Method for Fuzzy Multi-Attribute Decision-Making with Fuzzy Reciprocal Preference Relation on Alternatives under Partical Weight Information

2011 ◽  
Vol 58-60 ◽  
pp. 869-874
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Preference Relation ◽  
Triangular Fuzzy Numbers ◽  
Attribute Weights ◽  
Translation Function ◽  
Goal Programming Model ◽  
Subjective Preference ◽  
Multi Attribute Decision Making

The fuzzy multi-attribute decision-making (FMADM) problems, in which the information about attribute weights is partly known, the attribute values take the form of triangular fuzzy numbers, and the decision maker (DM) has fuzzy reciprocal preference relation on alternatives, are investigated. Firstly, some concepts, such as the multiply between two triangular fuzzy numbers, the projection of triangular fuzzy numbers vectors, etc, are given. Secondly, in order to reflect to the DM’s subjective preference information on alternatives, we make the objective decision information uniform by using a translation function and establish a goal programming model, and then the attribute weights is obtained by solving the model, thus the weighted attribute values of all alternatives are gained. The concept of fuzzy positive ideal solution (FPIS) of alternatives is introduced, and the alternatives are ranked by using the projection of the weighted attribute values of every alternative on FPIS. The method not only can sufficiently utilize the objective information and meet the DM’s subjective preferences on alternatives as much as possible, but also it is characterized by simple operation and easy to implement on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

A Method for Multi-Attribute Decision-Making with Complementary Preference Information on Alternatives

2013 ◽  
Vol 658 ◽  
pp. 541-545
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Goal Programming ◽  
Programming Model ◽  
Preference Relation ◽  
Weighting Method ◽  
Preference Information ◽  
Attribute Weights ◽  
Translation Function ◽  
Goal Programming Model ◽  
Multi Attribute Decision Making

The multi-attribute decision making (MADM) problem, in which the information about attribute weights are known partly and the decision maker (DM) has fuzzy complementary preference relation on alternatives, is investigated in this paper. Firstly, The objective decision-making information based on the subjective fuzzy complementary preference information on alternatives is uniformed by using a translation function. Secondly, a goal programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Based on these values, the ranking priorities or selecting the best on alternatives are processed. The method can sufficiently utilize the objective information of alternatives and meet the subjective requirements of the DM as much as possible, and it is also characterized by simple operation and easy to implement on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

Method Based on the Minimum Deviation for Multi-Attribute Decision-Making and its Application

2014 ◽  
Vol 989-994 ◽  
pp. 2547-2550
Author(s):  
Hong An Zhou
Keyword(s):  
Decision Making ◽  
Quadratic Programming ◽  
Programming Model ◽  
Existence Of Solution ◽  
Weighting Method ◽  
Preference Information ◽  
Minimum Deviation ◽  
Attribute Weights ◽  
Subjective Preference ◽  
Multi Attribute Decision Making

The multi-attribute decision making (MADM) problem is studied, in which the information about attribute weights is unknown and the decision maker (DM) has avail preference information on alternatives. Firstly, a quadratic programming model based on the minimum deviation between the objective decision-making information and the subjective preference information on alternatives is established. Secondly, the existence of solution to the model is proved and the calculated formula of the attribute weights are given, thus the overall values of the alternatives are gained by using the additive weighting method. Based on these values, the selecting the best on alternatives is processed. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.

A Multi-Attribute Group Decision-Making Method Based on Linguistic Intuitionistic Fuzzy Numbers and Dempster–Shafer Evidence Theory

2020 ◽  
Vol 19 (02) ◽  
pp. 499-524 ◽  
Author(s):  
Peide Liu ◽  
Xiaoxiao Liu ◽  
Guiying Ma ◽  
Zhaolong Liang ◽  
Changhai Wang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Programming Model ◽  
Comprehensive Evaluation ◽  
Evidence Theory ◽  
Intuitionistic Fuzzy Numbers ◽  
Attribute Weights ◽  
Intuitionistic Fuzzy

In this paper, we propose a multi-attribute group decision-making (MAGDM) method based on Dempster–Shafer Evidence Theory (DST) and linguistic intuitionistic fuzzy numbers (LIFNs), in which both the expert weights and attribute weights are unknown. Firstly, we represent LIFNs as basic probability assignments (BPAs) by DST based on linguistic scale function (LSF), and a linear programming model is proposed to combine the objective weights and subjective weights of attributes to obtain the combined weights. At the same time, the experts’ weights are obtained through Jousselme distance. Secondly, we use the weights to correct the evidence, and the comprehensive evaluation value of each alternative is calculated by the combination rule of evidence. Further, a new MAGDM approach with DST and LIFNs is presented. Finally, we give an example to explain the proposed method and compare it with other methods to show the feasibility and superiority.

scholarly journals A New Multi-Attribute Decision-Making Framework for Policy-Makers by Using Interval-Valued Triangular Fuzzy Numbers

