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To address the uncertainty and imprecision in a complex system, the concept of the linear Diophantine fuzzy set (LDFS) was introduced, which is a fuzzy set extension that eliminates the constraints of current methodologies and gives the decision-maker complete freedom to select the grades, producing results that are expressive and flexible. A circular intuitionistic fuzzy set (C-IFS) is depicted by a circle with the membership and non-membership values as its center coordinates, addressing the ambiguity regarding membership and non-membership values. In this paper, we propose the notion of a circular linear Diophantine fuzzy set (C-LDFS) as a hybrid structure of both circular intuitionistic fuzzy sets and linear Diophantine fuzzy sets. In addition, some fundamental set operations on C-LDFSs are presented. Furthermore, a similarity metric for C-LDFS is also introduced in the paper. Additionally, we confirm the axiomatic requirement of the similarity measure and highlight a few of its traits. Finally, the proposed similarity metric is implemented in clinical decision-making to illustrate its efficacy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce to a pair of fuzzy graphic rational F-contraction multivalued mappings and to study the necessary condition for the existence of common fixed points of fuzzy multivalued mappings in the setup of generalized parametric metric space endowed with a directed graph. A non-trivial example is presented to support the results presented herein. Our results improve and extend some recent results in the existing literature. [ABSTRACT FROM AUTHOR]

Third-order fuzzy differential subordination studies were recently initiated by developing the main concepts necessary for obtaining new results on this topic. The present paper introduces the dual concept of third-order fuzzy differential superordination by building on the known results that are valid for second-order fuzzy differential superordination. The outcome of this study offers necessary and sufficient conditions for determining subordinants of a third-order fuzzy differential superordination and, furthermore, for finding the best subordinant for such fuzzy differential superordiantion, when it can be obtained. An example to suggest further uses of the new outcome reported in this work is enclosed to conclude this study. [ABSTRACT FROM AUTHOR]

The best way to deal with complicated life scenarios that accompany the decision-making process is to update previous concepts constantly. Therefore, researchers must constantly discover powerful mathematical tools that suit the accompanying circumstances. In this regard, we combine both soft set, neutrosophic set, and interval setting under Q-two-dimensional universal information to introduce a new hybrid innovative model called interval valued-Q-neutrosophic soft sets. The core goal of this model is to keep the features of previous models like soft sets, neutrosophic sets, and Q-Fuzzy sets in dealing with the lack of uncertainty and neutrality associated with real-life issues. This new approach allows decisionmakers to employ interval-valued form with Q-two-dimensional universal information, which provides them with more stability and feasibility in describing uncertain information more completely and accurately. Under the our propose model, we discuss effectively set-theory operations such as subset, union, intersection, complement, AND operation, and OR operation for interval valued-Q-neutrosophic soft sets, as well as some special operations like the necessity and possibility operations of an interval valued-Q-neutrosophic soft sets. In addition, we presented many properties supported by numerical examples that explain how they work. Finally, this new model has been successfully tested in dealing with one of the medical diagnostic problems based on hypothetical data for a respiratory disease. Building an algorithm based on the aggregation operator for interval valued-Q-neutrosophic soft set data solved this issue (i.e., selecting the optimal alternative). [ABSTRACT FROM AUTHOR]

Nowadays, obesity is recognized as a worldwide epidemic that has become a major cause of death and comorbidities. Recommending appropriate treatment is critical in the global health environment. For obesity treatment to be effective, the person must be able to follow a specific diet that meets his needs so that he can follow it for a long time or forever to maintain fitness. This research aims to determine the best diet among the trusted diets for every person based on his needs and circumstances. This occurs when applying a decision-making technique based on the effective fuzzy soft multiset concept. For this purpose, the definition of the effective fuzzy soft multiset as well as its types, operations, and properties are introduced. Furthermore, a decision-making method is proposed based on the effective fuzzy soft multiset environment. Using matrices operations, one can easily apply the decision-making process based on this new extension of sets to choose the optimal diet for everyone. Finally, an extensive comparative analysis of the previous methods is undertaken and also summarized in a chart to attract focus on the benefits of the suggested algorithm and to demonstrate how they differ from the current one. [ABSTRACT FROM AUTHOR]

The miRNA is a tiny, single-stranded RNA of nearly 22 nucleotides long that is transcribed from DNA and controls the genes in protein synthesis process. As expression levels of miRNAs vary significantly between cancerous and non-cancerous cells. Therefore, miRNAs can play a vital role in the development of cancer. Cancer classification from miRNA gene expression data is an area of interest to the bioinformatics and computational biology researches in recent past. However, traditional machine learning classifiers often do not produce the desired results due to lack of training patterns present in miRNA data. Additionally they are not often able to deal with overlapping, vague, uncertain, ambiguous and indiscernible cancer subtypes classes of the miRNA data. Motivated from the above said issues, we propose a novel semi-supervised fuzzy-rough based extreme learning machine (SSFRELM) method. Two stages are involved in the proposed method, where in the first stage, the soft class labels of the unlabeled samples are assigned using fuzzy-rough set theory, those are subsequently applied on the semi-supervised extreme learning machine in the second stage. The proposed SSFRELM method can improve classification accuracy since it utilizes unlabeled patterns together with limited labeled patterns in the learning process to develop the semi-supervised extreme learning machine and can handle the overlapping, vague, uncertainty, ambiguity, and indiscernibility usually present in miRNA gene expression data as it uses fuzzy-rough set theory. The proposed method is assessed using eight publicly available miRNA gene expression datasets from five different cancer types with respect to various classification evaluation measures in comparison to four other state-of-the-art methods. Experimental results justify that the proposed method outperformed the other counter-parts methods for cancer pattern classification. Paired t-test results also confirm the statistical significance of the better results achieved by the proposed SSFRELM over other methods for most of the cases. [ABSTRACT FROM AUTHOR]

