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 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.