scholarly journals Picture fuzzy set-based decision-making approach using Dempster–Shafer theory of evidence and grey relation analysis and its application in COVID-19 medicine selection

2021 ◽  
Author(s):  
Amalendu Si ◽  
Sujit Das ◽  
Samarjit Kar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Grey Relation Analysis ◽  
Dempster Shafer Theory ◽  
Picture Fuzzy Set ◽  
Relation Analysis ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Grey Relation

scholarly journals Evidence Theory in Picture Fuzzy Set Environment

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Harish Garg ◽  
R. Sujatha ◽  
D. Nagarajan ◽  
J. Kavikumar ◽  
Jeonghwan Gwak
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Evidence Theory ◽  
Belief Function ◽  
Uncertain Information ◽  
Interval Probability ◽  
Dempster Shafer Theory ◽  
Effective Manner ◽  
Picture Fuzzy Set ◽  
Shafer Theory

Picture fuzzy set is the most widely used tool to handle the uncertainty with the account of three membership degrees, namely, positive, negative, and neutral such that their sum is bound up to 1. It is the generalization of the existing intuitionistic fuzzy and fuzzy sets. This paper studies the interval probability problems of the picture fuzzy sets and their belief structure. The belief function is a vital tool to represent the uncertain information in a more effective manner. On the other hand, the Dempster–Shafer theory (DST) is used to combine the independent sources of evidence with the low conflict. Keeping the advantages of these, in the present paper, we present the concept of the evidence theory for the picture fuzzy set environment using DST. Under this, we define the concept of interval probability distribution and discuss its properties. Finally, an illustrative example related to the decision-making process is employed to illustrate the application of the presented work.

An extension of case-based decision theory by using Dempster–Shafer theory of evidence

2018 ◽  
Vol 13 (1) ◽  
pp. 179-189 ◽  
Author(s):  
Fei Du ◽  
Feiyan Liu
Keyword(s):  
Decision Making ◽  
Decision Theory ◽  
Future Research ◽  
Traditional Concept ◽  
Content Type ◽  
Dempster Shafer Theory ◽  
Computational Procedures ◽  
Shafer Theory ◽  
Theory Of Evidence ◽  
Case Based

Purpose This study aims to propose a new decision-making method by integrating case-based decision theory and the Dempster–Shafer theory of evidence. Design/methodology/approach The study developed the entire computational procedures for the proposed method and used a numerical example to illustrate its method. Findings The results show that not only the own experiences of the decision-maker but also the opinions of other persons contribute to the selection. Case-based decision theory provides a fundamental technique for the decision-making procedure, and the Dempster–Shafer theory of evidence offers support to deal with the different sources of decision information. Research limitations/implications In case-based decision theory, the utility is a subjective concept, which cannot be measured easily in numbers. Thus, future research should seek a new method to replace the utility. In addition, how to assess the importance of different persons’ experiences and opinions is an important component of this method. Originality/value The contributions of the paper are mainly reflected in three aspects. The first is to expand the traditional concept of “case” of case-based decision theory to multiple sources of cases, which include not only the decision-maker’s own experiences but also other persons’ opinions. The second is to provide a decision-making framework by integrating case-based decision theory and the Dempster–Shafer theory of evidence. The third is to develop the entire computational procedures for the proposed method.

LINGUISTIC AGGREGATION OPERATORS FOR LINGUISTIC DECISION MAKING BASED ON THE DEMPSTER-SHAFER THEORY OF EVIDENCE

2010 ◽  
Vol 18 (03) ◽  
pp. 287-304 ◽  
Author(s):  
J. M. MERIGÓ ◽  
M. CASANOVAS ◽  
L. MARTÍNEZ
Keyword(s):  
Decision Making ◽  
Aggregation Operators ◽  
Weighted Averaging ◽  
New Approach ◽  
Dempster Shafer Theory ◽  
Wide Range ◽  
Different Types ◽  
Linguistic Decision Making ◽  
Shafer Theory ◽  
Theory Of Evidence

In this paper, we develop a new approach for decision making with Dempster-Shafer theory of evidence by using linguistic information. We suggest the use of different types of linguistic aggregation operators in the model. We then obtain as a result, the belief structure — linguistic ordered weighted averaging (BS-LOWA), the BS — linguistic hybrid averaging (BS-LHA) and a wide range of particular cases. Some of their main properties are studied. Finally, we provide an illustrative example that shows the different results obtained by using different types of linguistic aggregation operators in the new approach.

Research on Multi-Attribute Decision Making Using Grey Relation Analysis, Information Axiom and Fuzzy Preferences

2008 ◽  
Vol 44-46 ◽  
pp. 587-594 ◽  
Author(s):  
Xian Fu Cheng
Keyword(s):  
Decision Making ◽  
Information Content ◽  
Data Series ◽  
Grey Relation Analysis ◽  
Fuzzy Preferences ◽  
Information Axiom ◽  
Multi Attribute Decision Making ◽  
Relation Analysis ◽  
Grey Relation ◽  
The Ideal

The grey relation analysis is a kind of quantitative analysis method based on factors compared. The information axiom of axiomatic design provides a mean of evaluation by comparing the information content of several alternatives, based on which a new method for multi-attribute decision making is proposed. First, according to decision matrix of all decision making criteria, the ideal alternative composed of the best reference data series among all alternatives is constructed. Then the information content is used to evaluate the relation grade between an individual alternative and the ideal alternative. The fuzzy preferences are utilized to determine the weight of each criterion. The total information content of every alternative is calculated, and arrayed in order, so the optimal alternative can be selected. For requirements of evaluation, the calculation formula of information content is amended. Finally, an example is given to illustrate the effectiveness and feasibility of the proposed method.

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