An Extended TODIM Method Based on Novel Score Function and Accuracy Function under Intuitionistic Fuzzy Environment

2019 ◽  
Vol 27 (06) ◽  
pp. 905-930 ◽  
Author(s):  
Dong Zhang ◽  
Xin Bao ◽  
Chong Wu
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Choquet Integral ◽  
Score Function ◽  
Accuracy Function ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Nonlinear Programming Model ◽  
Todim Method ◽  
The Difference

Recently, multi-attribute decision making (MADM) approaches concerning decision maker’s psychological behaviors have received increasing attention, but few of them have taken all the criteria interactions (positive, negative and dependent interactions) into consideration. In this paper, we combine the TODIM (an acronym in Portuguese of interactive and multi-criteria decision making) method with the 2-additive fuzzy measure and Choquet integral theory to demonstrate how criteria interactions can be determined and further extend it into intuitionistic fuzzy environment. To begin with, we propose the novel score function and accuracy function to compare the difference among intuitionistic fuzzy sets, which have been proven to be more effective and rational than the existing measure functions. Next, we construct the nonlinear programming model based on maximum-entropy principal to obtain the optimal criteria interactions. Further, 2-additive Choquet-based dominance degree is defined whereby we put forward the 2-additive Choquet integral-based TODIM method under intuitionistic fuzzy environment to handle more challenging MADM problems. Finally, we present results of a didactic example, which concerns selection of suppliers for a manufacturing company, to evaluate the validity and rationality of proposed approach.

scholarly journals Interval-Valued Intuitionistic Fuzzy Multicriteria Group Decision Making Based on VIKOR and Choquet Integral

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Chunqiao Tan ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Decision Making Problem ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

An effective decision making approach based on VIKOR and Choquet integral is developed to solve multicriteria group decision making problem with conflicting criteria and interdependent subjective preference of decision makers in a fuzzy environment where preferences of decision makers with respect to criteria are represented by interval-valued intuitionistic fuzzy sets. First, an interval-valued intuitionistic fuzzy Choquet integral operator is given. Some of its properties are investigated in detail. The extended VIKOR decision procedure based on the proposed operator is developed for solving the multicriteria group decision making problem where the interactive criteria weight is measured by Shapley value. An illustrative example is given for demonstrating the applicability of the proposed decision procedure for solving the multi-criteria group decision making problem in interval-valued intuitionistic fuzzy environment.

scholarly journals An Intuitionistic Fuzzy Stochastic Decision-Making Method Based on Case-Based Reasoning and Prospect Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Peng Li ◽  
Yingjie Yang ◽  
Cuiping Wei
Keyword(s):  
Decision Making ◽  
Prospect Theory ◽  
Programming Model ◽  
Score Function ◽  
Multicriteria Decision Making ◽  
Expected Utility Theory ◽  
Fuzzy Decision Making ◽  
Case Based Reasoning ◽  
Intuitionistic Fuzzy ◽  
Case Based

According to the case-based reasoning method and prospect theory, this paper mainly focuses on finding a way to obtain decision-makers’ preferences and the criterion weights for stochastic multicriteria decision-making problems and classify alternatives. Firstly, we construct a new score function for an intuitionistic fuzzy number (IFN) considering the decision-making environment. Then, we aggregate the decision-making information in different natural states according to the prospect theory and test decision-making matrices. A mathematical programming model based on a case-based reasoning method is presented to obtain the criterion weights. Moreover, in the original decision-making problem, we integrate all the intuitionistic fuzzy decision-making matrices into an expectation matrix using the expected utility theory and classify or rank the alternatives by the case-based reasoning method. Finally, two illustrative examples are provided to illustrate the implementation process and applicability of the developed method.

