed by considering Pythagorean fuzzy values (PFVs) instead of numbers for the degrees of the truth, the indeterminacy and the falsity, which is a new extension of intuitionistic fuzzy valued neutrosophic set (IFVNS). By means of PFVNSs, the degrees of the truth, the indeterminacy and the falsity can be given in Pythagorean fuzzy environment and more sensitive evaluations are made by a decision maker in decision making problems compared to IFVNSs. In other words, such sets enable a decision maker to evaluate the degrees of the truth, the indeterminacy and the falsity as PFVs to model the uncertainty in the evaluations. First of all, we propose the concepts of Pythagorean fuzzy t-norm and t-conorm and show that some Pythagorean fuzzy t-norms and t-conorms are expressed via ordinary continuous Archimedean tnorms and t-conorms. Then we define the concepts of PFVNS and PFVNV and provide a tool to construct a PFVNV from an ordinary neutrosophic fuzzy value. We also define some set theoretic operations between PFVNSs and some algebraic operations between PFVNVs via t-norms and t-conorms. With the help of these algebraic operations we propose some weighted aggregation operators. To measure discrimination information of PFVNVs, we define a simplified neutrosophic valued modified fuzzy cross-entropy measure. Moreover, we introduce a multi-criteria decision making method in Pythagorean fuzzy valued neutrosophic environment and practice the proposed theory to a real life multi-criteria decision making problem. Finally, we study the comparison analysis and the time complexity of the proposed method. [ABSTRACT FROM AUTHOR]

This paper aims to present some novel prioritized aggregation operators for aggregating complex intuitionistic fuzzy values (CIFVs). The aggregation operators are developed by assigning non-negative real numbers called as priority degrees among strict priority levels. The presented work is divided into three folds. The first fold is that uncertainties in the data are represented using CIFVs which have the characteristic of portraying membership and non-membership degrees over the unit disc of the complex plane. The second fold is to present prioritized averaging and geometric operators without priority degrees, prioritized averaging and geometric operators with priority degrees, prioritized ordered weighted averaging and geometric operators with priority degrees based on basic unit interval monotonic (BUM) function for aggregating dependent CIFVs. A number of propositions related to proposed operators are proved. The third fold is that a group decision-making approach based on proposed operators is developed and is applied on a decision-making problem. The results of proposed method are compared with several existing studies. The comparative study results reveal that the proposed approach is valid and gives fair results. The characteristics of the developed method are also compared with several existing approaches which highlight the superiority of the presented work over prevailing techniques. Besides this, the role of the priority degrees on aggregation result is also discussed in detail. [ABSTRACT FROM AUTHOR]

The novel multivalued neutrosophic aggregation operators are proposed in this paper to handle the complicated decision-making situations with correlation between specific information and partitioned parameters at the same time, which are based on weighted power partitioned Hamy mean (WMNPPHAM) operators for multivalued neutrosophic sets (MNS) proposed by combining the Power Average and Hamy operators. Firstly, the power partitioned Hamy mean (PPHAM) is capable of capture the correlation between aggregation parameters and the relationship among attributes dividing several parts, where the attributes are dependent definitely within the interchangeable fragment, other attributes in divergent sections are irrelevant. Secondly, because MNS can effectively represent imprecise, insufficient, and uncertain information, we proposed the multivalued neutrosophic PMHAM (WMNPHAM) operator for MNS and its partitioned variant (WMNPPHAM) with the characteristics and examples. Finally, this multiple attribute group decision making (MAGDM) technique is proven to be feasible by comparing with the existing methods to confirm this method's usefulness and validity. [ABSTRACT FROM AUTHOR]

This paper describes a novel multi-attribute group decision-making (MAGDM) algorithm based on complex intuitionistic fuzzy values (CIFVs). The present work is divided into three parts. In the first part, the uncertainties in the data are expressed in CIFVs with two membership degrees over the unit disc of the complex plane. The second part states some new operational laws based on tangential functions and the aggregation operators to aggregate the different CIFVs. The properties related to the proposed operations and operators are studied. A nonlinear multi-objective optimization model has been formulated by considering the maximizing and minimizing satisfaction and dissatisfaction degrees respectively to derive the attribute weights for the MAGDM problems. The model has been solved using the particle swarm optimization algorithm. Finally, a numerical example illustrates a MAGDM algorithm based on proposed operators. The reliability and effectiveness of the proposed method is explored by comparing it with several general studies. [ABSTRACT FROM AUTHOR]