Informatica ◽  
2021 ◽  
pp. 1-36
Author(s):  
Ayoub Mohammadian ◽  
Jalil Heidary Dahooie ◽  
Ali Reza Qorbani ◽  
Edmundas Kazimieras Zavadskas ◽  
Zenonas Turskis
Keyword(s):  
Decision Making ◽  
Fuzzy Numbers ◽  
Triangular Fuzzy Numbers ◽  
Policy Makers ◽  
Multi Attribute Decision Making ◽  
Decision Making Framework ◽  
Interval Valued

MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON POSSIBILITY VARIANCE COEFFICIENT OF TRIANGULAR INTUITIONISTIC FUZZY NUMBERS

2013 ◽  
Vol 21 (02) ◽  
pp. 223-243 ◽  
Author(s):  
SHU-PING WAN
Keyword(s):  
Decision Making ◽  
Mathematical Programming ◽  
Fuzzy Numbers ◽  
Programming Model ◽  
Optimal Solution ◽  
Programming Models ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Multi Attribute Decision Making ◽  
Ranking Order

Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.

scholarly journals A Heterogeneous Multiattribute Group Decision-Making Method Based on Intuitionistic Triangular Fuzzy Information

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Jun Xu ◽  
Jiu-Ying Dong ◽  
Shu-Ping Wan ◽  
De-Yan Yang ◽  
Yi-Feng Zeng
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Entropy Method ◽  
Triangular Fuzzy Numbers ◽  
Decision Matrix ◽  
Interval Numbers ◽  
Attribute Weights ◽  
Relative Closeness

How to aggregate decision information in heterogeneous multiattribute group decision making (HMAGDM) is vital. The aim of this paper is to develop an approach to aggregating decision data into intuitionistic triangular fuzzy numbers (ITFNs) for heterogeneous MAGDM problems with real numbers (RNs), interval numbers (INs), triangular fuzzy numbers (TFNs), trapezoidal fuzzy numbers (TrFNs), and triangular intuitionistic fuzzy number (TIFNs). Using the relative closeness of technique for order preference by similarity to ideal solution (TOPSIS) and geometry entropy method, we first present a general approach to aggregating heterogeneous information into ITFNs, which takes the group consistency of experts into account. Based on the collective intuitionistic triangular fuzzy decision matrix and extended TOPSIS, a multiple objective mathematical program is constructed to determine the optimal attribute weights. Subsequently, a new method to solve HMAGDM problems is presented based on the aforementioned discussion. A trustworthy service selection example is provided to verify the practicality and effectiveness of the proposed method.

Uncertain Linguistic Multi-Attribute Group Decision Making Method with Multi-Granularity Based on Projection and Dominance Degree

2014 ◽  
Vol 722 ◽  
pp. 386-389
Author(s):  
Er Dong Han ◽  
Peng Guo
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Weight Vector ◽  
Attribute Weights ◽  
Multiple Attribute ◽  
Goal Programming Model ◽  
Set Up ◽  
Linguistic Assessment

In order to solve multiple attribute group decision making problems with multi-granularity uncertain linguistic assessment information, where the information of attribute weights are incomplete, a group decision making method based on projection and dominance degree is proposed. Firstly, the uncertain linguistic evaluation matrices with multi-granularity are transformed to two-tuple decision matrices according to the continuous interval two-tuple ordered weighted harmonic (ITC-OWH) operator. By using projection method, a goal programming model is set up to determine the attribute weights vector of individual decision maker. Then, integrative attribute dominance degree between pairwise comparisons of arbitrary alternatives are computed, a group integrative dominance degree matrix is obtained based on integrative dominance degree matrices and expert weight vector. The priority-time matrix is given to calculate the general priority time of alternatives, consequently, the rank result of alternatives can be determined.

scholarly journals AN EXTENSION OF THE RATIO SYSTEM APPROACH OF MOORA METHOD FOR GROUP DECISION-MAKING BASED ON INTERVAL-VALUED TRIANGULAR FUZZY NUMBERS

2015 ◽  
Vol 22 (1) ◽  
pp. 122-141 ◽  
Author(s):  
Dragisa STANUJKIC
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
System Approach ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Performance Ratings ◽  
Triangular Fuzzy Numbers ◽  
Moora Method ◽  
Interval Valued

Decision-making in fuzzy environment is often a very complex, especially when related to predictions and assessments. The Ratio system approach of the MOORA method and Intervalvalued fuzzy numbers have already proved themselves as the effective tools for solving complex decision-making problems. Therefore, in this paper an extension of the Ratio system approach of the MOORA method, which allows a group decision-making as well as the use of interval-valued triangular fuzzy numbers, is proposed. Interval-fuzzy numbers are rather complex, and therefore, they are not practical for direct assigning performance ratings. For this reason, in this paper it has also been suggested the approach which allows the expression of individual performance ratings using crisp, interval or fuzzy numbers, and their further transformation into the group performance ratings, expressed in the form of interval-valued triangular fuzzy numbers, which provide greater flexibility and reality compared to the use of linguistic variables. Finally, in this paper the weighted averaging operator was proposed for defuzzification of interval-valued triangular fuzzy numbers.

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