The increasing pollution of river systems poses a significant challenge to water quality management and public health. This study was conducted to evaluate the water quality of the Gomati River in India, focusing on the impact of anthropogenic activities on pollution levels across different seasons. The primary objective was to develop a comprehensive assessment model using an effective weighted fuzzy soft expert system (WFSES) to derive a weighted water pollution score (WWP-score) for rating water pollution levels based on various water quality parameters. To achieve this, we employed a fuzzy soft set (FSS) methodology integrated with a weighted fuzzy soft set (WFSS) model to analyze water quality indices at six sampling stations along the Gomati River, the largest river in Tripura, India. Originating from the Raima and Sarma streams, the river flows westward through key regions, providing 249.39 million cubic meters of water annually, essential for drinking, agriculture, fishing, and transportation. The study utilized crisp data summaries of key water quality parameters, including pH, total dissolved solids, total suspended solids, electrical conductivity, biochemical oxygen demand, dissolved oxygen, total hardness, chloride, total alkalinity, and total coliform, across the pre-monsoon, monsoon, and post-monsoon seasons from May 2022 to April 2023, guided by the distribution of waste discharge points. Fuzzy membership functions were defined for these parameters, and the root mean square (RMSQR) operation was used to combine multiple FSSs. The results revealed that the WWP-scores, a measure of water quality, ranged from 0.744 to 0.872 across the sampling stations, with Srimantapur exhibiting the highest level of pollution and Udaipur showing comparatively better quality. These scores indicate that water quality at all sites falls into the poor category, with Srimantapur experiencing the most severe contamination due to high levels of coliform bacteria and organic pollutants. The analysis highlights the impact of domestic wastewater and agricultural runoff on the river's health. This research offers a novel application of FSS and WFSS theory in environmental management, providing a robust framework for evaluating and ranking water quality across multiple parameters. The findings are valuable to the scientific community as they offer detailed insights into the pollution dynamics of the Gomati River and propose a methodological approach for assessing water quality in other river systems facing similar challenges. The study's results underscore the need for targeted pollution control measures and continuous monitoring to safeguard water resources and public health. [ABSTRACT FROM AUTHOR]

This paper presents the novel concept of rough intuitionistic fuzzy ideals within the realm of BCK-algebras and investigates their fundamental properties. Furthermore, we introduce a set-valued homomorphism over a BCK-algebra, laying the foundation for the establishment of T-rough intuitionistic fuzzy ideals. The characterization of these innovative ideals is accomplished by employing the (α , β) -cut of intuitionistic fuzzy sets in the context of BCK-algebras. [ABSTRACT FROM AUTHOR]

This paper attempts to demystify the stability of CoCoSo ranking method via a comprehensive simulation experiment. In the experiment, matrices of different dimensions are generated via Python with fuzzy data. Stability is investigated via adequacy and partial adequacy tests. The test passes if the ranking order does not change even after changes are made to entities, and the partial pass signifies that the top ranked alternative remains intact. Results infer that CoCoSo method has better stability with respect to change of alternatives compared to criteria; and CoCoSo method shows better stability with respect to partial adequacy test for criteria. [ABSTRACT FROM AUTHOR]

This paper is dedicated to defining and studying for the first time a two-fold algebra over the neutrosophic real number ring by merging the fuzzy set mapping with the algebraic operations of the neutrosophic real number ring. Also, we study the elementary algebraic properties of the defined two-fold algebra through its algebraic operations and substructures such as homomorphisms and ideals. [ABSTRACT FROM AUTHOR]

There is some uncertainty in the nature of tunnel excavation operations and this is an important part of the uncertainty due to unknown geological and geotechnical conditions. This paper proposes a risk assessment approach for problems which may arise during tunneling operations. A new model has been developed for the risk management of line 3 of the Mashhad subway (Iran’s second biggest city) applying a hybridization of game theory and fuzzy theory. Using questionnaires, appropriate responses to key risks are suggested based on modelling of game theory and categorized and ranked by importance. Linear programming problems are introduced to compute the average, optimistic, and pessimistic game values and their corresponding optimal strategies. This is the first work in this field to discuss geological and geotechnical risks in a hierarchy fashion. Hierarchy means that the ranking is done at different levels and each level has its own importance. The results indicate that providing the engineering geological profile along the route using obtained information and changing the excavation parameters based on it, is the most significant risk response. Using geophysical methods for subsurface studies and Excavating trenches for shallow investigations on the tunnel excavation route is ranked at the next level of importance. [ABSTRACT FROM AUTHOR]

This study analyzed data from the Korea Welfare Panel Study to identify changing patterns in social exclusion among South Korean youth and determine the influencing factors. The study examined 345 youth from 2012 to 2021. A fuzzy set theory and growth mixture model was used to measure social exclusion and identify patterns and the associated factors during this timeframe. The main findings are as follows. First, the social exclusion gap among South Korean youth that emerged a decade ago has continued, with high, middle, and low levels of exclusion identified. Second, the analysis revealed that looking at the demographics, being female, having less education and lower personal and household income increased the likelihood of falling into a relatively higher level of social exclusion. Based on the results, policy recommendations are suggested to mitigate the social exclusion gap among Korean youth. [ABSTRACT FROM AUTHOR]

Due to excellent mechanical and metallurgical properties, metal matrix composites (MMCs) are in high demand for numerous engineering applications across multiple industrial sectors. However, presence of reinforcement particles in MMCs adversely affects their machinability leading to increased tool wear and cutting force requirement. To simultaneously achieve better product quality and higher tool life, there is a need to determine the optimal values for various drilling parameters affecting those characteristics. This paper proposes application of the Combined Compromise Solution (CoCoSo) method in five different fuzzy environments for solving the parametric optimization problems of two aluminium MMC (Al-MMC) drilling processes. Fuzzy CoCoSo, intuitionistic fuzzy CoCoSo, Pythagorean fuzzy CoCoSo, neutrosophic fuzzy CoCoSo and hesitant fuzzy CoCoSo are applied to search out the optimal combinations of the input parameters for the considered Al-MMC drilling operations. For the first Al-MMC drilling process, all the five approaches recommend higher helix angle = 40°, moderate spindle speed = 500 rpm and lower feed rate = 0.1 mm/rev as the optimal combination to simultaneously optimize surface roughness, cutting force and drilling temperature. Furthermore, a similar trend is also observed in the results of the second Al-MMC drilling process, where all these methods propose relatively moderate spindle speed = 2000 rpm and lower feed rate = 50 mm/min along with 3% mica reinforcement and a polycrystalline diamond drilling tip to achieve the best drilling performance. Finally, the results are compared with those achieved using the standalone CoCoSo and other fuzzy-based approaches. It is observed that CoCoSo method can effectively determine the optimal parametric combinations and the results are quite consistent throughout all the fuzzy environments under consideration. Furthermore, the fuzzy CoCoSo approaches can effectively deal with the subjectivity in opinions of the decision makers (stakeholders) while assigning relative importance to the responses according to their requirements. [ABSTRACT FROM AUTHOR]

