Techniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the α-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the α-level cl...

The generalized fuzzy valued θ-Choquet integrals will be established for the given μ-integrable fuzzy valued functions on a general fuzzy measure space, and the convergence theorems of this kind of fuzzy valued integral are being discussed. Furthermore, the whole of integrals is regarded as a fuzzy valued set function on measurable space, the double-null asymptotic additivity and pseudo-double-...

A new methodology is introduced for designing and tuning the scaling gains of the conventional fuzzy logic controller (FLC) based on its well-tuned linear counterpart. The conventional FLC with a linear rule base is very similar to its linear counterpart. The linear three-term controller has proportional, integral and/or derivative gains. Similarly, the conventional fuzzy three-term controller ...

By using the concepts of fuzzy number fuzzy measures and fuzzy valued functions a theory of fuzzy integrals is investigated. In this paper we have established the fuzzy version of Generalised monotone Convergence theorem and generalised Fatous lemma. 1. Introduction In the preceding paper [2], it is introduced that a concept of fuzzy number fuzzy measures, defined the fuzzy integral of a functi...

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image data compression, mining, knowledge discovery, the analysis of linguistic expressions. As a generalization F-transform, this article, we introduce continuous F-transform its inverse, an integral operator induced by kernel function. Through relation between membership functions kernels, s...

This paper proposes the adaptive fuzzy total sliding-mode control systems with integral (I-AFTSMC) and proportional-integral (PI-AFTSMC) learning algorithms for the unknown nonlinear systems. These AFTSMC systems are comprised of a fuzzy total sliding-mode controller and a robust controller. The fuzzy total sliding-mode controller is utilized to approximate an ideal controller and the robust co...

This paper focusses on the investigation of a pattern recognition method based on the fuzzy integral. Until now this method has used a general fuzzy measure, which is characterized by exponential complexity. Naturally this led to some difficulties in practical applications of this pattern recognition method. In this paper, a heuristic algorithm for the identification of the 2-additive fuzzy mea...