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Generalized Fuzzy Information Entropy Measure: A Case Study for the Selection of Diamond Among Various Brands

[ Vol. 12 , Issue. 3 ]

Author(s):

Jain Sarika, Kumar Vijay* and Saxena Arti   Pages 223 - 229 ( 7 )

Abstract:


Background: Diamond is a precious stone and is considered as a safe investment, provided purchased from a trustworthy certified brand. The buyer should be very much cautious in purchasing precious stones and therefore needs decision making skills. The selection of a diamond depends on various factors like shape and 4C’s: Cut, color, clarity, carat weight. Every buyer is not aware of these factors. A customer has no choice to rely on the brand.

Objectives: In this paper, we proposed a model for the selection of diamond among various brands. The model presents a detailed review for the analysis and the design of decision making process. The process can be patented for further application in other domain of research.

Methods: We develop a hypothetical case study based on the information about customers, available jewellery brands and their factors, which affects the purchase of the diamond with assigned degree of membership, non- membership and hesitation index by using one parametric Tsalli’s entropy measure for various values of the parameter (α) under intuitionistic fuzzy environment.

Results: For various values of parameter (α), different decision values have been discussed as explained in Tables (6-13).

Conclusion: From the tables, it is concluded that the customers 1 c and 3 c can purchase a diamond of the brand 2 b , customer 2 c can purchase a diamond of brand 1 b and customer 4 c can purchase a diamond of brand 4 b . The proposed model can be applicable to other decision making problems.

Keywords:

Fuzzy sets, intuitionistic fuzzy sets, fuzzy relations, Tsalli`s entropy, fuzzy information measure, diamond brands.

Affiliation:

Department of Mathematics, Faculty of Engineering and Technology, Manav Rachna International University, Faridabad, Department of Mathematics, Faculty of Engineering and Technology, Manav Rachna International University, Faridabad, Department of Mathematics, Faculty of Engineering and Technology, Manav Rachna International University, Faridabad

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