Curriculum evaluation shoulders the important task of measuring the realization of talent cultivation. Effective curriculum evaluation enables the school to optimally arrange courses and improve the overall quality of students. To implement the curriculum evaluation effectively, this paper constructs a multiple attribute group decision-making (MAGDM) method according to the characteristics of curriculum evaluation. In view of the nonlinearity and hesitation of decision maker's cognition, unbalanced double hierarchy linguistic term sets (UDHLTSs) are utilized to fully represent the individual cognition of decision makers. Based on this, a novel MAGDM method with UDHLTSs is proposed. Firstly, to facilitate the analysis and treatment of UDHLTSs, the basic theories of UDHLTSs are perfected or complemented. Based on this, the unbalanced double hierarchy linguistic aggregation operator is defined and its properties are analyzed. Secondly, the weight determination method based on SWARA model is proposed to determinate the importance of each evaluation index under UDHLTSs environment. Thirdly, given the appetite of different decision-makers towards risk, an extended S-ARAS method is proposed based on S-utility function. Finally, to illustrate its effectiveness and rationality, the proposed method is applied in the case study of curriculum evaluation in university and compare with other methods. [ABSTRACT FROM AUTHOR]

Decision making is a universal behavior based on human cognitive information. In the real world, information related to human cognition is characterized by uncertainty and partial reliability, which is challenging to express with traditional and precise concepts. To better describe this type of uncertain information, Z-number is introduced by Zadeh, which contains uncertain information with both probability and fuzziness. Recently, Yager proposed the fusion of multiple multi-criteria aggregate functions, especially the fusion of multiple OWA-type aggregate functions, to deal with the group decision problem. However, such aggregation functions exhibit limitations in facing the uncertainty of expert information in real-world decision-making scenarios. To overcome this shortcoming, this paper extends Yager's aggregation method to the Z-number field and further propose a new group decision-making method based on the OWA aggregation operator and Z-number. The maximum entropy optimization model based on a genetic algorithm is used to determine the hidden probability distribution in Z-numbers to aggregate the Z-numbers, which solves the problem of information loss caused by ignoring the hidden probability distribution in the existing Z-number aggregation methods, and greatly preserves the original meaning of Z-number. Some numerical examples are used to demonstrate the rationality and effectiveness of the proposed method. Finally, a comparative analysis with existing methods expounds on the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Heronian mean (HM) operators, which can capture the interrelationship between input arguments with the same importance, have been a hot research topic as a useful aggregation technique. In this paper, we propose the generalized normalized cross weighted HM operators on the unit interval which can not only capture the interrelationships between input arguments but also aggregate them with different weights, some desirable properties are derived. Then, generalized cross weighted HM operators are extended to real number set and applied to binary classification. We list the detailed steps of binary classification with the developed aggregation operators, and give a comparison of the proposed method with the existing ones using the Iris dataset with 5-fold cross-validation (5-f cv), the accuracy of the proposed method for the training sets and the testing sets are both 100%. [ABSTRACT FROM AUTHOR]

In this paper, the use of the Fermatean fuzzy number (FFN) in a significant research problem of disaster decision-making by defining operational laws and score function is demonstrated. Generally, decision control authorities need to brand suitable and sensible disaster decisions in the direct conceivable period as unfitting decisions may consequence in enormous financial dead and thoughtful communal costs. To certify that a disaster comeback can be made, professionally, we propose a new disaster decision-making (DDM) technique by the Fermatean fuzzy Schweizer-Sklar environment. First, the Fermatean fuzzy Schweizer-Sklar operators are employed by decision-makers to rapidly analyze their indefinite and vague assessment information on disaster choices. Then, the DDM technique based on the FFN is planned to identify highly devastating disaster choices and the best available choices. Finally, the proposed regret philosophy DDM technique is shown functional to choose the ideal retort explanation for a communal fitness disaster in Pakistan. The dominance and realism of the intended technique are further defensible through a relative study with additional DDM systems. [ABSTRACT FROM AUTHOR]

