During the procedure of fuzzy modeling, we use various methods to update the parameters of membership functions and the shapes of MFs change during the training procedure. So it is obvious that the shape and the distribution of MFs (not a single MF) must implicate some kinds of knowledge of target function (the function to fit) or the problem we try to model. This paper introduced the entropy E...

This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear using techniques from measurement theory. 3.

This paper presents a method to construct more general fuzzy complex numbers and sets from ordinary fuzzy complex numbers by introduced the ordered sequences of membership functions. It is concluded that multifuzzy complex set is an extension of Buckley fuzzy complex set. Also, two types of multi-fuzzy complex numbers based on the forms z x iy = + and z re = θ are investigated. Multi-Fuzzy Comp...

In this paper, we consider fractional Liu process. First, the membership functions, expected values and variances of arithmetic and geometric fractional Liu process are given. Then we suppose that stock price follows geometric fractional Liu process and formulate fractional Liu’s stock model. Based on this model, European option pricing formulas are obtained.

A novel approach to fuzzy modeling based on the tuning of parametric conjunction operations is proposed. First, some novel methods for the construction of parametric generalized conjunction operations simpler than the known parametric classes of conjunctions are considered and discussed. Second, several examples of function approximation by fuzzy models, based on the tuning of the parameters of...