This article introduces the fuzzy relation. This is the expansion of usual relation, and the value is given at the fuzzy value. At rst, the deenition of the fuzzy relation characterized by membership function is described. Next, the deenitions of the zero relation and universe relation and basic operations of these relations are shown. In this paper C 1 , C 2 are non empty sets. Let us consider...

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...

A sum of real numbers equals the mutual entropy of a fuzzy set and its complement set. A " fuzzy " or multivalued set is a point in a unit hypercube. Fuzzy mutual (Kullback) entropy arises from the logarithm of a unique measure of fuzziness. The proof uses the logistic map, a diffeomorphism that maps extended real space onto the fuzzy cube embedded in it. The logistic map equates the sum of a v...

Abstract. Combining both kinds of fuzzy logic forms including fuzzy T-S model and adaptive fuzzy logic systems, this paper presents an observer-based ∞ H control scheme for a class of uncertain nonlinear timedelay systems. Firstly, the fuzzy T-S model is used to approximate the nonlinear systems, and an observer is designed to observe the system states, and the fuzzy control law of the fuzzy mo...

A. George and P. Veeramani, 1994. On some results in fuzzy metric space, Fuzzy Sets and Systems, vol. 64, 395-399. B. Schweizer, H. Sherwood, and R. M. Tardi®,1988. Contractions on PMspace examples and counter examples, Stochastica vol. 1, 5–17. D. Mihet, 2004. A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, vol. 144, 431–439. D. Mihet, 2008. Fuzzy -contractive mapp...

‎‎In this paper‎, ‎we define fuzzy subnexuses over a nexus $N$‎. ‎Define and study the notions of the prime fuzzy subnexuses and the fractions‎‎induced by them‎. ‎Finally‎, ‎we show that if S is a meet‎‎closed subset of the set Fsub(N), ‎of fuzzy subnexuses of a nexus N‎, ‎and‎‎h= ⋀S ϵ S, ‎then the fractions S^-1 N and h^-1 N are isomorphic as meet-semilattices‎.

This paper is concerned with H sampled-data control for uncertain fuzzy systems. A new approach to sampled-data control is introduced. The system is modelled as a continuous-time fuzzy system, while in practice, the control input has a piecewise-continuous delay. Sufficient conditions for the closed-loop system with a sampled-data state feedback controller to achieve a prescribed H disturbance ...

We introduce the category IVRel(H) consisting of interval-valued H-fuzzy relational spaces and relation preserving mappings between them and we study structures of the category IVRel(H) in the viewpoint of the topological universe introduced by Nel. Thus we show that IVRel(H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IVRel(H) is C...

Given a nonempty set X, a fuzzy ideal I on X is a collection of subsets of X closed under finite union and subset operations. In this paper we define a space to be locally I fuzzy compact space if every point in the space has an I fuzzy compact neighbourhood. Basic results concerning locally I fuzzy compact spaces are given relating to subspaces, preservation of functions, and products. Classic...