Purpose: Single-valued neutrosophic sets (SVNSs) are efficient models to address the complexity issues potentially with three components, namely indeterminacy, truthness and falsity. Taking advantage of SVNSs, this paper introduces some new aggregation operators (AOs) for information fusion of single-valued neutrosophic numbers (SVNNs) to meet multi-criteria group decision-making (MCGDM) challenges. Design/methodology/approach: Einstein operators are well-known AOs for smooth approximation, and prioritized operators are suitable to take advantage of prioritized relationships among multiple criteria. Motivated by the features of these operators, new hybrid aggregation operators are proposed named as "single-valued neutrosophic Einstein prioritized weighted average (SVNEPWA) operator" and "single-valued neutrosophic Einstein prioritized weighted geometric (SVNEPWG) operators." These hybrid aggregation operators are more efficient and reliable for information aggregation. Findings: A robust approach for MCGDM problems is developed to take advantage of newly developed hybrid operators. The effectiveness of the proposed MCGDM method is demonstrated by numerical examples. Moreover, a comparative analysis and authenticity analysis of the suggested MCGDM approach with existing approaches are offered to examine the practicality, validity and superiority of the proposed operators. Originality/value: The study reveals that by choosing a suitable AO as per the choice of the expert, it will provide a wide range of compromise solutions for the decision-maker. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the concept of intuitionistic fuzzy hypersoft to pology. Certain properties of intuitionistic fuzzy hypersoft (IFH) to pology like IFH basis, IFH subspace, IFH interior and IFH cloure are investigated. Furthermore, the multicriteria decision making (MCDM) algorithms with aggregation operators based on IFH topology are developed. In Algorithm 1 and Algorithm 2, MCDM problem is applied for IFH sets and IFH topology, respectively. Any real-life implementations of the proposed MCDM algorithms are demonstrated by numerical illustrations. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy sets (T2FSs) were introduced by L. A. Zadeh in 1975 as an extension of type-1 fuzzy sets (T1FSs). In this extension, the degree to which an element belongs to a set is just a label of the linguistic variable “TRUTH,” which allows to represent reality in a more appropriate way. On the other hand, negations play an essential role within fuzzy sets theory. In fact, they are necessary in order to obtain, for example, complements of fuzzy sets, dual of a t-norm or a t-conorm, entropies, implications, as well as to study the possible contradictions appearing in a fuzzy system. However, meanwhile negations on [0, 1] (set of the membership degrees of a fuzzy set) have been deeply studied throughout the literature, the same has not happened with the negations on ${\bf M}$ = $\text{Map} \;([\text{0}, \text{1}],[\text{0}, \text{1}])$ , set of functions from [0, 1] to [0, 1] (and also set of the membership degrees of a T2FS), and so many aspects of the negations on ${\bf M}$ have not yet been investigated. In a previous paper, the axioms that an operation must satisfy to be considered a negation or a strong negation on a bounded partially ordered set were established. A family of strong negations on L and set of normal and convex functions of ${\bf M}$ were also presented. Moreover, let us note that the main characteristic of fuzzy systems is just the flexibility in order to be able to represent knowledge according to each situation, offering different models among which the expert can choose the one that best suits his/her criteria. Thus, it seems useful to find broad sets of negations in ${\bf M}$ and in L, which, as far as we know, have not been done by other researchers. According to these ideas, in this paper, the authors first present new negations and strong negations on L, and then show, for the first time, some negations on ${\bf M}$ with respect to each of the two partial orders defined in this set. [ABSTRACT FROM AUTHOR]

The 3D extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS) aim to describe experts' judgments more informatively and explicitly. In this paper, generalized three dimensional spherical fuzzy sets are presented with their arithmetic, aggregation, and defuzzification operations. Weighted Aggregated Sum Product A Ssessment (WASPAS) is a combination of two well-known multi-criteria decisionmaking (MCDM) methods, which are weighted sum model (WSM) and weighted product model (WPM). The aim of this paper is to extend traditionalWASPASmethod to spherical fuzzy WASPAS (SF-WASPAS) method and to show its application with an industrial robot selection problem. Additionally, we present comparative and sensitivity analyses to show the validity and robustness of the given decisions. [ABSTRACT FROM AUTHOR]

Spherical fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture fuzzy sets and Pythagorean fuzzy sets in order to deal with uncertainty and fuzziness information. This paper presents a multi-attribute group decision making method based on novel sine aggregation operators to help decision makers choose the optimal alternative. Moreover, the well-known sine trigonometry function preserves the periodic and symmetric nature about the origin, and hence, it satisfies the decision makers preferences over the multi-time phase parameters. Keeping these features and the importance of the spherical fuzzy (SF) sets, the objective of this paper is to present some robust sine trigonometric (ST) operation laws for SF sets. Associated with these laws, we define some series of new aggregation operators (AOs) named as ST-weighted averaging and geometric operators to aggregate the spherical fuzzy information. Afterward, we present group decision making techniques to solve the multi-attribute group decision making problems based on proposed AOs and illustrate with a numerical example of an internet finance soft power evaluation problem to validate it. Also, we conduct some comparison analysis to study the reasonability and practicality of the proposed method. [ABSTRACT FROM AUTHOR]

In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function solutions to the four usual distributive equations of ordinal sum fuzzy implications. And then sufficient and necessary conditions for ordinal sum implications distributing over overlap and grouping functions are given. [ABSTRACT FROM AUTHOR]

The q-rung orthopair fuzzy set (q-ROFS), initiated by Yager, is a novel tool to dispose of indeterminacy that considers the membership μ and non-membership ν , which satisfy the limited condition 0 ≤ μ q + ν q ≤ 1 . It can be employed in characterizing the vague preference more precisely and flexibly than intuitionistic fuzzy set and Pythagorean fuzzy set. q-ROFS has attracted deep concern of numerous researchers, which is mainly distributed in diverse research points such as comparison methods, aggregation operators, decision making methods, calculus, information measure, preference relation, graph and application scenarios. As a result of this growth, we give an overview of q-ROFS for offering a clear perspective on novel trends. A total of 80 q-ROFS related publications of Web of Science are in-depth analysis. Some significant results related to annual trends, country level, institutional level, journal level, highly cited papers, and research landscape are generated and illustrated. Eighteen future research directions or challenges related to the q-ROFS theory are indicated. Finally, the co-authorship analysis, the co-citation analysis, the co-occurrence analysis and the bibliographic coupling analysis are derived by VOSviewer software. [ABSTRACT FROM AUTHOR]