In 1965, fuzzy set theory was born, providing a valuable tool to study phenomena where decision-making based on dichotomy is not a simple task. This work is framed in the ideas of fuzzy analytic geometry; more precisely, this paper is devoted to introducing the idea of a fuzzy tangent line to a fuzzy circle in this geometry. For this purpose, three methods are proposed and studied. Moreover, we provide results that establish the conditions for which the proposed methods define the same fuzzy tangent line. [ABSTRACT FROM AUTHOR]

Aptamers are very interesting peptide molecules or oligonucleic acid. They are used to bind particular target molecules. Aptamers play vital roles in various practical applications and physiological functions. Consequently, several diseases can be treated using therapies based on aptamer proteins and designing the binding of aptamers to specific proteins is essential to advance understanding into processes of interaction between aptamer-protein. Despite the wide applications of aptamers, identification of interaction between aptamer protein is always inadequate and challenging. Therefore, it is necessary to develop a computational approach for achieving good predictions of interaction between aptamer-protein. In the present study, a novel method for enhancing the prediction of interacting aptamer-target pairs based on sequence features obtained from both aptamers and their target proteins by employing a novel k-mean based intuitionistic fuzzy rough feature selection method is proposed. Firstly, an intuitionistic fuzzy rough set model based on k nearest neighbour concept is proposed. Then, a novel feature selection technique is introduced by using this model. Furthermore, non-redundant and relevant features are selected from training as well as testing datasets by using proposed feature selection technique. Secondly, SMOTE (Synthetic Minority Oversampling Technique) is applied to obtain the optimal balanced training and testing datasets. Thirdly, we apply various machine learning algorithms on optimally balanced reduced training and testing datasets to evaluate their performances. Experimental results shows that the best prediction performance is obtained by boosted random forest learning algorithm. Using a 10 fold cross-validation test, the proposed method is a good performer, with sensitivity of 91.3, 86.4, specificity of 91.9, 84.8, overall accuracy of 91.60%, 85.60%, Mathews correlation coefficient of 0.832, 0.713, AUC (area under curve) of 0.969, 0.908, and g-means of 91.5, 85.5 on optimal balanced reduced training and testing datasets consisting of aptamer-protein interacting pairs. Finally, a comparative study of the best obtained results with the existing best results is presented, which clearly indicates that our proposed approach is the best performing approach till date. [ABSTRACT FROM AUTHOR]

Nowadays, obesity is recognized as a worldwide epidemic that has become a major cause of death and comorbidities. Recommending appropriate treatment is critical in the global health environment. For obesity treatment to be effective, the person must be able to follow a specific diet that meets his needs so that he can follow it for a long time or forever to maintain fitness. This research aims to determine the best diet among the trusted diets for every person based on his needs and circumstances. This occurs when applying a decision-making technique based on the effective fuzzy soft multiset concept. For this purpose, the definition of the effective fuzzy soft multiset as well as its types, operations, and properties are introduced. Furthermore, a decision-making method is proposed based on the effective fuzzy soft multiset environment. Using matrices operations, one can easily apply the decision-making process based on this new extension of sets to choose the optimal diet for everyone. Finally, an extensive comparative analysis of the previous methods is undertaken and also summarized in a chart to attract focus on the benefits of the suggested algorithm and to demonstrate how they differ from the current one.

Abstract The increasing pollution of river systems poses a significant challenge to water quality management and public health. This study was conducted to evaluate the water quality of the Gomati River in India, focusing on the impact of anthropogenic activities on pollution levels across different seasons. The primary objective was to develop a comprehensive assessment model using an effective weighted fuzzy soft expert system (WFSES) to derive a weighted water pollution score (WWP-score) for rating water pollution levels based on various water quality parameters. To achieve this, we employed a fuzzy soft set (FSS) methodology integrated with a weighted fuzzy soft set (WFSS) model to analyze water quality indices at six sampling stations along the Gomati River, the largest river in Tripura, India. Originating from the Raima and Sarma streams, the river flows westward through key regions, providing 249.39 million cubic meters of water annually, essential for drinking, agriculture, fishing, and transportation. The study utilized crisp data summaries of key water quality parameters, including pH, total dissolved solids, total suspended solids, electrical conductivity, biochemical oxygen demand, dissolved oxygen, total hardness, chloride, total alkalinity, and total coliform, across the pre-monsoon, monsoon, and post-monsoon seasons from May 2022 to April 2023, guided by the distribution of waste discharge points. Fuzzy membership functions were defined for these parameters, and the root mean square (RMSQR) operation was used to combine multiple FSSs. The results revealed that the WWP-scores, a measure of water quality, ranged from 0.744 to 0.872 across the sampling stations, with Srimantapur exhibiting the highest level of pollution and Udaipur showing comparatively better quality. These scores indicate that water quality at all sites falls into the poor category, with Srimantapur experiencing the most severe contamination due to high levels of coliform bacteria and organic pollutants. The analysis highlights the impact of domestic wastewater and agricultural runoff on the river's health. This research offers a novel application of FSS and WFSS theory in environmental management, providing a robust framework for evaluating and ranking water quality across multiple parameters. The findings are valuable to the scientific community as they offer detailed insights into the pollution dynamics of the Gomati River and propose a methodological approach for assessing water quality in other river systems facing similar challenges. The study's results underscore the need for targeted pollution control measures and continuous monitoring to safeguard water resources and public health.

