A score function based on relative entropy and its application in intuitionistic normal fuzzy multiple criteria decision making

Article type: Research Article

Authors: Wang, Jian-qiang | Li, Kang-jian | Zhang, Hong-yu | Chen, Xiao-hong

Affiliations: Business School, Central South University, Changsha, China

Note: [] Corresponding author. Jian-qiang Wang, Business School, Central South University, Changsha, 410083, China. Tel.: +86 731 88830594; Fax: +86 731 88710006; E-mail: jqwang@csu.edu.cn

Abstract: In this paper, after analyzing on shortcomings of the existing score functions of intuitionistic fuzzy set (IFS), a new score function based on relative entropy is presented. The risk attitudes of the decision makers are also defined. Examples have been given to show the validity of this score function. Meanwhile, the definition of the intuitionistic normal fuzzy number and their operational laws and intuitionistic normal fuzzy weighted arithmetic averaging operator are proposed. As for the intuitionistic normal fuzzy multi-criteria decision-making problems in which criteria weights remain fixed and the criteria values of alternatives are in the form of intuitionistic normal fuzzy numbers. An intuitionistic normal fuzzy multi-criteria decision-making approach based on the relative score function is proposed. Finally, an example is provided to show the feasibility and validity of the approach.

Keywords: Intuitionistic fuzzy multi-criteria decision-making, intuitionistic normal fuzzy numbers, relative entropy, score function

DOI: 10.3233/IFS-120662

Journal: Journal of Intelligent & Fuzzy Systems, vol. 25, no. 3, pp. 567-576, 2013