Recent technological advancements in computing, sensing and communication have led to the development of cyber-physical manufacturing processes, where a computing subsystem monitors the manufacturing process performance in real-time by analyzing sensor data and implements the necessary control to improve the product quality. This paper develops a predictive control framework where control actions are implemented after predicting the state of the manufacturing process or product quality at a future time using process models. In a cyber-physical manufacturing process, the product quality predictions may be affected by uncertainty sources from the computing subsystem (resource and communication uncertainty), manufacturing process (input uncertainty, process variability and modeling errors), and sensors (measurement uncertainty). In addition, due to the continuous interactions between the computing subsystem and the manufacturing process, these uncertainty sources may aggregate and compound over time. In some cases, some process parameters needed for model predictions may not be precisely known and may need to be derived from real time sensor data. This paper develops a dynamic Bayesian network approach, which enables the aggregation of multiple uncertainty sources, parameter estimation and robust prediction for online control. As the number of process parameters increase, their estimation using sensor data in real-time can be computationally expensive. To facilitate real-time analysis, variance-based global sensitivity analysis is used for dimension reduction. The proposed methodology of online monitoring and control under uncertainty, and dimension reduction, are illustrated for a cyber-physical turning process. [ABSTRACT FROM AUTHOR]

In this paper, we considered the defined intuitionistic fuzzy numbers (IFNs) on real numbers and proposed a new method based on Hamacher operators to operate with membership and non-membership degrees of the given IFN in aggregation process. Also, a new method will be introduced to compute the distance between IFNs. These methods will be applied to solve multi-attribute group decision-making (MAGDM) problems, in which IFNs were used to model the arising uncertainty from human judgments or assessments. To do it, Choquet integral, as a powerful tool in both independent and interactive criteria, will be used individually or as a tool to provide appropriate conditions for application of TOPSIS method. The applicability of these methods is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

Interval numbers are widely used in many fields to provide information about different scenarios. This paper presents several new uncertain average formulations using the ordered weighted average, prioritized, probabilistic and induced operators. First, the work introduces the uncertain prioritized induced probabilistic ordered weighted average (UPIPOWA) operator that its main applicability is in complex group decision making problems. Also, a wide range of special cases and extensions using quasi-arithmetic means are presented, such is the case of the quasi-arithmetic UPIPOWA (QUPIPOWA) operator. The study analyzes the applicability of this new approach in economic variables, specifically are imports and exports. Particularly, the paper focuses on measuring the imports and exports for Latin America for 2017. [ABSTRACT FROM AUTHOR]

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria. [ABSTRACT FROM AUTHOR]

This paper aims to present Bipolar valued probabilistic hesitant fuzzy sets (BVPHFSs) by combining bipolar fuzzy sets and probabilistic hesitant fuzzy sets (PHFSs). PHFSs are a strong version of hesitant fuzzy sets (HFSs) in terms of evaluated as probabilistic of each element. Probabilistic hesitant fuzzy sets (PHFSs) are a set structure that argues that each alternative should be evaluated probabilistically. In this framework, the proposed cluster allows probabilistic evaluation of decision- makers' opinions as negative. Thus, this case proposes flexibility about selection of an element and aids to overcome with noise channels. Furthermore, some new aggregation operators are discussed called bipolar valued probabilistic hesitant fuzzy weighted average operator (BVPHFWA), Generalized bipolar valued probabilistic hesitant fuzzy weighted average operator (GBVPHFWA), bipolar valued probabilistic hesitant fuzzy weighted geometric operator (BVPHFWG), Generalized bipolar valued probabilistic hesitant fuzzy weighted geometric operator (GBVPHFWG), bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric operator (BVPHFHWAG) and Generalized bipolar valued probabilistic hesitant fuzzy hybrid weighted arithmetic and geometric (GBVPHFHWAG) and some basic properties are presented. A score function is defined ranking alternatives. Moreover, two different algorithms are put forward with helping to TOPSIS method and by using aggregation operators over BVPHFSs. The validity of proposed operators are analyzed with an example and results are compared in their own. [ABSTRACT FROM AUTHOR]

