Takagi–Sugeno (TS) fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear inputoutput submodels. In this paper, the TS fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation. The TS fuzzy representation of a nonlinear...

Implicit modelling is a powerful technique to design geometric shapes, where a geometric object is described by a real function. In general, the real functions used in implicit modelling are unbounded and can take any values in space R. In general, the shapes described by different level sets of an unbounded implicit function can be varied significantly and are very unpredictable. In addition, ...

We prove that the number of conjugacy classes of maximal subgroups of bounded order in a finite group of Lie type of bounded rank is bounded. For exceptional groups this solves a longstanding open problem. The proof uses, among other tools, some methods from Geometric Invariant Theory. Using this result we provide a sharp bound for the total number of conjugacy classes of maximal subgroups of L...

In the present paper, we prove that the classical sets ∞(F ), c(F ), c0(F ) and p(F ) of sequences of fuzzy numbers are normed quasilinear spaces and the β−, α−duals of the set 1(F ) is the set ∞(F ). Besides this, we show that ∞(F ) and c(F ) are normed quasialgebras and an operator defined by an infinite matrix belonging to the class ( ∞(F ) : ∞(F )) is bounded and quasilinear. Finally, as an...

Although, in literature various results can be found claiming that fuzzy controllers are universal approximators, recently it was shown [3, 4] that for Sugeno-controllers this property does not hold any longer if the number of the rules is bounded. Namely, it was shown that the set of Sugeno-controllers is nowhere dense in the space of continuous functions. In this paper a generalization of the...

it is well known fact that binary relations are generalized mathematical functions. contrary to functions from domain to range, binary relations may assign to each element of domain two or more elements of range. some basic operations on functions such as the inverse and composition are applicable to binary relations as well. depending on the domain or range or both are fuzzy value fuzzy set, i...

in this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring r. these fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

and Applied Analysis 3 Conversely, if the pair of functions α and β satisfy the conditions 1 – 4 , then there exists a unique u ∈ E1 such that u λ α− λ , β λ for each λ ∈ 0, 1 , 9 . The fuzzy number u corresponding to the pair of functions α and β is defined by u : R → 0, 1 , u x sup{λ : α x ≤ λ ≤ β x }, 5 . A sequence u uk of fuzzy numbers is a function u from the set N, the set of all positiv...

In 2001 we introduced the notions of possibilistic mean value and variance of fuzzy numbers. In this paper we list some works that use these notions. We shall mention some application areas as well. 1 Possibilistic mean value, variance, covariance and correlation A fuzzy number A is a fuzzy set R with a normal, fuzzy convex and continuous membership function of bounded support. The family of fu...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...