Time-sequential hesitant fuzzy entropy, cross-entropy and correlation coefficient and their application to decision making

In decision making problems, the hesitance of the decision maker to the same decision object is reflected not only in the length of multiple possible memberships under, but also in the time dimension. The newly proposed time-sequential hesitant fuzzy set (TSHFS) can show the hesitance in decision making information from the view of time dimension, and in which the concept of hesitance of hesitant fuzzy sets is improved from a constructive perspective. However, it is difficult to further explore the application prospects of TSHFS in decision making as the current measurement methods, such as entropy, cross-entropy, and correlation coefficient, could not be leveraged directly in the TSHFS environment. For that entropy, cross-entropy, and correlation coefficient are important metric components of fuzzy sets and in related scenarios, we propose corresponding methods for TSHFS in this work. Meanwhile, to make full use of the importance of attribute information in the decision matrix and make the decision results have better discrimination ability, hesitant fuzzy diffusion decision model is proposed. The proposed entropy measures are constructed on trigonometric functions, the new cross-entropy measure and correlation coefficients are derived from classical counterparts, which enrich ways to deal with problems under the TSHFS environment, especially referring to decision making. In hesitant fuzzy diffusion decision model, the prior ordered value is defined as the final decision result to measure relationships among alternatives. The effectiveness and advantages of proposed entropy measures, cross-entropy measure, correlation coefficients, and the proposed decision model are demonstrated through the application of decision making.