Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Abstract

Entropy has continuously arisen as one of the pivotal issues in optimization, mainly in portfolios, as an indicator of risk measurement. Aiming to simplify operations and extending applications of entropy in the field of LR fuzzy interval theory, this paper first proposes calculation formulas for the entropy of function via the inverse credibility distribution to directly calculate the entropy of linear function or simple nonlinear function of LR fuzzy intervals. Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. Compared to the existing simulation algorithms, the numerical results show that the advantage of the algorithms is well displayed in terms of stability, accuracy, and speed. On the whole, the simplified calculation formulas and the effective simulation algorithms proposed in this paper provide a powerful tool for the LR fuzzy interval theory, especially in entropy optimization.

On Fuzzy Simulations for Expected Values of Functions of Fuzzy Numbers and Intervals

“…It is clear that the regular fuzzy intervals are also of great importance no matter in theoretical developments like its variance research in [24] and the entropy calculation and simulation in [25], or in practical applications like the portfolio optimization in [26]. One of the representative form of regular fuzzy interval is the commonly used trapezoidal fuzzy number.…”

Generalized Belief Entropy and Its Application in Identifying Conflict Evidence

“…In data fusion, when evidence is highly conflicting [3], [7]- [9], [18], [19], [64], it often leads to counter-intuitive results. So some scholars have proposed some methods to solve this problem [65]- [75], which are mainly divided into two aspects: modifying Dempster's rule of combination and evidence [16], [17], [23], [25], [26], [76], [77].…”