The novel entropy measurements of Z⁺-numbers and their application on multi-attribute decision making problem

Article type: Research Article

Authors: Wu, Min-Chao^a | Mao, Jun-Jun^{b; c; *} | Yao, Ai-Ting^a | Wu, Tao^{b; c}

Affiliations: [a] School of Computer Sciences and Technique, Anhui University, Hefei, China | [b] School of Mathematical Sciences, Anhui University, Hefei, China | [c] Key Laboratory of Intelligent Computing & Signal Processing, Ministry of Education, Anhui University, Hefei, China

Correspondence: [*] Corresponding author. Jun-jun Mao. E-mail: maojunjun@ahu.edu.cn.

Abstract: Z+-numbers, which carry more information than Z-numbers, are studied in this paper. Based on existed models, two more scientific and reasonable probability models of Z+-numbers are developed. In order to utilize Z+-numbers to solve practical problems, the α-cut set of Z+-numbers and corresponding utility function are proposed. Meanwhile, according to the structure of Z+-numbers, the entropy, cross-entropy and comprehensive cross-entropy are introduced to measure the uncertainty and fuzziness of Z+-numbers information. Furthermore, a linear programming model based on proposed three kinds of entropy is designed to obtain the weight vector of criteria in decision-making problems. Finally, we provide an example by selecting an optimal design of electricity vehicles charge station(DEVCS) combined the PROMETHEE method with Z+-numbers, and the feasibility of the proposed method are verified.

Keywords: Z⁺-numbers, entropy, comprehensive cross-entropy, PROMETHEE method, multi-criteria decision-making

DOI: 10.3233/JIFS-190300

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 1, pp. 131-148, 2021