A Novel Method for Fuzzy Multi-Criteria Decision Making

2014 ◽  
Vol 13 (03) ◽  
pp. 497-519 ◽  
Author(s):  
Meimei Xia ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Weight Vector ◽  
Decision Makers ◽  
Decision Matrix ◽  
Novel Method ◽  
The Individual ◽  
Ideal Group ◽  
The Ideal

To determine the weight vector and to aggregate the individual opinions are necessary steps in the classical methods for multi-criteria group decision-making problems in which the weight vectors of the decision makers and the criteria are incompletely known. In this paper, we propose a simple but efficient approach which can avoid these steps by establishing some optimal models. To get the optimal group decision matrix, we first propose two kinds of models among which the former focuses on minimizing the deviations between individual decision matrix and the ideal group one, while the latter aims at minimizing the deviations between the estimated group opinion and the ideal group one. To get the overall performances of alternatives, another two types of models are further established, one of which is to minimize the distance between the evaluation value under each criterion and the ideal overall value for each alternative, and the other is to minimize the distance between the estimated overall value and the ideal overall one. The proposed models can be used to deal with group decision-making under intuitionistic fuzzy, interval-valued fuzzy or other fuzzy environments, and can also provide the decision makers more choices by containing the parameter which can be assigned different values according to different actual situations. Several examples illustrate the practicability of the proposed methods.

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.

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.

Reducing the Risk of Wrong Choice in Group Decision Making by Optimal Weight Allocating to Decision Makers

2018 ◽  
Vol 7 (2) ◽  
pp. 1-23 ◽  
Author(s):  
Mohammad Azadfallah
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Potential Risk ◽  
Group Decision ◽  
Decision Makers ◽  
Topsis Method ◽  
Numerical Examples ◽  
Multiple Attribute ◽  
Key Issues ◽  
The Ideal

How to determine a weight for decision makers (DMs) is one of the key issues in Multiple Attribute Group Decision Making (MAGDM). While, some experts (or DMs) clearly wiser and more powerful in such matters than others, it has often seen that experts play their roles with same weights of importance. Meanwhile, it will lead to the wrong choice (or decision risk) and loss of values. Since, in the absence of any other standards about how to reduce this potential risk for bias, in this article, based on judgment matrices and error analysis, the author presents two new algorithm taken from crisp (the correlation-based approach) and interval (the ideal-based approach) TOPSIS method, respectively. Finally, two numerical examples are given to demonstrate the feasibility of the developed method.

scholarly journals AHP-Group Decision Making Based on Consistency

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 242 ◽  
Author(s):  
Juan Aguarón ◽  
María Teresa Escobar ◽  
José Moreno-Jiménez ◽  
Alberto Turón
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Decision Makers ◽  
Local Context ◽  
Consensus Matrix ◽  
Stability Intervals ◽  
The Individual ◽  
Individual Consistency

The Precise consistency consensus matrix (PCCM) is a consensus matrix for AHP-group decision making in which the value of each entry belongs, simultaneously, to all the individual consistency stability intervals. This new consensus matrix has shown significantly better behaviour with regards to consistency than other group consensus matrices, but it is slightly worse in terms of compatibility, understood as the discrepancy between the individual positions and the collective position that synthesises them. This paper includes an iterative algorithm for improving the compatibility of the PCCM. The sequence followed to modify the judgments of the PCCM is given by the entries that most contribute to the overall compatibility of the group. The procedure is illustrated by means of its application to a real-life situation (a local context) with three decision makers and four alternatives. The paper also offers, for the first time in the scientific literature, a detailed explanation of the process followed to solve the optimisation problem proposed for the consideration of different weights for the decision makers in the calculation of the PCCM.

scholarly journals RISKY MULTI-CRITERIA GROUP DECISION MAKING ON GREEN CAPACITY INVESTMENT PROJECTS BASED ON SUPPLY CHAIN

2017 ◽  
Vol 18 (3) ◽  
pp. 355-372 ◽  
Author(s):  
Yan SONG ◽  
Shuang YAO ◽  
Donghua YU ◽  
Yan SHEN
Keyword(s):  
Decision Making ◽  
Supply Chain ◽  
Group Decision Making ◽  
Group Decision ◽  
Cloud Model ◽  
Decision Makers ◽  
Capacity Investment ◽  
Decision Matrix ◽  
Investment Projects ◽  
Green Capacity

