Interval-valued intuitionistic fuzzy programming technique for multicriteria group decision making based on Shapley values and incomplete preference information

2016 ◽  
Vol 21 (19) ◽  
pp. 5787-5804 ◽  
Author(s):  
Wenkai Zhang ◽  
Yanbing Ju ◽  
Xiaoyue Liu
Keyword(s):  
Group Decision ◽  
Fuzzy Programming ◽  
Programming Technique ◽  
Preference Information ◽  
Incomplete Preference ◽  
Shapley Values ◽  
Multicriteria Group Decision Making ◽  
Intuitionistic Fuzzy Programming Technique ◽  
Intuitionistic Fuzzy Programming ◽  
Interval Valued

An Interactive Signed Distance Approach for Multiple Criteria Group Decision-Making Based on Simple Additive Weighting Method with Incomplete Preference Information Defined by Interval Type-2 Fuzzy Sets

2014 ◽  
Vol 13 (05) ◽  
pp. 979-1012 ◽  
Author(s):  
Ting-Yu Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Information ◽  
Incomplete Preference ◽  
Signed Distance ◽  
Decision Making Problem ◽  
Simple Additive Weighting ◽  
Interval Type

Interval type-2 fuzzy sets (T2FSs) with interval membership grades are suitable for dealing with imprecision or uncertainties in many real-world problems. In the Interval type-2 fuzzy context, the aim of this paper is to develop an interactive signed distance-based simple additive weighting (SAW) method for solving multiple criteria group decision-making problems with linguistic ratings and incomplete preference information. This paper first formulates a group decision-making problem with uncertain linguistic variables and their transformation to interval type-2 trapezoidal fuzzy numbers. Concerning the relative importance of multiple decision-makers and group consensus of fuzzy opinions, a procedure using hybrid averages is then employed to construct a collective decision matrix. By an appropriate extension of the classical SAW approach, this paper utilizes the concept of signed distances and establishes an integrated programming model to manage multi-criteria group decisions under the incomplete and inconsistent preference structure. Further, an interactive procedure is established for group decision making. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a collaborative decision-making problem of patient-centered care (PCC).

Synthesizing Different Preference Information by Fuzzy Programming Method

2011 ◽  
Vol 328-330 ◽  
pp. 2352-2357
Author(s):  
Jing Yang
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Fuzzy Programming ◽  
Fuzzy Linear Programming ◽  
Decision Makers ◽  
Preference Ordering ◽  
Utility Value ◽  
Preference Information ◽  
Preference Strength ◽  
Judgment Matrix

Group decision making problems with different forms of preference information are discussed. Firstly, four forms of preference information ( i.e. preference ordering, utility value, AHP judgment matrix and fuzzy judgment matrix) are introduced and the computing formulas are given to transform different forms of preference information into the form of fuzzy judgment matrix. A new method that involves in different preference strength of experts is studied. Then, the assessment of the group priorities is formulated as a fuzzy linear programming problem, maximizing the group’s overall satisfaction to get the group solution. The method can easily deal with missing judgments and different partiality intensity by decision makers. At the end, the feasibility and effectiveness of method is explained by an example.

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 Multifuzzy Cubic Sets and Their Correlation Coefficients for Multicriteria Group Decision-Making

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jun Ye ◽  
Shigui Du ◽  
Rui Yong
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Correlation Coefficients ◽  
Decision Makers ◽  
Special Cases ◽  
Multicriteria Group Decision Making ◽  
Ranking Of Alternatives ◽  
Interval Valued ◽  
Weighted Correlation

The notion of multifuzzy sets (MFSs) or multi-interval-valued fuzzy sets (MIVFSs) provides a new method to represent some problems with a sequence of the different and/or same fuzzy/interval-valued fuzzy membership values of an element to the set. Then, a fuzzy cubic set (FCS) consists of a certain part (a fuzzy value) and an uncertain part (an interval-valued fuzzy value) but cannot represent hybrid information of both MFS and MIVFS. To adequately depict the opinion of several experts/decision-makers by using a union/sequence of the different and/or same fuzzy cubic values for an object assessed in group decision-making (GDM) problems, this paper proposes a multifuzzy cubic set (MFCS) notion as the conceptual extension of FCS to express the hybrid information of both MFS and MIVFS in the fuzzy setting of both uncertainty and certainty. Then, we propose three correlation coefficients of MFCSs and then introduce correlation coefficients of MFSs and MIVFSs as special cases of the three correlation coefficients of MFCSs. Further, the multicriteria GDM methods using three weighted correlation coefficients of MFCSs are developed under the environment of MFCSs, which contains the MFS and MIVFS GDM methods. Lastly, these multicriteria GDM methods are applied in an illustrative example on the selection problem of equipment suppliers; then their decision results and comparative analysis indicate that the developed GDM methods are more practicable and effective and reflect that either different correlation coefficients or different information expressions can also impact on the ranking of alternatives. Therefore, this study indicates the main contribution of the multifuzzy cubic information expression, correlation coefficients, and GDM methods in the multifuzzy setting of both uncertainty and certainty.

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