The main objective of the paper is to hybridize the triangular fuzzy number and the quadripartitioned neutrosophic set and develop the triangular fuzzy quadripartitioned neutrosophic set. The triangular fuzzy numbers have great potential to express uncertainty systematically. So, the combination of the triangular fuzzy numbers and quadripartitioned neutrosophic sets is an intelligent mathematical tool that will be a helpful mathematical tool for decision-making. We define some operations on the triangular fuzzy quadripartitioned neutrosophic sets such as union, intersection, and complement. We establish some important theorems on operations like union, intersection in between three triangular fuzzy quadripartitioned neutrosophic sets in an elaborate way. We have defined unity and null triangular fuzzy quadripartitioned neutrosophic sets and established some mathematical operations on them. We establish some fundamental properties of the developed triangular fuzzy quadripartitioned neutrosophic sets. [ABSTRACT FROM AUTHOR]

Purpose of this study is to formulate a working definition of information to meet the needs of computer science. There is currently no strict definition of this term. There is a methodological contradiction: the development and application of information technologies requires accuracy and rigor, but at the same time the development is based on a vague, intuitive concept. Materials and methods. The materials for the study are existing classical approaches to understanding information, and the main method is the analysis of these approaches. The proposed definition is constructed taking into account two mathematical transformations: the selection of a certain subset and the mapping between sets. To formalize the allocation procedure, it is used apparatus of fuzzy sets. Results. A definition of information is proposed as the result of a mapping in which the selection of a subset from a set of prototypes leads to the selection of a corresponding subset from a set of images. The selected subset can be understood as fuzzy, then an equivalent definition of information is acceptable as a result of mapping, in which an increase in the heterogeneity of the distribution of the presence indicator on the set of prototypes leads to an increase in the heterogeneity of the distribution of the corresponding indicator on the set of images. The essence of the new definition is demonstrated using models of population dynamics in discrete time. The significance of the proposed approach for information technology is revealed using the example of the numerical method of multi-extremal optimization. It is shown that the proposed definition makes it possible to formulate effective stopping conditions for the numerical method of stochastic optimization, which guarantees the receipt of a given amount of information. Conclusion. The proposed understanding of information allows us to overcome the shortcomings of previous approaches to understanding the essence of information, retains all the advantages of the classical approach and is consistent with other well-known approaches in the field of computer science. This definition can be used to improve numerical optimization methods, as well as other information technology tools.

This study evaluated a hydraulic pump house in Iran by identifying and assessing potential failures. The research team used fuzzy Shannon entropy to determine the weight of risk priority number (RPN) criteria. A combination of WASPAS and FMEA methods was used to evaluate and rank failures. The proposed ranking closely aligned with expert opinions, demonstrating the model’s effectiveness. Inadequate feeding rates were identified as the most critical failure. The study’s findings suggest its applicability to other decision problems in uncertain conditions, emphasizing the impact of risk assessment indicators, cost index, and fuzzy uncertainty modeling on failure ranking.

Twin support vector machine (TSVM) is an effective machine learning tool for classification problems. However, TSVM classifier works on empirical risk principle only and also while training, each sample contributes equally, even if it is a noise or an outlier. It does not incorporate the uncertainties associated with data into modeling and hence its generalization ability declines. To address these issues, intuitionistic fuzzy regularized least square twin support vector machine having intuitionistic fuzzy network has been proposed in this paper. The non-parallel classifiers are obtained by solving two systems of linear equations only rather than the solution of two quadratic programming problems as in TSVM, which leads to speed up the training process. Moreover, the method follows both structural risk and empirical risk minimization principles. In order to de-escalate the effect of pollutant patterns, their contribution of the patterns into learning the decision function has been made according to their importance in the classification. The significance of the training patterns is measured in terms of intuitionistic fuzzy numbers based on their geometrical locations and surroundings. The method is further extended to find non-parallel decision planes in the feature space using nonlinear kernel function, which also gives rise to the solution of two systems of linear equations. To show the efficacy of the proposed method, computer simulations on fourteen standard and six big UCI datasets using linear and Gaussian kernels are performed and their results have been compared with well-established methods in the literature. The experimental results are represented in terms of accuracy, computational time, F-measure, sensitivity and specificity rates. The outcomes demonstrate that the proposed method outperforms the existing methods and is also feasible for big datasets. The comparison and statistical inferences using two non-parametric: Friedman and Nemenyi tests, conclude that the proposed approach is fast and yields better generalization. [ABSTRACT FROM AUTHOR]

The rapid development of renewable energy presents challenges to the security and stability of power systems. Aiming at addressing the power system scheduling problem with load demand and wind power uncertainty, this paper proposes the establishment of different error fuzzy sets based on the Wasserstein probability distance to describe the uncertainties of load and wind power separately. Based on these Wasserstein fuzzy sets, a distributed robust chance-constrained scheduling model was established. In addition, the scheduling model was transformed into a linear programming problem through affine transformation and CVaR approximation. The simplex method and an improved differential evolution algorithm were used to solve the model. Finally, the model and algorithm proposed in this paper were applied to model and solve the economic scheduling problem for the IEEE 6-node system with a wind farm. The results show that the proposed method has better optimization performance than the traditional method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of cubic soft (CS) algebra, CS o-subalgebra, and CS ideals within the framework of B-algebra. We provide comprehensive characterizations of these new structures, elucidating their unique properties and interrelationships. Specifically, we present detailed conditions under which a CS subalgebra can be classified as a closed CS ideal. Our analysis explores the intricate relationships among closed cubic soft ideals, cubic soft subalgebras, and cubic soft o-subalgebras. By doing so, we aim to provide a deeper understanding of how these structures interact and coexist within the broader context of B-algebra The findings offer significant insights into the application and theoretical underpinnings of cubic soft sets in algebraic systems, contributing to the ongoing evolution of fuzzy set theory and its applications in various mathematical domains. Our work not only broadens the scope of B-algebra but also enhances its utility in solving complex problems where traditional algebraic approaches may fall short. Through this exploration, we seek to advance the field and open new avenues for research and practical applications in mathematical sciences. [ABSTRACT FROM AUTHOR]