Green capacity investment projects have rapidly emerged involving suppliers, customers, and manufacturing organizations in supply chain systems with environmental challenges. This paper focuses on and identifies both primary strategic and operational elements that will aid managers in evaluating and making risky multi-criteria decisions on green capacity investment projects. We propose a cloud prospect value consensus process consisting of feedback and adjustment mechanisms that provide modification instructions to the corresponding decision makers for a decision matrix based on the cloud model and prospect theory, which considers psychological behavior, disagreements between decision makers, and the ambiguity of linguistic variable assessment across multi-criteria risks. The new model increases the efficiency and accuracy of decision making. To verify the feasibility and validity of the Cloud Prospect Value Consensus Degree based on the Feedback adjustment mechanism, its performance is compared with three state-of-the-art multi-criteria group decision-making methods.

A Novel Method to Assign Weights to Decision Makers for each Criterion in Group Decision Making Under Multiple Criteria with Crisp and Interval Data

2018 ◽  
Vol 5 (2) ◽  
pp. 15-46 ◽  
Author(s):  
Mohammad Azadfallah
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Interval Data ◽  
Decision Makers ◽  
Ideal Solution ◽  
Optimal Weights ◽  
Novel Method ◽  
Negative Ideal Solution ◽  
Individual Group Member

This article focuses on determining the weights of decision makers (DMs) in multi-criteria group decision making (MCGDM) environments with both crisp and interval data, in which the weights of DMs are derived from the decision matrices and DMs, have different weights for different criteria. In order to determine the optimal weights of DMs for each criterion, a new TOPSIS-based approach is introduced. In the proposed method, the DMs weight for each criterion is depends on the distances from each individual group member decision to the positive and negative ideal solution. In other words, the DM has a large weight if his/ her decision information is close (far) to the positive (negative) ideal solution, and has a small weight if his/ her decision information is far (close) from the positive (negative) ideal solution. Finally, a numerical example is given to demonstrate the feasibility of the developed methods.

Doubly Extended Fuzzy TOPSIS Method for Group Decision Making

2019 ◽  
Vol 66 (1) ◽  
pp. 27-50
Author(s):  
Dariusz Kacprzak
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Group Decision ◽  
Real Life ◽  
Fuzzy Topsis ◽  
Decision Makers ◽  
Final Decision ◽  
Topsis Method ◽  
Decision Matrix

Multiple Criteria Decision Making methods, such as TOPSIS, have become very popular in recent years and are frequently applied to solve many real-life situations. However, the increasing complexity of the decision problems analysed makes it less feasible to consider all the relevant aspects of the problems by a single decision maker. As a result, many real-life problems are discussed by a group of decision makers. In such a group each decision maker can specialize in a different field and has his/her own unique characteristics, such as knowledge, skills, experience, personality, etc. This implies that each decision maker should have a different degree of influence on the final decision, i.e., the weights of decision makers should be different. The aim of this paper is to extend the fuzzy TOPSIS method to group decision making. The proposed approach uses TOPSIS twice. The first time it is used to determine the weights of decision makers which are then used to calculate the aggregated decision matrix for all the group decision matrices provided by the decision makers. Based on this aggregated matrix, the extended TOPSIS is used again, to rank the alternatives and to select the best one. A numerical example illustrates the proposed approach.

Research on the IAMM and IGMM Operators in Group Decision Making with Intuitionistic Preference Relations

2013 ◽  
Vol 753-755 ◽  
pp. 2806-2815
Author(s):  
Jun Ling Zhang ◽  
Jian Wu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Geometric Mean ◽  
Arithmetic Mean ◽  
Decision Makers ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
The Individual

Preference relations are the most common techniques to express decision makers preference information over alternatives or criteria. This paper focus on investigating effective operators for multiple attribute group decision making with intuitionistic fuzzy preference relations. Firstly, we extend arithmetic mean method operator and geometric mean method operator for accommodating intuitionistic fuzzy information to present the intuitionistic arithmetic mean method (IAMM) operator and the intuitionistic geometric mean method (IGMM) operator. Then the compatibility properties of intuitionistic preference relations obtained by IAMM and IGMM are analyzed, we found that aggregation of individual judgments and aggregation of individual priorities provide the same priorities of alternatives, and that if all the individual decision makers have acceptable consensus degree, then the collective preference relations obtained also are of acceptable consensus degree. Finally, the results are verified by an illustrative example carried out in the background of parts supplier selection.

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.

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.

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