A Single-valued neutrosophic set (SVNS) has recently been explored as a comprehensive tool to assess uncertain information due to varied human cognition. This notion stretches the domain of application of the classical fuzzy set and its extended versions. Various comparison measures based on SVNSs like distance measure, similarity measure, and, divergence measure have practical significance in the study of clustering analysis, pattern recognition, machine learning, and computer vision-related problems. Existing measures have some drawbacks in terms of precision and exclusion of information and produce unreasonable results in categorization problems. In this paper, we propose a generic method to define new divergence measures based on common aggregation operators and discuss some algebraic properties of the proposed divergence measures. To further appreciate the proposed divergence measures, their application to pattern recognition has been investigated in conjunction with the prominent existing comparison measures based on SVNSs. The comparative assessment sensitivity analysis of the proposed measures establishes their edge over the existing ones because of appropriate classification results. [ABSTRACT FROM AUTHOR]

Dombi operations have the advantage of flexible operations corresponding to a changeable parameter. Then, in the existing literature, the Dombi operations lack the periodic/multitemporal operation property, and also there are no trigonometric Dombi aggregation operators for multiple attribute decision making (MADM), which show their limitation and research gap in multiple periodic MADM applications. To address their limitation and research gap, the main objective of this paper is to propose some single-valued neutrosophic element (SvNE) trigonometric Dombi aggregation operators for MADM problems. Based on this motivation, this study mainly includes the following contexts. First, we propose the trigonometric Dombi operations and the trigonometric Dombi operation laws of SvNEs based on sine and arcsine functions. Second, we establish the SvNE arcsine and sine trigonometric Dombi weighted average (SvNEASTDWA) and SvNE arcsine and sine trigonometric Dombi weighted geometric (SvNEASTDWG) operators and discuss their features. Third, a MADM technique is developed in terms of the SvNEASTDWA and SvNEASTDWG operators to tackle periodic/multitemporal MADM problems. Finally, the proposed technique is applied to a case study on the selection of COVID-19 vaccines to validate its rationality and validity under the scenario of SvNEs. Comparative results reveal that the established MADM technique using the SvNEASTDWA and SvNEASTDWG operators can show the advantage of both periodicity and flexibility and meet the flexible and multitemporal MADM requirements in actual applications. [ABSTRACT FROM AUTHOR]

In this paper, a two-sided matching decision model based on interval-valued intuitionistic fuzzy environment is proposed to maximize the demand of individual differences. Firstly, the attribute feature table and weight matrix of both agents are constructed, and a formula for calculating the comprehensive advantage in the interval-valued intuitionistic fuzzy environment is given, namely the interval-valued intuitionistic fuzzy comprehensive advantage aggregation operator (IIFCAAO); Secondly, the interval-valued intuitionistic fuzzy decision matrix of both agents is calculated by using the comprehensive advantage aggregation operator, and the interval-valued intuitionistic fuzzy decision matrix is transformed into a score function matrix by using a score function formula; Thirdly, the two-sided matching model is established to maximize the score; Finally, the scientificity and practicability of the model are verified by an example of college students changing their majors. [ABSTRACT FROM AUTHOR]

The geometric-arithmetic mean inequality is undoubtedly the most important one in the area of information aggregation. Recently, some q-rung orthopair fuzzy aggregation operators were proposed based on the Hamacher operations. In this paper, we give a detailed theoretical and practical analysis of the developed Hamacher arithmetic and geometric operators for q-rung orthopair fuzzy values. First, we investigate the monotonicity of these Hamacher aggregation operators on q-rung orthopair fuzzy values with respect to the parameter within Hamacher operations. Then, we discuss the limiting cases of these q-rung orthopair fuzzy Hamacher aggregation operators as the parameter therein approaches to zero or infinity and give a new characterization of the boundedness of these aggregation operators. Subsequently, we establish the geometric-arithmetic mean inequality for q-rung orthopair fuzzy information based on Hamacher operations. Finally, we present a decision making method by use of these aggregation operators and apply it to the problem of enterprise resource planning system selection. [ABSTRACT FROM AUTHOR]

This research paper introduces novel aggregation methods known as the picture fuzzy soft-max Einstein interactive weighted average (PiFSMEIWA) and the picture fuzzy soft-max Einstein interactive weighted geometric (PiFSMEIWG) operators. These operators are specifically developed to improve the decision-making process by offering a comprehensive framework for aggregating multiple criteria when selecting sustainable biomass resources for bioenergy production. The PiFSMEIWA operator combines the benefits of the soft-max function and Einstein interactive operations to create an all-encompassing framework for information aggregation. Conversely, the PiFSMEIWG operator broadens the capabilities of PiFSMEIWA by integrating weighted geometric aggregation through the soft-max function, effectively managing uncertain and imprecise information while considering the decision maker's (DM's) preferences. To exemplify the practical application of these operators, a case study concentrating on the selection of sustainable biomass resources for bioenergy production is presented. This case study takes into consideration diverse factors such as biomass availability, environmental impact, economic feasibility, and social acceptance. Through the utilization of the proposed aggregation operators, a picture fuzzy decision-making model is devised to assist in the selection of biomass resources. This model examines various criteria and assesses the suitability of different biomass resources based on their overall performance. The experimental results underscore the efficacy and resilience of the proposed operators and decision-making model in dealing with uncertainty and imprecision. The study's findings offer valuable insights for policymakers, researchers, and stakeholders involved in the selection of biomass resources. [ABSTRACT FROM AUTHOR]

