Fuzzy Choquet Research Articles

Data envelopment analysis with interactive fuzzy variables

In this article, we develop a novel fuzzy data envelopment analysis (DEA) model, using fuzzy Choquet integral as an aggregating tool, to evaluate the efficiency of the decision making units (DMUs). The proposed model can be used to evaluate the efficiency of the DMU with interactive fuzzy variables (fuzzy inputs or fuzzy outputs), the classical fuzzy DEA model is a special form of this novel fuzzy DEA model. At the end of the article, we will use numerical examples to illustrate the performance of the proposed model.

GRA method based on spherical linguistic fuzzy Choquet integral environment and its application in multi-attribute decision-making problems

The key objective of the proposed work in this paper is to introduce a new version of picture linguistic fuzzy set, so-called spherical linguistic fuzzy sets. The novel concept of spherical linguistic fuzzy set consists of linguistic term, positive, neutral and negative membership degrees which satisfies the conditions that the square sum of its membership degrees is less than or equal to 1. In this paper, we investigate the basic operations of spherical linguistic fuzzy sets and discuss some related results. We extend operational laws of aggregation operators and propose spherical linguistic fuzzy Choquet integral weighted averaging (SLFCIWA) operator based on spherical fuzzy numbers. Further, the proposed SLFCIWA operator of spherical fuzzy number is applied to multi-attribute group decision-making problems. Also, we propose the GRA method to aggregate the spherical fuzzy information. To implement the proposed models, we provide some numerical applications of group decision-making problems. Also compared with the previous model, we conclude that the proposed technique is more effective and reliable.

Smart medical device selection based on intuitionistic fuzzy Choquet integral

This paper presents a novel approach for evaluating the smart medical device selection process in a group decision-making setting in an uncertain decision environment. Intuitionistic fuzzy Choquet integral (IFCI) approach is applied to treat the uncertainty and vagueness in the decision-making process. IFCI also considers the interactions among the decision criteria in the data provided by the decision makers. In this paper, the emphasis is placed upon the selection of wearable monitoring devices for cardiac patients. The goal is to present the complexity of the problem, raise interest among specialists in the healthcare industry and assess smart medical devices under different evaluation criteria. The problem is formulated as a multi-criteria decision model with ten criteria and eight alternatives. The results of the IFCI model are analyzed using 9 sensitivity analysis scenarios, which prove the adequacy of the obtained results. The result of the proposed method is also compared with the IF extensions of the VIKOR, TOPSIS, COPRAS, MOORA and MULTIMOORA models in order to validate and verify the obtained outcome. The Spearman coefficient of correlation is applied to check the stability of the variations in the rankings. The results indicate that the model and the rankings it generates are sufficiently stable.

Gray Method for Multiple Attribute Decision Making with Incomplete Weight Information under the Pythagorean Fuzzy Setting

Abstract In this study, we developed an approach to investigate multiple attribute group decision-making (MAGDM) problems, in which the attribute values take the form of Pythagorean fuzzy numbers whose information about attribute weights is incompletely known. First, the Pythagorean fuzzy Choquet integral geometric operator is utilized to aggregate the given decision information to obtain the overall preference value of each alternative by experts. In order to obtain the weight vector of the criteria, an optimization model based on the basic ideal of the traditional gray relational analysis method is established, and the calculation steps for solving Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of gray relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. Then, a relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of gray relation to both the positive-ideal solution and negative-ideal solution simultaneously. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

A extended intuitionistic fuzzy Choquet integral correlation coefficient based on Shapley index in multi-criteria decision making

A extended intuitionistic fuzzy Choquet integral correlation coefficient based on Shapley index in multi-criteria decision making

Convex Aggregation Operators and Their Applications to Multi-Hesitant Fuzzy Multi-Criteria Decision-Making

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore, if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multi-hesitant fuzzy sets (MHFSs) can deal effectively with a case where some values are repeated more than once in a MHFS. In this paper, the novel convex combination of multi-hesitant fuzzy numbers (MHFNs) is introduced. Some aggregation operators based on convex operation, such as generalized multi-hesitant fuzzy ordered weighted average (GMHFOWA) operator, generalized multi-hesitant fuzzy hybrid weighted average (GMHFHWA) operator, generalized multi-hesitant fuzzy prioritized weighted average (GMHFPWA) operator and generalized multi-hesitant fuzzy Choquet integral weighted average (GMHFCIWA) operator, are developed and corresponding properties are discussed in detail. Then, based on the proposed aggregation operators, a novel approach for multi-criteria decision-making (MCDM) problem is proposed for ranking alternatives. Finally, an example is provided to verify the developed approach and demonstrate its validity and feasibility and the study is supported by a sensitivity analysis and a comparison analysis.

