The Novel Entropy Measurements Of Z(+)-Numbers And Their Application On Multi-Attribute Decision Making Problem

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 a-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.