An improved fuzzy TODIM method based on entropy measure under Intuitionistic Fuzzy Information

2021 ◽  
Vol 23 (05) ◽  
pp. 464-470
Author(s):  
Sunit Kumar ◽  
◽  
Satish Kumar ◽  
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Function ◽  
Entropy Measure ◽  
Multi Criteria Decision Making ◽  
Fuzzy Information ◽  
Numerical Example ◽  
Intuitionistic Fuzzy ◽  
Todim Method

Intuitionistic fuzzy set (IFS) is one of the most extensive and important tool to accommodate more uncertainties than existing fuzzy set structures. In the present paper, we describe an improved entropy based on TODIM procedure for handling multi-criteria decision-making (MCDM) under IF setting and also the weight information is partially known. First, we study the basic notions and operating laws of IFSs, also the accuracy and score function of it. The new entropy has been proposed. Secondly, the IF information-based decision-making technique for MCDM is presented. Lastly, a numerical example is given related, to demonstrate that their results are credible and feasible.

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

2017 ◽  
Vol 25 (05) ◽  
pp. 821-849 ◽  
Author(s):  
Fanyong Meng ◽  
Chunqiao Tan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment ◽  
Operational Laws ◽  
Choquet Integrals ◽  
The Given ◽  
Interval Valued

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.

scholarly journals A New Multiple Criteria Decision Making Method and its Application in Cloud Computing for Education

2015 ◽  
Vol 10 (8) ◽  
pp. 21
Author(s):  
Heng Sun
Keyword(s):  
Decision Making ◽  
Cloud Computing ◽  
Membership Function ◽  
Fuzzy Set ◽  
Choquet Integral ◽  
Intuitionistic Fuzzy Set ◽  
Multiple Criteria Decision Making ◽  
Score Function ◽  
Multiple Criteria ◽  
Intuitionistic Fuzzy

Cloud computing can extend the traditional education framework. In education, cloud can provide students and teachers with tools to deploy computing resources on-demand for lectures and labs according to their learning needs. But how to select a perfect cloud server is a key point, which is considered as a multiple criteria decision making problem. So, in this paper, intuitionistic fuzzy set is first introduced to express the decision maker’s views. Intuitionistic fuzzy set (IFS) includes a membership function and a non-membership function. More importantly, a new operator with choquet integral is developed to deal with assessment of education using cloud computing. Meanwhile, score function and accuracy function are demonstrated to obtain the final result. Finally, we develop this method to apply in a case study to show its applicability.

NONLINEAR ASSIGNMENT-BASED METHODS FOR INTERVAL-VALUED INTUITIONISTIC FUZZY MULTI-CRITERIA DECISION ANALYSIS WITH INCOMPLETE PREFERENCE INFORMATION

2012 ◽  
Vol 11 (04) ◽  
pp. 821-855 ◽  
Author(s):  
TING-YU CHEN
Keyword(s):  
Decision Analysis ◽  
Programming Model ◽  
Score Function ◽  
Multiple Criteria ◽  
Incomplete Preference ◽  
Intuitionistic Fuzzy ◽  
Uncertainty Index ◽  
Nonlinear Programming Model ◽  
Ranking Order ◽  
Interval Valued

In the context of interval-valued intuitionistic fuzzy sets, this paper develops nonlinear assignment-based methods to manage imprecise and uncertain subjective ratings under incomplete preference structures and thereby determines the optimal ranking order of the alternatives for multiple criteria decision analysis. By comparing each interval-valued intuitionistic fuzzy number's score function, accuracy function, membership uncertainty index, and hesitation uncertainty index, a ranking procedure is employed to identify criterion-wise preference of alternatives. Based on the criterion-wise rankings and a set of known but incomplete information about criterion weights, a nonlinear assignment model is constructed to estimate criterion weights and to order the priority of various alternatives. Considering multiple criteria evaluation problems with preference conflict about criterion importance, an integrated nonlinear programming model is further established with regard to incomplete and inconsistent weight information. These proposed nonlinear assignment-based methods can obtain an aggregate ranking that effectively combines the relative performance of each alternative in each criterion. In addition, this overall ranking most closely agrees with the criterion-wise rankings. Finally, the feasibility of the proposed method is illustrated by a practical example of selecting a suitable bridge construction method.

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