For the elderly, falls can be extremely fatal. However, due to the physical decline of the elderly, it is difficult to avoid falls. Therefore, to the greatest extent feasible lessen the harm that falls on the elderly inflict, so that they can be found in the first time of falls, this study based on wearable devices, proposed a fall monitoring system using an improved K-nearest neighbor algorithm. The improved fuzzy K-nearest neighbor algorithm combined with support vector machine algorithm is applied to improve the efficiency and accuracy of the algorithm, and reduce the false positive rate and false negative rate as much as possible. The suggested model's average precision in the simulation experiment is 97.5%. The specificity was 97.6%. The sensitivity was 97.5%. The convergence performance is also good, 24 iterations can reach the optimal. In the actual experiment, the average accuracy reached 98.7%; The false alarm rate is only 0.7%; The negative rate was 2.5%; Its performance is superior to other two algorithms. This shows that the proposed method has excellent accuracy, false positive rate and false negative rate in practical application, which has important significance for the health and safety of the elderly. [ABSTRACT FROM AUTHOR]

This article examines the approximate solution of the Geophysical Korteweg-de Vries (GKdV) equation in a fuzzy environment. The Adomian decomposition method (ADM) and ADM-Pade approximation technique have been implemented to solve the governing equation. Environmental or climate changes, along with the propagation of air or water waves, can lead to uncertainties or ambiguities in initial or boundary conditions, as well as in parameter associated with the Coriolis effect. To address these uncertainties, this work aims to find the approximate fuzzy solution to the said physical problem by applying a double parametric approach with the help of ADM. To validate the obtained solution, comparisons are made between the fuzzy solutions and existing precise (crisp) solutions in specific cases. Furthermore, in another scenario involving the fuzzy solution, the ADM-Pade approach is employed. This implementation yields an approximate solution that exhibits higher accuracy and closely resembles a solitary wave solution, demonstrating a rapid convergence rate. The analysis of special cases shows a direct relationship between wave height and the Coriolis parameter and an inverse relationship between wavelength and the Coriolis parameter. Finally, the article includes 2D and 3D graphs, along with plots of fuzzy solutions, to enhance understanding of the fuzzy nature of the solutions. [ABSTRACT FROM AUTHOR]

When selling food products, it's important to choose the appropriate sales channel. These channels connect producers with consumers. The aim of this study was to select a channel for the sale of cabbage to end customers. In this paper, six different sales channels that are used in the Semberija region for the sale of cabbage were observed. These sales channels were evaluated using 11 different criteria. In order to choose the sales channel that best meets the set objectives, a fuzzy set approach was used. This approach was chosen because qualitative criteria were used and expert ratings were in the form of linguistic values. Based on the input of seven experts who are professors at agricultural faculties in Bijeljina, it was found that consumer habits were the most important criterion, followed by the criterion compliance with environmental standards, while the smallest weight value was given to the criterion delivery method. Using the RAWEC (Ranking of Alternatives with Weights of Criterion) method, it was shown that online sales yield the best results, after that follows Producer-sales agent-consumer, while according to experts, the sales channel is the best rated Producer-wholesalerretailer- consumer. This is because various tools can be utilized on the Internet for selling agricultural products. Based on the conducted research, the contribution of this study lies in the selection of sales channels using the integration of the MEREC and RAWEC methods. [ABSTRACT FROM AUTHOR]

This paper's findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible function classes must first be defined. This work deals with fuzzy differential subordinations, ideas borrowed from fuzzy set theory and applied to complex analysis. This work examines the characteristics of analytic functions and presents a class of operators in the open unit disk J η , ς κ (a , e , x) for ς > − 1 , η > 0 , such that a , e ∈ R , (e − a) ≥ 0 , a > − x . The fuzzy differential subordination results are obtained using (GFT) concepts outside the field of complex analysis because of the operator's compositional structure, and some relevant classes of admissible functions are studied by utilizing fuzzy differential subordination. [ABSTRACT FROM AUTHOR]

Quality of Life (QoL) is a multifaceted concept encompassing economic, social, environmental, psychological, and physical dimensions of an individual’s life, including personal living conditions, happiness, well-being, and life satisfaction. As a vital criterion for sustainable development and active social policy in countries, QoL has been significantly influenced by the dynamic technological evolution of social media. However, the comprehensive impact of social media, including its role in disseminating disinformation – a major social and socio-economic concern – on QoL remains underexplored. This research aims to develop a novel fuzzy model to assess the level of disinformation on digital platforms and its correlation with the population’s QoL. Employing a mathematical approach rooted in expert evaluation, this study leverages intellectual knowledge analysis and fuzzy set theory. Grounded in data from real respondents and knowledge-based models, this study pioneers an information model to evaluate inhabitants’ QoL, incorporating factors such as financial concerns, perception of disinformation, and its influence on digital platforms. The fuzzy estimation model, verified with data from 3,036 respondents, quantitatively assesses citizens’ QoL. An illustrative application of the model demonstrates its effectiveness. The findings are particularly valuable for policymakers, experts in economic and innovative development, aiding the creation of regulatory and monitoring mechanisms to foster sustainable economic growth and devise effective development strategies. [ABSTRACT FROM AUTHOR]

