Fuzzy integrals as image lters provide a standard representational form which generalize linear lters such as the averaging lter, morphological lters such as at dilations and erosions, and order statistic lters such as the median lter. However, fuzzy integral lters are computationally intensive. Computing the output value obtained by fuzzy integral ltering at a point involves sorting all the pi...

The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functio...

When a class of fuzzy value functions constitute a metric space, the completeness and separability is an important problem that must be considered to discuss the approximation of fuzzy systems. In this paper, Firstly, a new tK-integral norm is defined by introducing two induced operators, and prove that the class of tK-integrable fuzzy value functions is a metric space. And then, the integral t...

in this paper‎, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

In this paper, multi-dimensional Wiener-Liu process is proposed. Wiener-Liu process is a type of hybrid process, it corresponds to Brownian motion (Wiener process) in stochastic process and Liu process in fuzzy process. In classical analysis, the basic operations are differential and integral. Correspondingly, Ito-Liu formula plays the role of Ito formula in stochastic process and Liu formula i...

Based on similarities between fuzzy set theory and mathematical morphology Grabisch proposed a fuzzy morphology based on the Sugeno fuzzy integral [2]. This paper shows how these ideas can be applied to practical problems. Fast implementable definitions for erosion and dilation based on the fuzzy integral are given, their properties are discussed and some application examples are presented.

The purpose of this paper is to study the fuzzy fractional differentialequations. We prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. Fuzzy derivative is considerin the Goetschel-Voxman sense and fractional derivative is consider in theRiemann Liouville sense. At the end, we...

This paper presents a performance based comparative study of various fuzzy logic controllers (FLCs) to control the speed of squirrel-cage induction motor (SCIM) by replacing the conventional proportional??integral (PI) controller. The fuzzy logic based controller does not require any identification of motor dynamic to control its speed and also assures the disturbance rejection with high robust...