We investigate amenability and weak amenability of the l1-algebra of polynomial hypergroups. We derive conditions for (weak) amenability adapted to polynomial hypergroups and show that these conditions are often not satisfied. However, for the hypergroup induced by Chebyshev polynomials of the first kind we prove amenability.

The theory of hyperstructures has been introduced byMarty in 1934 during the 8th Congress of the Scandinavian Mathematicians [4]. Marty introduced the notion of a hypergroup and since then many researchers have worked on this new topic of modern algebra and developed it. The notion of a hyperfield and a hyperring was studied first by Krasner [2] and then some authors followed him, for example, ...

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphi...

In this paper, the notion of fuzzy n-polygroups (Fn -polygroups) is introduced and some related properties are investigated. In this regards, the concepts of normal  F-subpolygroups and homomorphisms of Fn-polygroups are adopted. Also, the quotient of Fn-polygroups by defining regular relations are studied. Finally, the classical isomorphism theorems of groups are generalized to Fn-polygroups p...

This paper deals with hypergroupoids obtained from n-ary relations. We give conditions for an n-ary relation such that the hypergroupoid associated with it is a hypergroup. First we analyze this construction using a ternary relation and then we generalize it for an n-ary relation.

The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value space...

R. Babuska, Fuzzy Modeling for Control, Kluwer Academic Publ., Dordrecht, 1998, 288 p. B. Bouchon-Meunier, L. Foulloy, M. Ramdani, Logique Floue Exercices Corriges et Exemples d' Applications, Cepadues Editions. Toulouse, 199B, 200 p. G.Q. Chen, Fuzzy Logic in Data Modeling Semantics, Constraints and Database Design, Kluwer Academic Publ., Boston. 1998, 240 p. K.J. Cios. W. Pedrycz, R.S. Swinia...

The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parametrization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces...

Fuzzy inference systems and neural networks are complementary technologies in the design of adaptive intelligent systems. Artificial Neural Network (ANN) learns from scratch by adjusting the interconnections between layers. Fuzzy Inference System (FIS) is a popular computing framework based on the concept of fuzzy set theory, fuzzy if-then rules, and fuzzy reasoning. A neuro-fuzzy system is sim...