Type-2 fuzzy information systems (TFISs-2), one interesting form of complex data, are extensions of fuzzy information systems. Uncertainty measurement and attribute reduction of TFISs-2 are key issues when describing and analyzing complex fuzzy data. However, existing researches mainly focus on the traditional fuzzy data, and seldom consider type-2 fuzzy data. This paper focuses on finding an effective indicator to measure the uncertainty of TFISs-2, and carries out the research of attribute reduction based on this indicator. Firstly, the weighted membership distance and the weighted membership similarity are defined, which are used to describe the relation between two objects in TIFSs-2, and σ similarity relations are introduced. Secondly, a fuzzy neighborhood structure is defined based on σ similarity relations. The classical rough set model is extended on TFISs-2, and the definitions of upper and lower approximation, accuracy and roughness are given. Then, a novel indicator called σ self-information is used to describe the uncertainty of TFISs-2, and a heuristic greedy selection attribute reduction algorithm is proposed. Finally, the experimental results show that the constructed uncertainty measurement indicator is suitable for TFISs-2, and the proposed attribute reduction method is effective. This study is beneficial to promote the understanding of complex fuzzy data, and contributes to the data analysis and processing of TFISs-2. [ABSTRACT FROM AUTHOR]

In this paper, an improved algorithm has been proposed for solving fully fuzzy transportation problems. The proposed algorithm deals with finding a starting basic feasible solution to the transportation problem with parameters in fuzzy form. The proposed algorithm is an amalgamation of two existing approaches that can be applied to a balanced fuzzy transportation problem where uncertainties are represented by trapezoidal fuzzy numbers. Instead of transforming these uncertainties into crisp values, the proposed algorithm directly handles the fuzzy nature of the problem. To illustrate its effectiveness, the article presents several numerical examples in which parameter uncertainties are characterized using trapezoidal fuzzy numbers. A comparative analysis is performed between the algorithm's outcomes and the existing results. The existing results are compared with the obtained results. A case study has also been discussed to enhance the significance of the algorithm. [ABSTRACT FROM AUTHOR]

This research delves into the comprehensive study of the mathematical model governing the propagation of tsunami waves along ocean coastlines in imprecise or uncertain environment. The model is based on the widely used shallow-water assumption, which can be represented by a system of non-linear fuzzy partial differential equations. Utilizing fuzzy numbers to represent the problem's uncertainty may have distinct advantages from a certain perspective. As such, this work employs the homotopy perturbation method (HPM) to obtain fuzzy approximate analytical solutions for the governing model under various coastal slopes and ocean depths. The addition of uncertainty to the model may add complexity to the methodology. Therefore, a double parametric approach has been integrated into the HPM procedure. This approach allows us to analyze the impact of coastal slope and sea depth on tsunami wave characteristics, specifically wave velocity and run-up height, in uncertain environments. Furthermore, the numerical results obtained for fuzzy tsunami wave velocity and wave height resemble the real behavior of tsunamis. These can be seen through the given fuzzy plots, both in 2D and 3D forms. Finally, to validate the obtained solutions, a comparison has been made between the special case of the present fuzzy solutions and the existing precise (crisp) solutions. [ABSTRACT FROM AUTHOR]

The integration of sustainable indicators into supply-chain management (SCM), including cost, innovation capability, quality, service capability, long-term cooperation, environmental management system, pollution reduction, green image, social responsibility, and employment practices, has become essential for conducting strategic analyses of the entire supply-chain process competitive advantage. This study proposes a fuzzy integration multi-criteria decision-making (MCDM) method to solve SCM issues. To navigate this complexity, a multi-criterion decision-making (MCDM) framework is employed, integrating MCDM methods with fuzzy logic to effectively address subjective environmental criteria. This innovative approach not only enhances supply-chain management (SCM) but also emphasizes the necessity for ongoing innovation in tackling contemporary supply-chain challenges. It serves as a cornerstone for sustainable supplier selection practices and optimizing SCM processes. In this study, a hybrid fuzzy MCDM method is proposed for supplier selection. The method addresses supplier selection by utilizing evaluations from expert decision-makers based on predetermined criteria. This comprehensive approach ensures that all relevant factors are considered, promoting sustainable and efficient supply-chain management. [ABSTRACT FROM AUTHOR]

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of (∈, ∈) and (∈, ∈ ∨ q)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of (α, β)-fuzzy subalgebras and (α, β)-fuzzy ideals on equality algebras. Also, by using the notion of (∈, ∈)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of X, and we proved that the set of all classes of X by these order is a poset. [ABSTRACT FROM AUTHOR]

Let $ (X, f) $ (X , f) be a dynamical system, i.e. X is a compact metric space and f is a continuous self-map on X and let $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) be the sets of all non-empty compact subsets of X, Borel probability measures on X and upper semi-continuous fuzzy sets on X, respectively. Then $ K(X) $ K (X) , $ M(X) $ M (X) and $ \mathbb {F}(X) $ F (X) are metric spaces under Hausdorff metric, prohorov metric and level-wise metric, respectively. Therefore, $ (X, f) $ (X , f) naturally induces three new systems $ (K(X), \bar {f}) $ (K (X) , f ¯) , $ (M(X), \hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X), \tilde {f}) $ (F (X) , f ~). In this article, we investigate the connection of $ (r,s) $ (r , s) -sensitivity, $ (r,s) $ (r , s) -asymptotic sensitivity, $ (r,s) $ (r , s) -Li-Yorke sensitivity and Δ-transitivity of $ (X, f) $ (X , f) and its induced systems $ (K(X),\bar {f}) $ (K (X) , f ¯) , $ (M(X),\hat {f}) $ (M (X) , f ^) and $ (\mathbb {F}(X),\tilde {f}) $ (F (X) , f ~) and we obtain some desired results. For instance, we prove that $ (K(X),\bar {f}) $ (K (X) , f ¯) is $ (r,s) $ (r , s) -sensitive ⇔ $ (\mathbb {F}^{1}(X),\widetilde {f_{g}}) $ (F 1 (X) , f g ~) is $ (r,s) $ (r , s) -sensitive for each $ g\in D_{m}(I) $ g ∈ D m (I) satisfying $ g^{-1}(1)=\{1\} $ g − 1 (1) = { 1 } ; $ (X,f) $ (X , f) is Δ-transitive ⇔ $ (K(X),\bar {f}) $ (K (X) , f ¯) is Δ-transitive ⇔ $ (M(X),\hat {f}) $ (M (X) , f ^) is Δ-transitive $ \Leftrightarrow \,(\mathbb {F}^{1}(X),\tilde {f}) $ ⇔ (F 1 (X) , f ~) is Δ-transitive. [ABSTRACT FROM AUTHOR]