Relevancy transformation operators (RET operators) have been widely used in fuzzy systems modelling and the construction of weighted aggregation functions. Several construction methods of RET operators based on different aggregation functions such as t-norm, t-conorm and copula, have been proposed. In this paper, the attention is paid to the expression of RET operators, which is an important feature from an application the point of view. Polynomial RET operators are introduced as those RET operators in the form of polynomial functions of two variables. A complete characterisation of polynomial RET operators of degree less than 4 are presented. [ABSTRACT FROM AUTHOR]

Multiple criteria decision-making (MCDM) based on interval intuitionistic fuzzy value (IVIFV) is a process of aggregating decision criteria represented by multiple interval-valued intuitionistic fuzzy numbers to select the optimal alternative. Among them, an aggregation operator is an indispensable tool, and the properties of an aggregation operator directly affect the decision results. Existing aggregation operators based on IVIFV have satisfactory results in eliminating the correlation between criteria and removing the influence of outliers on the results. However, there are some unreasonable results due to some undesired properties of IVIFVs. In this paper, IVIFV operation under the Dempster-Shafer theory (DST) framework is applied to combine the power average and Muirhead mean operators and interval intuitionistic fuzzy power Muirhead mean operators under DST framework are presented. Then a method based on the presented operators for MCDM problems is proposed. Finally, a set of numerical experiments are conducted to demonstrate the proposed method. The experimental results suggest that the proposed method not only retains the robustness of the power average operator and the capability of the Muirhead mean operator, but also eliminates a shortcoming that existing interval intuitionistic fuzzy operators cannot handle the case where the weights are in IVIFVs. [ABSTRACT FROM AUTHOR]

European Capitals of Culture (ECoC) is an initiative that promotes European cultural diversity with the aim of economic, cultural, and social revitalization. Measuring complex impacts is a constant challenge for both practitioners and academia. Thus, the paper presents a comprehensive impact assessment framework (iECoC) quantified through an integral aggregation operator based on a novel use of fuzzy measure (Choquet integral). The iECoC results in a single number, but has an inherent value of reviling its segmented structure, which separately depicts the impact on three segments: culture, economy, and community, thus providing insights into trends for sectoral decision-making. The impact is measured in three years span on the example of Novi Sad—European Capital of Culture 2022. [ABSTRACT FROM AUTHOR]

In daily life, the decision making problem is a complicated work related to uncertainties and vagueness. To overcome this vagueness and uncertainties, many fuzzy sets and theories have been presented by different scholars and researchers. EDAS (Evaluation based on distance from average solution) method plays a major role in decision-making problems. Especially, when multi-attribute group decision-making (MAGDM) problems have more conflicting attribute. In this paper, a new approach known as Spherical fuzzy rough-EDAS (SFR-EDAS) method is used to handle these uncertainties in the MAGDM problem. The aggregation operators have the ability to combine different sources of information, which plays an essential role in decision making (DM) problem. Keeping in view the increasing complexity of the DM problem, it will be useful to combine the aggregation operators with the fuzzy sets in solving DM problem. Therefore, an aggregation operator known as SFR-EDAS method is utilized. For this propounded some new averaging and geometric aggregation is investigated. Moreover, the essential and desirable properties with some particular cases are deliberated and discussed detail. To evaluate the emergency program, a MAGDM approach is used based on the new introduced operators. Later on, the viability and applicability the proposed method is certified by a detailed analysis with the other existing approaches. [ABSTRACT FROM AUTHOR]

Copyright of Industria Textila is the property of Institutul National de Cercetare-Dezvoltare pentru Textile si Pielarie and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The linguistic interval-valued Pythagorean fuzzy (LIVPF) sets, which absorb the advantages of linguistic terms set and interval-valued Pythagorean fuzzy sets, can efficiently describe decision makers' evaluation information in multi-attribute group decision-making (MAGDM) problems. When investigating aggregation operators of linguistic interval-valued Pythagorean fuzzy (LIVPF) information, we have to consider two important issues, viz. the operational rules of LIVPF numbers and aggregation functions. The classical Archimedean t-norm and t-conorm (ATT) are a famous t-norm and t-conorm, which can produce some special cases. Recently, ATT has been widely applied in different fuzzy decision-making information. Hence, in this paper, for the first issue, we propose some novel operational rules of LIVPF numbers based on ATT. The new operational laws are flexible and can generate some useful operations. For the second issue, we choose a powerful function, i.e., the extended power average (EPA) operator as the aggregation function. The prominent advantages of EPA are that it not only considers the relationship among input arguments, but also dynamically changes the weights of input arguments by employing a parameter. Hence, our proposed novel aggregation operators for LIVPFNs are flexible and is suitable to handle MAGDM problems in actual life. Afterward, we further present a novel MAGDM method under LIVPF conditions. The main finding of our study is a new MAGDM method, which is more powerful and flexible than existing ones. Finally, we apply the method in a sustainable building materials selection to show its effectiveness. Additionally, comparison analysis is provided to demonstrate the advantages and superiorities of the proposed method. [ABSTRACT FROM AUTHOR]

