We investigate interpretations ‖ψ‖D of formulas ψ in a first order fuzzy logic in models D which are based on Ω-sets, i.e. sets with similarity relations with values in a complete MV-algebra Ω. These interpretations are fuzzy sets in some Ωsets. We show that if φ : D1 → D2 is a strong homomorphism between two models then there are also strong relationships between interpretations ‖ψ‖D1 and ‖ψ‖D...

Starting with the underlying motivation of developing a general theory of L-fuzzy sets where L is a multilattice (a particular case of non-deterministic algebra), we study the relationship between the crisp notions of congruence, homomorphism and substructure on some non-deterministic algebras which have been used in the literature, i.e. hypergroups, and join spaces. Moreover, we provide suitab...

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

The notion of S-fuzzy left h-ideals in a hemiring is introduced and it’s basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finitevalued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuz...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

In this paper, we have developed an algebraic theory, suitable for the analysis of fuzzy systems. We have used the notions of semiring and semimodule, introduced the notion of semilinear space and gave numerous examples of them and defined also the notions of linear dependence and independence. Then, we have shown that the composition operation, which plays an essential role in the analysis of ...

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

in this note, by considering the notions of the intuitionistic general l-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{l}$, there exists a minimal intuitionistic general l-fuzzy automaton recognizing $mathcal{l}$.we prove that the minimal intuitionistic general l-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, be...

A new definition of boundedness of linear order-homomorphisms (LOH)in $L$-topological vector spaces is proposed. The new definition iscompared with the previous one given by Fang [The continuity offuzzy linear order-homomorphism, J. Fuzzy Math. 5 (4) (1997)829$-$838]. In addition, the relationship between boundedness andcontinuity of LOHs is discussed. Finally, a new uniform boundednessprincipl...