The International Regulations for Preventing Collisions at Sea 1972 (COLREGs) have been the cornerstone of maritime navigation since their introduction. Knowledge and implementation of these rules are paramount in collision avoidance at sea. However, terms found in these rules are sometimes imprecise or fuzzy, as they are written by humans for humans, giving them some freedom in interpretation. The term Very Large Ship used in Rule 7 of the COLREGs is, by its nature, fuzzy. While human navigators understand this term's meaning, it could be challenging for machines or autonomous ships to understand such an unprecise expression. Fuzzy sets could easily describe unprecise terms used in maritime navigation. A fuzzy set consists of elements with degrees of membership in a set, making them perfect for interpreting some terms where boundaries are unclear. This research was conducted among 220 navigational experts to describe linguistic variables used in maritime regulations. This research consists of an internationally distributed questionnaire. Membership data were collected with the adapted horizontal method, and the results were statistically analyzed, followed by regression analyses to describe the range and shape of membership functions. A conceptual model of the implementation of linguistic variables is presented. The novelty of this study derives from the data collecting, modeling, and quantification of the important but neglected linguistic term Very Large Ship based on a large number of navigational experts. The same quantification method could be easily used for other COLREGs linguistic variables, which could easily lift barriers to advances in intelligent solutions based on fuzzy sets. The obtained quantified fuzzy sets can be used in decision support or control systems used by conventional or autonomous ships in the future. [ABSTRACT FROM AUTHOR]

With the advancement of information technology, the Internet is pivotal in today's society, serving as a global connectivity platform. Leveraging Internet technology within an enterprise can improve operational efficiency and curtail costs. However, traditional Internet platform selection methods cannot simultaneously handle quantitative and qualitative information, fuzzy semantics, and incomplete expert-provided information. To address these limitations, this study integrated the fuzzy analytic hierarchy process (FAHP) and the weighted aggregated sum product assessment (WASPAS) approaches to tackle Internet platform selection problems within an incomplete information environment. To demonstrate the validity of this research approach, this study utilized a construction industry Internet platform selection case to confirm the efficacy of the proposed novel fuzzy analytic hierarchy process-based method. Comparative analysis against the weighted sum model (WSM), weighted product model (WPM), FAHP, and typical WASPAS approaches was conducted with numerical verification, revealing that the proposed method in this study effectively manages comprehensive information and yields more rational outcomes for construction industry Internet platforms. [ABSTRACT FROM AUTHOR]

Optimization problem such as linear programming problem under epistemic uncertainty for instance fuzzy has been studied in this paper. Here, coefficients are assumed as crisp however, decision variables and the right-hand side vector of the constraints are presumed as uncertain in nature for the considered problem. Using the concept of fuzzy centre and fuzzy arithmetic a new method for the solution has been developed. First, solution of fuzzy centre for r = 0 has been obtained. And then as the upper bound of the solution can be expressed in term of fuzzy centre and lower bound, then using this an equivalent crisp system is solved to obtain the lower bound of the solution. Next again using the solution of lower bound and centre upper bound has been computed. Similarly lower and upper bounds for r = 1 have been obtained. Finally using these solutions fuzzy feasible optimal solution can be obtained. Various example problem has been solved using the proposed method and obtained results are compared with the existing results to show the advantage and validation. [ABSTRACT FROM AUTHOR]

Compared to traditional resources, user-side resources are of various types and have more significant uncertainty about their regulatory capacity, leading to difficulties in coordinating decisions about their simultaneous participation in the electric energy and peaking ancillary services markets. This paper proposes a joint bidding decision-making method for the day-ahead electricity energy and peak shaving auxiliary service market based on distributed robust opportunity constraints, which addresses the problem of difficulty in using an accurate probability density distribution to represent the uncertainty process of user-side resources. Firstly, a data-driven method for characterizing the uncertainty of load regulation capacity is investigated, and fuzzy sets are constructed without assuming specific probability distributions of random variables. Then, to minimize the risk expectation of the joint bidding cost on the customer side, a bidding strategy that considers the uncertainty is proposed. Finally, an example simulation verifies the reasonableness and effectiveness of the proposed joint bidding method, and the results show that the constructed model overcomes the problem of over-conservatism of the robust model, and the computational adaptability is better than that of the stochastic model, which achieves a better balance between robustness and economy.

Under-five mortality remains a significant global health challenge, with millions of children dying before their fifth birthday each year. This study explores the application of fuzzy Bayesian inference for under-five mortality data using Tanzania as a case study. Fuzzy Bayesian inference has emerged as a promising technique that combines the flexibility of fuzzy set theory with the probabilistic framework of Bayesian inference. The study employs fuzzy sets and membership functions to represent the linguistic terms and their degrees of membership, along with the Poisson distribution to model the mortality rate. The results demonstrate the potential of fuzzy Bayesian inference for analyzing under-five mortality rates. This approach provides a more nuanced understanding of the complex mortality patterns.

To address the shortcomings of the cubic intuitionistic fuzzy sets (CIFSs) for the entitlement of multi-argument approximate function, the cubic intuitionistic fuzzy hypersoft set (Ω-set) is an emerging study area. This type of setting associates the sub-parametric tuples with the collection of CIFSs. Categorizing the evaluation of parameters into their corresponding sub-parametric values based on non-overlapping sets has significance in decision making and optimization related situations. Some operations of Ω-set are proposed in this study, along with certain practical features. We provide the complement, P-order, and R-order subsets, P-union (∪P), R-union (∪R), P-intersection (∩P) and R-intersection (∩R) of Ω-sets. The internal cubic intuitionistic fuzzy hypersoft set (ΩI-set) and the external cubic intuitionistic fuzzy hypersoft set (ΩE-set) are also proposed in this paper, which will aid researchers in applying this new theory to other areas of study. We show a few examples in this context and look into some more aspects of ∪P, ∪R, ∩P and ∩R of ΩI-sets and ΩE-sets. Arguments for a few significant theorems about ΩI-sets and ΩE-sets are also presented. Lastly, an algorithm is presented that assists decision-makers in evaluating appropriate solar panels to establish solar plants. The proposed algorithm uses the idea of ∪P and ∪R for two Ω-sets constructed based on expert opinions of decision makers.

