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...

It is well know that when these concepts arose in PhD disertation of Sugeno in 1974 [1], a lot of works has been done as much in the theoretical branch as in the applied. As we know, the classical measure and the corresponding integral are based on the additivity property, but this property is uncommun in the applied context and could be too restrictive for the appliance. For instance, measurem...

Recently, Flores-Franulič et al. [A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 208 (2008) 55-59] proved the Stolarsky’s inequality for the Sugeno integral on the special class of continuous and strictly monotone functions. This result can be generalized to a general class of fuzzy convex functions in this paper. We also give a fuzzy integral inequal...

In this paper, we introduce the concept of fuzzy star-operations on an integral domain and show that the set of all fuzzy star-operations on the integral domain forms a complete lattice. We also characterize Pr3 ufer domains, psuedo-Dedekind domains, (generalized-) greatest common divisor domains, and other integral domains in terms of the invertibility of certain fractionary fuzzy ideals. c © ...

The problem of the integral evaluations of the state and control vectors in continuous multi-input-multi-output fuzzy control systems is investigated. The fuzzy controller is assumed to be nonlinearity in a bounded sector and the controlled plant a linear system described by the differential or integral equations. The stability problem is investigated and the problem of how to use the integral ...

This paper presents a novel method for combining multiple compensatory neural fuzzy networks (CNFN) using fuzzy integral. The fusion of multiple classifiers can overcome the limitations of a single classifier since the classifiers complement each other. A fuzzy integral is a better combination scheme than majority voting method that uses the subjectively defined relevance of classifiers. A comb...

Keywords: Fuzzy measure Sugeno integral Choquet integral Stolarsky's inequality a b s t r a c t Recently Flores-Franulič, Román-Flores and Chalco-Cano proved the Stolarsky type inequality for Sugeno integral with respect to the Lebesgue measure k. The present paper is devoted to generalize this result by relaxing some of its requirements. Moreover, Stolar-sky inequality for Choquet integral is ...

The systems represented by the Choquet or the multi-linear fuzzy integral with respect to fuzzy measure is equivalently decomposable into hierarchically sub-systems through the use of Inclusion-Exclusion Covering (IEC) (Theorem 4.1,4.2) . Hence, IEC is one of very useful concepts/indexes for structural analysis of the fuzzy integral systems (short for: the systems represented by the Choquet or ...