Induced aggregation operators are more suitable for aggregating the individual preference relations into a collective fuzzy preference relation. Therefore, in this paper, we introduce the notion of some new types of induced aggregation operators, based on the Aczel-Alsina operations. We construct some induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina ordered weighted averaging/geometric (I-IVITrFAAOWA/G) operator, induced interval-valued intuitionistic trapezoidal fuzzy Aczel-Alsina hybrid averaging/geometric (I-IVITrFAAHA/G) operator. Moreover, some dominant properties of these developed operators are studied in detail. Based on these proposed approaches, a model is a build up for multicriteria decision making (MCDM), and their stepwise algorithm is being presented. Finally, in utilizing the developed approach, an illustrative example is solved with the help of proposed operators. In the end, we utilize an applicable example for supplier selection to prove the proposed methods and compare the result with existing methods, which shows the superiority, competence, and ability of the developed model. [ABSTRACT FROM AUTHOR]

The development of information measures associated with interval-valued intuitionistic fuzzy values (IVIFVs) has been an important research area over the past few decades. In the literature, the existing decision -making method using IVIFVs has some drawbacks, and the identification degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable, useful, and comprehensive decision method is obvious. To obtain more accurate and reliable evaluation results, multiattribute group decision-making (MAGDM) problems, where the same attribute weights given by different decision-makers are different, are studied in this paper. First, the novel operational laws of IVIFVs and a new interval-valued intuitionistic fuzzy weighted arithmetic aggregation operator are defined to overcome the drawbacks of the IIFWA aggregation operator and avoid losing or distorting the original decision information in the process of aggregation. Second, the mean and variance of the possibility degrees of IVIFVs are defined based on the concept of a definite integral. Third, a novel MAGDM method based on the new aggregation operator and the mean and variance of the possibility degrees of IVIFVs is proposed to improve the identification of the evaluation results and ensure the effectiveness of the ranking order. Finally, the effectiveness and practicability of the proposed method are verified by an air combat training accuracy assessment example. This example can be used to assist decision-makers in evaluating air combat training hits in a timely and efficient manner, providing an objective, scientific basis for the realization and application of air combat training hit assessment and a new method and idea for MAGDM problems in an interval-valued intuitionistic fuzzy environment. [ABSTRACT FROM AUTHOR]

This paper intends to introduce mathematical tools for aggregation of the generalized hesitant fuzzy numbers in order to increase the use of them in the real world. The proposed operators, are based on general form of t-norm and t-conorm functions, enable us to do some mathematical computations and aggregate the given generalized hesitant fuzzy numbers. At first, some famous Archimedean t-norms and t-conorms, i.e., Algebraic, Einstein, Hamacher, and Frank t-norms and t-conorms, and their properties, have been developed to be employed with generalized hesitant fuzzy numbers. Then, several averaging and geometric-based aggregation operators for generalized hesitant fuzzy numbers have been proposed. Later on, a decision-making algorithm has been defined based on such operators to address the problems. The necessity and application of the proposed concepts have been explained by some numerical examples. [ABSTRACT FROM AUTHOR]

Interactive group evaluation is a decision-making method to obtain group consensus by constantly modifying the initial weight of experts. Probabilistic hesitant Pythagorean fuzzy set (PrHPFS) is to be added the corresponding probability values for each membership degree and non-membership degree on the hesitant Pythagorean fuzzy set (HPFS). It is not only a generalization of HPFS and the Pythagorean fuzzy set (PFS), but also a more comprehensive and accurate reflection of the initial decision information given by experts. Especially, it can deal with the decision-making problem of multi-attribute fuzzy information in a wider area. In this paper, some basic definitions and related operations of the probabilistic hesitant Pythagorean fuzzy numbers (PrHPFNs) are first reviewed, and propose score function and accuracy function in PrHPFNs environment. Secondly, the concepts of Hamming distance measure, weighted distance measure and degree of similarity are put forward in PrHPFNs space, and the degree of similarity of two probabilistic hesitant Pythagorean fuzzy matrices (PrHPFMs) is suggested through the aggregation operator formula of PFNs. Finally, an interactive group decision-making method is designed based on the PrHPFM and the degree of similarity under the PrHPFNs environment, the effectiveness of the method is verified by an example, so as to overcome the hesitant psychological state of experts and achieve the consistent consensus evaluation of group preference. [ABSTRACT FROM AUTHOR]