Some new Pythagorean fuzzy Choquet-Frank aggregation operators for multi-attribute decision making

Pythagorean fuzzy set (PFS) whose main feature is that the square sum of the membership degree and the non-membership degree is equal to or less than one, is a powerful tool to express fuzziness and uncertainty. The aim of this paper is to investigate aggregation operators of Pythagorean fuzzy numbers (PFNs) based on Frank t-conorm and t-norm. We first extend the Frank t-conorm and t-norm to Pythagorean fuzzy environments and develop several new operational laws of PFNs, based on which we propose two new Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy Choquet–Frank averaging operator (PFCFA) and Pythagorean fuzzy Choquet–Frank geometric operator (PFCFG). Moreover, some desirable properties and special cases of the operators are also investigated and discussed. Then, a novel approach to multi-attribute decision making (MADM) in Pythagorean fuzzy context is proposed based on these operators. Finally, a practical example is provided to illustrate the validity of the proposed method. The result shows effectiveness and flexible of the new method. A comparative analysis is also presented.

Application of Dual Hesitant Fuzzy Geometric Bonferroni Mean Operators in Deciding an Energy Policy for the Society

Dual hesitant fuzzy geometric Bonferroni mean is defined for dual hesitant fuzzy sets. Different properties of dual hesitant fuzzy geometric Bonferroni mean are discussed. Some special cases are studied in detail for dual hesitant fuzzy geometric Bonferroni mean. In addition, dual hesitant fuzzy weighted geometric Bonferroni mean and dual hesitant fuzzy Choquet geometric Bonferroni mean are proposed. A multicriteria decision-making method is discussed to find the best alternative among different alternatives by using proposed aggregated operators and an illustrated example is also given to understand our proposal.

Interval-valued Pythagorean fuzzy GRA method for multiple-attribute decision making with incomplete weight information

In this paper, the concept of multiple-attribute group decision-making (MAGDM) problems with interval-valued Pythagorean fuzzy information is developed, in which the attribute values are interval-valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval-valued Pythagorean fuzzy sets is the generalization of interval-valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval-valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval-valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval-valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval-valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval-valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive-ideal solution and negative-ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive-ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.

Shapley interval-valued dual hesitant fuzzy Choquet integral aggregation operators in multiple attribute decision making

Shapley interval-valued dual hesitant fuzzy Choquet integral aggregation operators in multiple attribute decision making

Single-Valued Neutrosophic Hesitant Fuzzy Choquet Aggregation Operators for Multi-Attribute Decision Making

This paper aims at developing new methods for multi-attribute decision making (MADM) under a single-valued neutrosophic hesitant fuzzy environment, in which each element has sets of possible values designed by truth, indeterminacy, and falsity membership hesitant functions. First, taking advantage of the Choquet integral and that it can reflect more correlations of attributes in MADM, two aggregation operators are defined based on the Choquet integral, specifically, the single-valued neutrosophic hesitant fuzzy Choquet ordered averaging (SVNHFCOA) operator and single-valued neutrosophic hesitant fuzzy Choquet ordered geometric (SVNHFCOG) operator, and their properties are also discussed in detail. Then, novel MADM approaches based on the SVNHFCOA and SVNHFCOG operators are established to process single-valued neutrosophic hesitant fuzzy information. Finally, this work provides a numerical example of investment alternatives to validate the application and effectiveness of the proposed approaches.

Some new interval-valued dual hesitant fuzzy Choquet integral aggregation operators and their applications

Some new interval-valued dual hesitant fuzzy Choquet integral aggregation operators and their applications

NON-ADDITIVE MULTIPLE CRITERIA APPROACH FOR THE EVALUATION OF INTERNATIONAL CLIMATE THINK TANKS

This paper outlines the application of non-additive measures and Choquet integral in the construction of a composite indicator to assess the performance of international climate think tanks and evaluate their influence in shaping climate policies and raising awareness among the general public. The composite index consists of 15 carefully selected indicators according to the feedback provided by Experts within the field and structured into three main pillars: Activities, Publications and Dissemination. In order compare Think Tanks of different size and hence to measure their efficiency, the standardized ranking is also computed dividing the Think Tank outcome in each criterion by the number of its researchers. The application of fuzzy measures and Choquet integral, allowing to take into account potential interactions existing among criteria, increases substantially the model capability both in eliciting effectively Experts’ preferences and in aggregating indicators. Moreover, we present a novel technique for the aggregation of Experts’ preferences where Decision Makers’ weights have been set proportionally to their consistency in evaluating the specific questionnaire.

