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

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

Volume: 12 Issue: 3

Author(s): Jain Sarika, Kumar Vijay*Saxena Arti

Affiliation:

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

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

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.

Cite this article as:

Sarika Jain , Vijay Kumar *, Arti Saxena , Generalized Fuzzy Information Entropy Measure: A Case Study for the Selection of Diamond Among Various Brands, Recent Patents on Engineering 2018; 12 (3) . https://dx.doi.org/10.2174/1872212112666180301143158