In this paper, two uncertain linguistic aggregation operators named the induced uncertain linguistic hybrid Shapley arithmetical averaging (IULHSAA) operator and the induced uncertain linguistic hybrid Shapley geometric mean (IULHSGM) operator are defined. These operators do not only globally consider the importance of the elements and their ordered positions but overall reflect the correlations between them, respectively. Furthermore, to reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive Shapley arithmetical averaging (IULHASAA) operator and the induced uncertain linguistic hybrid 2-additive Shapley geometric mean (IULHASGM) operator are defined. Moreover, if the weight information of experts and attributes is incompletely known, models for the optimal fuzzy measures are established. Meanwhile, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which considers the correlative characteristics between experts as well as between attributes. Finally, a numerical example is provided to illustrate the developed procedure. [ABSTRACT FROM AUTHOR]

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority. [ABSTRACT FROM AUTHOR]

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a Frank operator in the q-rung orthopair triangular fuzzy linguistic environment on the basis of the notion of the Frank operator and the q-rung orthopair fuzzy set. Firstly, the concept of a q-rung orthopair triangular fuzzy linguistic set (q-ROTrFLS) is proposed, then several basic operations, score, and accuracy functions to compare the q-ROTrFLS values are defined. Secondly, a series of q-rung orthopair triangular fuzzy linguistic Frank aggregation operators are developed, such as q-rung orthopair triangular fuzzy linguistic Frank weighted average (q- ROTrFLWA) operator, q-rung orthopair triangular fuzzy linguistic Frank weighted geometric (q-ROTrFLWG) operator, and we introduce several relevant properties of these operators and prove their validity, and show the relevant relationship between some operators. Thirdly, two different decision-making approaches are constructed in the q-rung orthopair triangular fuzzy linguistic environment. Furthermore, a practical example is given to explain the developed methods. Finally, a comparative study is conducted, and the relevant sensitivity analysis is also discussed, and the outcome shows the prominence and the effectiveness of the developed methods compared to previous studies. [ABSTRACT FROM AUTHOR]

In multi-attribute group decision-making (MAGDM) problems, prioritization is sometimes important. Several techniques and methods have been introduced in fuzzy systems to use prioritization. The main purpose of this paper is to propose prioritized aggregation operators (AOs) for intuitionistic fuzzy (IF) information. These AOs are symmetric in nature and are based on the novel Aczel–Alsina t-norm and t-conorm. Herein, we propose IF-prioritized Aczel–Alsina averaging (IFPAAA) and IF-prioritized Aczel–Alsina geometric (IFPAAG) operators. It is shown that these AOs satisfy the basic features of aggregation. Some additional results for these AOs are also investigated. These proposed operators can capture the prioritization phenomenon among the aggregated arguments, and the weights for prioritization are obtained from expert information. Finally, the proposed AOs are used in an MAGDM problem where a doctor is selected for a hospital. A comparison of the proposed prioritized AOs is also established with other well-known AOs to show the significance of the IFPAAA and IFPAAG operators. [ABSTRACT FROM AUTHOR]

Scientific progression has allowed researchers to develop novel and innovative ways to deal with uncertainty in data, allowing for the development of more precise and accurate data representation models. This paper aims to extend an already reported concept of Cubic Pythagorean fuzzy set to Cubic Pythagorean Fuzzy Soft Set (C P F S s) as it incorporates both interval-valued Pythagorean fuzzy sets (IVPFS) and Pythagorean fuzzy sets (PFS) at the same time, providing a more targeted approach to deal with uncertainty. This hybrid structure can better handle data in comparison to the ones in the literature by having the characteristics of PFS and soft sets, leading to a more targeted approach to handle attributes in decision-making studies. In this study, we defined various internals and externals of C P F S s , set operators, aggregation operators, and developed an algorithm based on distance measures for ( C P F S s ), which are applied in a disease diagnostic decision-making problem. [ABSTRACT FROM AUTHOR]

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach. [ABSTRACT FROM AUTHOR]

Recently, intuitionistic fuzzy pairs have been used as uncertainty estimations of the request services in service systems. In the present paper, three intuitionistic fuzzy characterizations of virtual service devices are specified: intuitionistic fuzzy traffic estimation, intuitionistic fuzzy flow estimation and intuitionistic fuzzy estimation about probability. Discussed herein are two approaches to the intuitionistic fuzzy estimation of the uncertainty of compositions of services. One of the approaches is based on the definitions of the intuitionistic fuzzy pairs for one service device. The other approach is based on the aggregation operators over intuitionistic fuzzy pairs. A total of six intuitionistic fuzzy estimations of the uncertainty of comprise service device are proposed. The proposed uncertainty estimations allow for the definition of new Quality of Service (QoS) indicators and can be used to determine the quality of service compositions across a wide range of service systems. [ABSTRACT FROM AUTHOR]