A New Intuitionistic Fuzzy Entropy of Order- $$\alpha $$ with Applications in Multiple Attribute Decision Making

2017 ◽  
pp. 212-219 ◽  
Author(s):  
Rajesh Joshi ◽  
Satish Kumar
Keyword(s):  
Decision Making ◽  
Multiple Attribute Decision Making ◽  
Fuzzy Entropy ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Intuitionistic Fuzzy Entropy

On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making

2021 ◽  
Vol 40 (1) ◽  
pp. 1191-1217
Author(s):  
Rajkumar Verma
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Fuzzy Entropy ◽  
Information Measures ◽  
Divergence Measures ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Intuitionistic Fuzzy Entropy ◽  
Entropy Measures

The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work develops and studies some parametric information measures under the intuitionistic fuzzy environment. First, the paper reviews the existing intuitionistic fuzzy divergence measures in detail with their shortcomings and then proposes four new order-α divergence measures between two IFSs. It is worth mentioning that the developed divergence measures satisfy several elegant mathematical properties. Second, we define four new entropy measures called order-α intuitionistic fuzzy entropy measures in order to quantify the fuzziness associated with an IFS. We prove basic and advanced properties of the order-α intuitionistic fuzzy entropy measures for justifying their validity. The paper shows that the introduced measures include various existing fuzzy and intuitionistic fuzzy information measures as their special cases. Further, utilizing the conventional multi-attributive border approximation area comparison (MABAC) model, we develop an intuitionistic fuzzy MABAC method to solve real-life multiple attribute group decision-making problems. Finally, the proposed method is demonstrated by using a practical application of personnel selection.

scholarly journals Lexicographic Orders of Intuitionistic Fuzzy Values and Their Relationships

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 166 ◽  
Author(s):  
Feng Feng ◽  
Meiqi Liang ◽  
Hamido Fujita ◽  
Ronald Yager ◽  
Xiaoyan Liu
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Scalar Product ◽  
Multiple Attribute Decision Making ◽  
Benchmark Problem ◽  
Score Functions ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Risk Investment ◽  
Membership Score

Intuitionistic fuzzy multiple attribute decision making deals with the issue of ranking alternatives based on the decision information quantified in terms of intuitionistic fuzzy values. Lexicographic orders can serve as efficient and indispensable tools for comparing intuitionistic fuzzy values. This paper introduces a number of lexicographic orders by means of several measures such as the membership, non-membership, score, accuracy and expectation score functions. Some equivalent characterizations and illustrative examples are provided, from which the relationships among these lexicographic orders are ascertained. We also propose three different compatible properties of preorders with respect to the algebraic sum and scalar product operations of intuitionistic fuzzy values, and apply them to the investigation of compatible properties of various lexicographic orders. In addition, a benchmark problem regarding risk investment is further explored to give a comparative analysis of different lexicographic orders and highlight the practical value of the obtained results for solving real-world decision-making problems.

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.

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