The class of the s-transitive (resp. w-transitive) fuzzy matrices contains properly the class of the max-min transitive fuzzy matrices for which reduction models are already known. It is shown that some basic properties of these models remain valid also for s-transitive (resp. w-transitive)fuzzy matrices.

Abstract In this paper, a stability control approach of flexible joint robot (FJR) based T-S fuzzy model using fuzzy Lyapunov function is proposed. First, the Takagi and Sugeno (T-S) fuzzy model is employed to approximate the flexible joint robot, then a fuzzy controller is developed based on parallel distributed compensation principle (PDC). The non-quadratic stability conditions for the flexi...

This paper is concerned with the issue of stability analysis and controller design for the discrete T-S fuzzy control system with time-delay under imperfect premise matching, in which the discrete T-S fuzzy time-delay model and fuzzy controller do not share the same membership functions. Some novel stability conditions including the information of membership functions of the discrete fuzzy time...

This paper introduces a new approach to topology, based on category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S.~E.~Rodabaugh, $(L,M)$-fuzzy topology of T.~Kubiak and A.~v{S}ostak, and $M$-fuzzy topology on $L$-fuzzy sets of C.~Guido. Moreover, its respe...

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 fuzzy model-based designs for control and synchronization of new chaotic system. The T–S fuzzy models for new chaotic systems are exactly derived. Then the asymptotic stability and synchronization are achieved by generalized backstepping method. On the other hand, this paper presents fuzzy model-based designs for synchronization of another chaotic system. Based on the T–S fu...

In this paper a new linear matrix inequality (LMI) based design method for T-S fuzzy classifier is proposed. The various design factors including structure of fuzzy rule and various parameters should be considered to design T-S fuzzy classifier. To determine these design factors, we describe a new and efficient two-step approach that leads to good results for classification problem. At first, L...

As a natural generalization of a measure space, Butnariu and Klement introduced T-tribes of fuzzy sets with T-measures. They gave a complete characterization of T-measures for a Frank triangular norm T. Here we characterize T-measures with respect to non-Frank strict triangular norms. We show the speciic roles of Frank triangular norms and a newly introduced family, nearly Frank triangular norm...

The purpose o f this paper i s to introduce and study the concepts of intuitionistic fuzzy π generalized s e m i c o n n e c t e d n e s s in intuitionistic fuzzy topological space. Some of their properties are explored.