Extension of VIKOR Method for Multi-Attribute Group Decision Making with Incomplete Weights

2014 ◽  
Vol 513-517 ◽  
pp. 721-724 ◽  
Author(s):  
Chen Guang Xu ◽  
Dong Xiao Liu ◽  
Min Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Fuzzy Decision ◽  
Vikor Method ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Magdm Problems ◽  
Interval Valued

In this paper, we First utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Interval-Valued Intuitionistic Fuzzy Assessments and Incomplete Weights

2014 ◽  
Vol 513-517 ◽  
pp. 725-728 ◽  
Author(s):  
Chen Guang Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Fuzzy Decision ◽  
Vikor Method ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Magdm Problems ◽  
Interval Valued

In this paper, we investigate the multi-attribute group decision making (MAGDM) problems in which all the information provided by the decision makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

scholarly journals Interval-Valued Intuitionistic Fuzzy Multiple Attribute Group Decision Making with Uncertain Weights

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Zhuosheng Jia ◽  
Yingjun Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Collective Decision ◽  
Decision Makers ◽  
Fuzzy Decision ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Interval Valued

The theory of interval-valued intuitionistic fuzzy sets (IVIFSs) has been an impactful and convenient tool in the construction of advanced multiple attribute group decision making (MAGDM) models to counter the uncertainty in the developing complex decision support system. To satisfy much more demands from fuzzy decision making problems, we propose a method to solve the MAGDM problem in which all the information supplied by the decision makers is expressed as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by an interval-valued intuitionistic fuzzy number, and the information about the weights of both decision makers and attributes may be completely unknown or partially known. Firstly, we introduce a consensus-based method to quantify the weights of all decision makers based on all interval-valued intuitionistic fuzzy decision matrices. Secondly, we utilize the interval-valued intuitionistic fuzzy weighted arithmetic (IVIFWA) operator to aggregate all interval-valued intuitionistic fuzzy decision matrices into the collective one. Thirdly, we establish an optimization model to determine the weights of attributes depending on the collective decision matrix and the given attribute weight information. Fourthly, we adopt the weighted correlation coefficient of IVIFSs to rank all the alternatives from the perspective of TOPSIS via the collective decision matrix and the obtained weights of attributes. Finally, some examples are used to illustrate the validity and feasibility of our proposed approach by comparison with some existing models.

scholarly journals A Consensus Reaching Model with Minimum Adjustments in Interval-Valued Intuitionistic MAGDM

2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Gai-li Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Novel Method ◽  
Consensus Index ◽  
Interval Valued ◽  
Consensus Reaching

This paper focuses on multiattribute group decision-making problems with interval-valued intuitionistic fuzzy values (IVIFVs) and develops a consensus reaching model with minimum adjustments to improve the consensus among decision-makers (DMs). To check the consensus, a consensus index is introduced by measuring the distance between each decision matrix and the collective one. For the group decision-making with unacceptable consensus, Consensus Rule 1 and Consensus Rule 2 are, respectively, proposed by minimizing adjustment amounts of individual decision matrices. According to these two consensus rules, two algorithms are devised to help DMs reach acceptable consensus. Moreover, the convergences of algorithms are proved. To determine weights of attributes, an interval-valued intuitionistic fuzzy program is constructed by maximizing comprehensive values of alternatives. Finally, alternatives are ranked based on their comprehensive values. Thereby, a novel method is proposed to solve MAGDM with IVIFVs. At length, a numerical example is examined to illustrate the effectiveness of the proposed method.

Taxonomy method for multiple attribute group decision making based on interval-valued intuitionistic fuzzy with entropy

2021 ◽  
pp. 1-15
Author(s):  
Lu Xiao ◽  
Guiwu Wei ◽  
Yanfeng Guo ◽  
Xudong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Intuitionistic Fuzzy Set ◽  
Decision Makers ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Multiple Attribute ◽  
Magdm Problems ◽  
Interval Valued

Interval-valued intuitionistic fuzzy set (IVIFS) is a flexible method to deal with uncertainty and fuzziness. For the past few years, extensive researches about the multi-attribute group decision making (MAGDM) problems based on IVIFSs has been extensively studied in many fields. In this study, the Taxonomy method based on IVIFSs (IVIF-Taxonomy) was proposed for MAGDM problems. For the sake of the objectivity of attribute weight, entropy is introduced into the proposed model. The IVIF-Taxonomy method fully considers the weight of the decision makers (DMs) and the homogeneity of the chosen alternatives, making it more realistic. In addition, we apply IVIF-Taxonomy method to fund selection to verify the validity of IVIF-Taxonomy method. Finally, the trustworthy of IVIF-Taxonomy method is proved by comparing with the aggregate operator, IVIF-TOPSIS method, IVIF-GRA method and modified IVIF-WASPAS method.

scholarly journals Hybrid Multiattribute Group Decision Making Based on Intuitionistic Fuzzy Information and GRA Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Jian Guo
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Ideal Solution ◽  
Decision Matrix ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Intuitionistic Fuzzy Entropy ◽  
Fuzzy Group Decision Making

Hybrid multiple attribute group decision making involves ranking and selecting competing courses of action available using attributes to evaluate the alternatives. The decision makers assessment information can be expressed in the form of real number, interval-valued number, linguistic variable, and the intuitionistic fuzzy number. All these evaluation information can be transformed to the form of intuitionistic fuzzy numbers. A combined GRA with intuitionistic fuzzy group decision-making approach is proposed. Firstly, the hybrid decision matrix is standardized and then transformed into an intuitionistic fuzzy decision matrix. Then, intuitionistic fuzzy averaging operator is utilized to aggregate opinions of decision makers. Intuitionistic fuzzy entropy is utilized to obtain the entropy weights of the criteria, respectively. After intuitionistic fuzzy positive ideal solution and intuitionistic fuzzy negative ideal solution are calculated, the grey relative relational degree of alternatives is obtained and alternatives are ranked. In the end, a numerical example illustrates the validity and applicability of the proposed method.

A Multi-Criteria Intuitionistic Fuzzy Group Decision Making Method for Supplier Selection with VIKOR Method

2012 ◽  
pp. 967-983
Author(s):  
Razieh Roostaee ◽  
Mohammad Izadikhah ◽  
Farhad Hosseinzadeh Lotfi ◽  
Mohsen Rostamy-Malkhalifeh
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Supplier Selection ◽  
Group Decision ◽  
Decision Makers ◽  
Uncertain Information ◽  
Vikor Method ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
The Right

Supplier selection, the process of finding the right suppliers who are able to provide the buyer with the right quality products and/or services at the right price, at the right time and in the right quantities, is one of the most critical activities for establishing an effective supply chain, and is typically a multi-criteria group decision problem. In many practical situations, there usually exists incomplete and uncertain information, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended VIKOR method for group decision making with intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision makers and in many of them the weights of criteria are pre-determined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, normalized Hamming distance is proposed to calculate the distance between intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper.

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 Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 281 ◽  
Author(s):  
Dajun Ye ◽  
Decui Liang ◽  
Pei Hu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Rough Sets ◽  
Group Decision ◽  
Intuitionistic Fuzzy Sets ◽  
Fuzzy Decision ◽  
Grey Correlation ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

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