The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

Abstract The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of Pythagorean (CPFS) in which sum q-power real part (imaginary part) support for and against limited by one; however, it difficult to express hesitant information. In this study, conception (Cq-ROHFS) combining Cq-ROFS (HFS) proposed, its properties are discussed, obviously, Cq-ROHFS can reflect uncertainties structure detailed evaluations. Further, some distance measures (DMs) cross-entropy (CEMs) developed based on multiple sets. Moreover, these proposed utilized solve a multi-criteria decision-making problem TOPSIS (technique order preference similarity ideal solution) method. Then, advantages superiority explained experimental results comparisons with existing methods.