This  paper extends the notion of fuzzy $BCK$-subalgebras to fuzzy hyper $BCK$-subalgebras and defines an extended fuzzy $BCK$-subalgebras. This study  considers  a type of fuzzy hyper  $BCK$-ideals  in this  hyperstructure  and  describes   the  relationship  between hyper  $BCK$-ideals and  fuzzy hyper  $BCK$-ideals.  In fact, it tries to introduce   a  strongly  regular  relation  on hyper $...

In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, co-weak isomorphism, equivalence relation, fuzzy relation, weak isomorphism.

Systems of fuzzy relation equations are considered as models of fuzzy inference systems. A proper use of an inference mechanism connected to a fuzzy relation modelling a fuzzy rule base is certified by keeping the fundamental interpolation condition. The paper aims at new solutions of systems of fuzzy relation equations and introduces new solvability criteria.

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

In 1965, Zadeh [30] introduced a concept of a fuzzy set as the generalization of a crisp set. Also, in 1971, he introduced a fuzzy relation naturally, as a generalization of a crisp relation in [31]. Nel [27] introduced the notion of a topological universe which implies concrete quasitopos [1]. Every topological universe satisfies all the properties of a topos except one condition on the subobj...

The design of a static output feedback fuzzy controller for nonlinear systems based on Takagi–Sugeno (T–S) fuzzy models is addressed. To avoid complex mathematical derivations and conservative results, a genetic algorithm (GA) is integrated with a linear matrix inequality (LMI) optimisation to seek the static output feedback gains that satisfy the Lyapunov stability inequalities with a decay ra...

This paper is concerned with stabilization problem of continuous-time Takagi-Sugeno fuzzy systems. To do this, the stabilization problem is investigated based on the new fuzzy Lyapunov functions (NFLFs). The NFLFs depend on not only the fuzzy weighting functions but also their first-time derivatives. The stabilization conditions are derived in terms of linear matrix inequalities (LMIs) which ca...

This paper examines the problem of designing robust H∞ controllers for for HIV/AIDS infection system with dual drug dosages described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H∞ controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for the s...