(This paper is an extended abstract for an invited talk at 29th Linz Seminar on Fuzzy Set Theory, February 2008.) Höhle has shown that fuzzy sets, valued in a frame (complete Heyting algebra) Ω, can be identified with certain sheaves over Ω: they are the subsheaves of constant sheaves, and more general sheaves can be got as quotients of the fuzzy sets. The technical development is complicated b...

Previously studied fuzzy bipolar conditions of type ”and if possible” are made of a mandatory condition c and an optional condition w. They allow expressing complex preferences of a conjunctive nature. We define in this paper, a new kind of fuzzy bipolar conditions of the form ”or else” which express complex preferences of a disjunctive nature. We show that the ”or else” form can be used as a n...

In this paper, we present a global optimal and stable fuzzy controller design method for both continuousand discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept ap...

This paper presents a method to find kicking range of sepak takraw game when player kicks back the ball to the other team. This research works considered how fuzzy logic can be applied for the sepak takraw game for addressing uncertainty in kicking range of the ball. Six different conditions are described. This research has chosen Tsukamoto’s fuzzy reasoning scheme, because the individual rule ...

The control of nonlinear systems is difficult because no systematic mathematical tools exist to help find necessary and sufficient conditions to guarantee their stability and performance. The problem becomes yet more complex if some of the plant parameters are unknown. By using a Takagi-Sugeno-Kang (TSK) fuzzy plant model [1]-[4], a nonlinear system can be expressed as a weighted sum of some si...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

A‎s we know, developing mathematical models and numerical procedures that would appropriately treat and solve systems of linear equations where some of the system's parameters are proposed as fuzzy numbers is very important in fuzzy set theory. For this reason, many researchers have used various numerical methods to solve fuzzy linear systems. In this paper, we define the concepts of midpoint a...

This paper proposes a new double-private protocol for fuzzy matching and -fuzzy matching. Many works have been done for private database search in which the keyword that a user inputs for the search is concealed to the database owner. In these database searches, the exactly matched data are returned to the user. Fuzzy matching has been proposed in which not exactly matched but nearly matched da...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

By integrating the stabilizability condition, the orthogonal-functions approach (OFA) and the hybrid Taguchi-genetic algorithm (HTGA), an integrative computational method is presented in this paper to design the stable and quadratic-optimal static output feedback parallel-distributed-compensation (PDC) controller such that (i) the TakagiSugeno (TS) fuzzy-model-based control system can be stabil...