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...

In this paper, we study the finitely many constraints of the fuzzyrelation inequality problem and optimize the linear objectivefunction on the region defined by the fuzzy max-product operator.Simplification operations have been given to accelerate theresolution of the problem by removing the components having noeffect on the solution process. Also, an algorithm and somenumerical and applied exa...

The purpose of this paper is to introduce and study a new class of generalized vector variational-like inequalities and generalized vector variational inequalities in fuzzy environment. By using the KKM-technique, Maximal Element Lemma and under suitable conditions, some existence theorems of solutions for these two kinds of vector variational inequalities in fuzzy environment are proved. The r...

Abstract -In this paper, the problem of H∞ filtering design is studied for nonlinear sampled-data systems using the Takagi-Sugeno (T-S) fuzzy model approach. Traditionally, the sufficient conditions for the existence of such H∞ filter are characterized in terms of the solution of a differential Hamilton-Jacobi inequality with jumps, which is equivalent to solving the partial differential inequa...

*Correspondence: [email protected] 1Department of Applied Mathematics, School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, China Full list of author information is available at the end of the article Abstract This study aims to explore modular inequalities of interval-valued fuzzy soft sets characterized by Jun’s soft J-inclusions. Using soft product operations...

This paper presents a robust ∞ H fuzzy controller for a class of T-S time-delay discrete fuzzy bilinear system (DFBS). Firstly, a discrete robust ∞ H fuzzy controller is proposed to stabilize the T-S time-delay DFBS with disturbance. Secondly, based on the Schur complement and some variable transformation, the stability conditions of the overall fuzzy control system are formulated by linear mat...

This paper presents a sequence of fuzzy mean difference divergence measures. The validity of these fuzzy mean difference divergence measures is proved axiomatically. In addition, it introduces a sequence of inequalities among some of these fuzzy mean difference divergence measures. The applications of proposed fuzzy mean difference divergence measures in the context of pattern recognition have ...

In this paper, the finitely many constraints of a fuzzy relationinequalities problem are studied and the linear objective function on the regiondefined by a fuzzy max-average operator is optimized. A new simplificationtechnique which accelerates the resolution of the problem by removing thecomponents having no effect on the solution process is given together with analgorithm and a numerical exa...

In this paper, we first use a fuzzy preference relation with a membership function representing preference degree forcomparing two interval-valued fuzzy numbers and then utilize a relative preference relation improved from the fuzzypreference relation to rank a set of interval-valued fuzzy numbers. Since the fuzzy preference relation is a total orderingrelation that satisfies reciprocal and tra...