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.

in this paper a linear fuzzy fredholm integral equation(ffie) with arbitrary fuzzy function input and symmetric triangular (fuzzy interval) output is considered. for each variable, output is the nearest triangular fuzzy number (fuzzy interval) to the exact fuzzy solution of (ffie).

In this paper, circuit implementation of diamond-shaped type-2 membership function in CMOS technology is presented. Designing of mixed analog/digital circuits provides a flexible configuration as well as the highly accurate performance, where analog circuits are employed to realize required functions, while the programmable units implemented using digital circuits. The current-mode approach is ...

Reinforcement Learning (RL) is a widely used learning paradigm for adaptive agents. Because exact RL can only be applied to very simple problems, approximate algorithms are usually necessary in practice. Many algorithms for approximate RL rely on basis-function representations of the value function (or of the Q-function). Designing a good set of basis functions without any prior knowledge of th...

The article provides an α-cut-based method that solves linear fractional programming problems with fuzzy variables and unrestricted parameters. parameters are considered as asymmetric triangular numbers, which is a generalization of the symmetric case. problem solved by using α-cut numbers wherein α- r-cut applied to objective function constraints, respectively. This reduces into equivalent bio...

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...

We extend our earlier results [1; 2; 4] on the issue of weighted aggregations to linguistic importance weighted aggregations when both the importances (interpreted as benchmarks) and the ratings are given by symmetric triangular fuzzy numbers. We show that (unlike the case with finite term sets) small changes in the membership functions of the weights can cause only small variations in the (cri...