Selection of sustainable urban transportation alternatives using an integrated intuitionistic fuzzy Choquet integral approach

Unrestrained urban development and rapid expansion of motorized vehicles inevitably lead to unsustainable transportation systems from economic, social and environmental points of view, not only endangering public health but also pressuring ecosystems. Trying to address these issues, transportation policy makers face major challenges in their attempts to identify sustainable transportation alternatives. To provide a systematic approach for such endeavors, this paper evaluates different public bus technologies as urban transportation alternatives. In order to incorporate expert opinion into the model environment, a set of sustainability related criteria is established and expert opinion regarding the sustainability of vehicle options are obtained based on each criterion. Since the fulfillment of a single criterion is not sufficient to deduct meaningful conclusions, the evaluation considered the dependencies among the decision criteria in search of compromising solutions. To address this, an aggregation method based on Intuitionistic Fuzzy Choquet Integral (IFCI) and Group Decision Making (GDM) techniques is proposed. A fuzzy pairwise-comparison measure identification method is used in IFCI in order to define its parameters. TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), another multi-criteria method that ignores interactions, and 2-additive Choquet integral are also employed. The outcomes of IFCI, 2-additive Choquet integral and TOPSIS are compared with one another. The findings indicate that dependencies among decision criteria significantly affect the selection process of the most sustainable urban transportation system and can alter the rankings.

PRIORITIZATION OF PETROLEUM SUPPLY CHAINS’ DISRUPTION MANAGEMENT STRATEGIES USING COMBINED FRAMEWORK OF BSC APPROACH, FUZZY AHP AND FUZZY CHOQUET INTEGRAL OPERATOR

Industries in every sector have observed tangible losses from a broad range of disruptions during recent years. Factors such as globalization and outsourcing have made supply chains more sophisticated and this makes disruption management more necessary. Any disruption in each part of supply chain makes the whole supply chain face derangement and at last, ultimate customers realize the shaped disadvantages. Since avoidance of disruption occurrence is not always possible, application of different strategies with the aid of minimization of negative effects seems necessary. That is why in this paper, different strategies for disruption management in petroleum products supply chain and suitable criteria for prioritizing them are recognized via Balanced Score Card approach measures. After that, by application of fuzzy Analytical Hierarchy Process and intuitionistic fuzzy Choquet integral operator, their priorities are specified in order to make a guideline for managers to set proper plans and manage such disruptions more accurately.

An Error Analysis Decision Making Method for Priority in Intuitionistic Preference Relation

This article describes how intuitionistic fuzzy sets theory, which is the generalisation of fuzzy sets theory, is a more suitable tool for dealing with imprecise information. The information provided by the decision maker is often imprecise in many situations. So, intuitionistic preference relation is a suitable tool for such cases. The estimation of the priority vector of the intuitionistic preference relation is an important part in decision making. In this article, an intuitionistic fuzzy Choquet integral is proposed and combined with the famous error propagation formula, and developed a method for the priority of an intuitionistic preference relation to estimate the ranking of the considered alternatives. Also, an experiment has been conducted to demonstrate and implementation of the proposed approach.

Some new Shapley dual hesitant fuzzy Choquet aggregation operators and their applications to multiple attribute group decision making-based TOPSIS

Some new Shapley dual hesitant fuzzy Choquet aggregation operators and their applications to multiple attribute group decision making-based TOPSIS

A Method for Multi-Attribute Group Decision Making Based on Generalized Interval-Valued Intuitionistic Fuzzy Choquet Integral Operators

As an extension of the classical averaging operators, Choquet integral has been shown a powerful tool for decision theory. In this paper, a method based on the generalized interval-valued intuitionistic fuzzy Choquet integrals w.r.t. the generalized interaction indices is proposed for multiattribute group decision making problems, where the importance of the elements is considered, and their interactions are reflected. Based on the given operational laws on interval-valued intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy Choquet integrals with respect to the generalized Shapley and Banzhaf indices are defined. Moreover, some of their properties are studied, such as idempotency, boundary, comonotonic linearity and μ–linearity. Furthermore, a decision procedure based on the proposed operators is developed for solving multi-attribute group decision making under interval-valued intuitionistic fuzzy environment. Finally, a numerical example is provided to illustrate the developed procedure.

On developing Sugeno fuzzy measure densities in problems of face recognition

Fuzzy measures and Choquet integral are efficient aggregation operators utilised intensively in decision-making theory. To produce sound classification results based on a family of classifiers, the parameters of the fuzzy measure (especially, so-called fuzzy densities) have to be determined. In this study, we propose a method based on particle swarm optimisation (PSO) and discuss in detail a new concept of a so-called positive and negative optimisation to fully utilise specific properties of classifiers to carry out efficient classification. A suite of experiments is conducted to illustrate this approach and discuss its scope of applicability.

Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.