Abstract In this manuscript we demonstrate interval-valued bipolar complex fuzzy set (IVBCFS) and then interval-valued bipolar complex fuzzy soft set (IVBCFSS), as a generalization of fuzzy set, interval-valued fuzzy set, bipolar fuzzy set, complex fuzzy set and soft set. We also initiate operational laws and basic results and properties for IVBCFS and IVBCFSS. Further explanation is given for the basic algebraic operations like complement, extended union, extended intersection, restricted union, and restricted intersection, AND product and OR product for IVBCFSS. Moreover, we demonstrate some fundamental aggregation operators like IVBCFS average aggregation, IVBCFS geometric and as well as their properties. To emphasize the usefulness and application of the system, we also develop the decision-making method and joint instances of the IVBCFSS (set-ups 1 and 2). In order to describe the effectiveness and influence of the approaching novel work, this study uses a comparative analysis of the new creating concept with prevailing ideas.

Introduction/purpose: The significance of studying voting behaviour is underscored by its ability to gauge the continuity or divergence of electoral politics from historical trends, elucidating the real impact of the transformative ballot box, and contributing to the examination of democracy as a value among both masses and elites. Additionally, it aids in comprehending the intricate process of political socialization. Methods: An inherent strength of the rough set lies in its reliance solely on raw data, devoid of external inputs. The decision-theoretic rough set framework, an evolution of the rough set, has garnered widespread application across diverse domains, serving as a proficient tool for acquiring knowledge, particularly in navigating situations marked by vagueness and uncertainty. Despite the proliferation of mathematical models designed to discern people's voting behavior, a decision-based rough set recommendation remains noticeably absent in existing literature. This paper introduces an innovative three-way decision approach grounded in linguistic information for identifying voting behavior. The proposed approach is based on a hybrid probabilistic rough fuzzy model incorporating linguistic information and providing insights into voting patterns. Results: The three-way decision hybrid models are tested on people and a highly satisfactory result was achieved for identifying their voting behaviours. The justification of results was validated through the mathematical process. Conclusion: A practical illustration is provided to highlight the importance of this hybrid model and to confirm its usefulness in identifying and forecasting voting behaviour

Railway projects are incredibly costly due to their complex nature. This study performs risk analysis and management of Pakistan railways ML-1 project expansion and upgradation that will be undertaken at US$6.8 billion under the China-Pakistan Economic Corridor (CPEC). The risks were identified based on an extensive literature review and their relevance to the CPEC. We employed fuzzy set theory (integrated with the risk severity index) to obtain the most severe risks. The novelty of this study is the technique employed to analyse and rank the risk, also there are no previous studies conducted that emphasized the construction risk of railway projects in Pakistan. The study is useful for all stakeholders of the project, as it can plan for them to tackle these risks and implement ML-1 successfully.

Abstract The main goal of this study is to establish common fuzzy fixed points in the context of complete b-metric spaces for a pair of fuzzy mappings that satisfy F-contractions. To strengthen the validity of the derived results, non-trivial examples are provided to substantiate the conclusions. Moreover, prior discoveries have been drawn as logical extensions from pertinent literature. Our findings are further reinforced and integrated by the numerous implications that this technique has in the literature. Using fixed point techniques to approximate the solutions of differential and integral equations is very useful. Specifically, in order to enhance the validity of our findings, the existence result of the system of non-linear Fredholm integral equations of second-kind is incorporated as an application.

Spherical fuzzy sets are more powerful in modelling the uncertain situations than picture fuzzy sets, fermatean fuzzy sets, Pythagorean fuzzy sets, intuitionistic fuzzy sets, and fuzzy sets. In this paper, we first define the variance and covariance of spherical fuzzy sets. Then, using variance and covariance, we define the unique spherical fuzzy set correlation metric in line with the statistical coefficient of correlation. Two spherical fuzzy sets are correlated in both direction and strength using the provided measure of correlation. We discussed its many characteristics. We compared the measure of correlation with the current ones through linguistic variables. We established its validity by showing its application in bidirectional approximate reasoning. We also resolve a pattern identification issue in the spherical fuzzy environment using the provided correlation function, and we compare the results with several current measurements.

The soft idea has a crucial impact on facing uncertainty, but extending soft, fuzzy soft, and vague soft settings is more comprehensive in expressing the problem ambiguity parameters than the soft set. Despite this advancement, the vague soft set falls short in addressing certain decision-making issues. This occurs when we have some external factors that can impact our final decision. These external factors can be represented in the effective parameter set. So, the objective of the current article is to incorporate the new concept of effectiveness into the concept of vague sets. This approach leads the researchers to create a novel and expanded framework for effective decision-making, surpassing any previously introduced methods in applicability. The article also provides an exploration of the types, concepts, and operations of effective vague soft sets, each illustrated with examples. Furthermore, the study delves into the examination of properties like De Morgan's laws, distributive, commutative, absorption, and associative properties for those new sets. Moreover, the framework of effective vague soft sets is used to develop a decision-making methodology. This technique simplifies the process of determining whether a student meets the requirements for a particular level of education or if a patient has a specific disease, among other applications. Additionally, to clarify the proposed algorithm, a detailed case study representing how to classify students toward specializations is examined in detail. Using matrix processes in this example, in addition to $ Wolfram \; Mathematica^{\circledR} $, not only renders computations simpler and quicker but also results in more precise optimum effective decisions. In the end, a detailed comparison with existing techniques is performed and summed up in a chart to illustrate the difference between them and the present one.