the aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. in thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle htimes h, otimesrangle$ in a particularcase.

In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.

Any complete hypergroup H may be represented as the union g g G H A ∈ =  , where G is a group and the subsets Ag of H satisfy certain properties. With any hypergroupoid 〈H, o〉 we may associate a particular fuzzy set μ . In this paper we determine sufficient and necessary conditions for a finite complete hypergroup 〈H, o〉, where p G (Z , ) ≅ + or 2p G (Z , ) ≅ + , p a prime number, such that t...

The notion of bipolar fuzzy set was initiated by Lee (2000) as a generalization of the notion fuzzy sets and intuitionistic fuzzy sets, which have drawn attention of many mathematicians and computer scientists. In this paper, we initiate a study on bipolar ( ,   )-fuzzy sets in -semihypergroups. By using the concept of bipolar ( ,   )-fuzzy sets (Yaqoob and Ansari, 2013), we introduce the ...

Using the notion of bipolar-valued fuzzy sets, the concepts of bipolar fuzzy (weak, s-weak, strong) hyper BCK-ideals are introduced, and their relations are discussed in [3]. Further properties are investigated in this article. We show that if Φ = (H ;μΦ , μ N Φ ) is a bipolar fuzzy (weak, strong) hyper BCK-ideal of a hyper BCK-algebra H, then the set I := {x ∈ H | μΦ(x) = μΦ(0), μΦ (x) = μΦ (0...

1 An approach to fuzzy control of nonlinear systems: Stability and design issues Wang, HO; Tanaka, K; Griffin, MF IEEE TRANSACTIONS ON FUZZY SYSTEMS 1029 STABILITY ANALYSIS AND DESIGN OF FUZZY CONTROL-SYSTEMS TANAKA, K; SUGENO, M FUZZY SETS AND SYSTEMS 1013 Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs Tanaka, K; Ikeda, T; Wang, HO IEEE TRANSACTIONS ON...

We prove that an hypersemigroup H is regular if and only, for any fuzzy subset f of H, we have f f ◦ 1 ◦ f and it is intra-regular if and only if, for any fuzzy subset f of H, we have f 1 ◦ f ◦ f ◦ 1. An hypersemigroup H is left (resp. right) quasi-regular if and only if, for any fuzzy subset f of S we have f 1 ◦ f ◦ 1 ◦ f (resp. f f ◦ 1 ◦ f ◦ 1) and it is semisimple if and only if, for any fuz...

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...

This paper proposes the control design of a nonlinear polynomial fuzzy system with ∞ H performance objective using a sum of squares (SOS) approach. Fuzzy model and controller are represented by a polynomial fuzzy model and controller. The design condition is obtained by using polynomial Lyapunov functions that not only guarantee stability but also satisfy the ∞ H performance objective. The desi...

This paper presents a fuzzy tracking control design based on H∞ performance for nonlinear systems. The Takagi-Sugeno fuzzy model is employed to approximate a nonlinear system. Based on the H∞ tracking performance, the nonlinear system output is controlled to track a reference signal, and at the same time the tracking performance is attenuated to a prescribed level. Linear matrix inequalities (L...