A new definition and formula of entropy for intuitionistic fuzzy sets

Article type: Research Article

Authors: Zhu, Yong-Jun^{a; b} | Li, Deng-Feng^{a; *}

Affiliations: [a] School of Ecomonics and Management, Fuzhou University, Fuzhou, Fujian, China | [b] College of Information Technology, Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China

Correspondence: [*] Corresponding author. Deng-Feng Li, School of Economics and Management, Fuzhou University, No. 2, Xueyuan Road, Daxue New District, Fuzhou District, Fuzhou, Fujian 350108, China. Tel./Fax: +86 0591 83768427; E-mail: lidengfeng@fzu.edu.cn.

Abstract: The entropy of an intuitionistic fuzzy set (IFS) is a measure of uncertainty related to the IFS. The purpose of this paper is to develop a new axiomatical entropy for an IFS. The axioms for a new entropy of an IFS are defined and a mathematical expression/formula of the new entropy of the IFS is given. The newly defined entropy concerns both the amount of information and reliability of the IFS. It is proven that the new entropy has some remarkable and useful properties. The examples and comparison analysis show the validity and applicability of the new entropy proposed in this paper.

Keywords: Intuitionistic fuzzy set, entropy, information, reliability, uncertainty

DOI: 10.3233/IFS-152031

Journal: Journal of Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3057-3066, 2016