Parameterized utility functions on interval-valued intuitionistic fuzzy numbers with two kinds of entropy and their application in multi-criteria decision making

In this study, the entropy of interval-valued intuitionistic fuzzy numbers (IVIFNs) is analyzed, and two kinds of entropy factors are proposed. By using the normalized score function, normalized Type-1 entropy factor, and normalized Type-2 entropy factor, a series of utility functions on IVIFNs are proposed. In particular, one of the proposed utility functions is structured based on integral. By using the proposed utility functions, IVIFNs can be compared and ranked. The characteristic of these proposed utility functions is that they are objective on comparing IVIFNs from the point of probability. Thereafter, two kinds of fuzzy multi-criteria decision-making methods in interval-valued intuitionistic fuzzy setting are introduced by using the proposed entropy functions. Finally, an example is given to demonstrate the effectiveness of the proposed utility functions and the fuzzy multi-criteria decision-making methods.