*Correspondence: [email protected] School of Mathematics Science, Liaocheng University, Liaocheng, Shandong 252059, China Abstract In order to generalize the notions of a (∈,∈ ∨q)-fuzzy subring and various (∈,∈ ∨q)-fuzzy ideals of a ring, a (λ,μ)-fuzzy subring and a (λ,μ)-fuzzy ideal of a ring are defined. The concepts of (λ,μ)-fuzzy semiprime, prime, semiprimary and primary ideals are introdu...

Fuzzy logic is understood as a logic with a comparative and truth-functional notion of truth. Arithmetical complexity of sets of tautologies (identically true sentences) and satissable sentences (sentences true in at least one interpretation) as well of sets of provable formulas of the most important systems of fuzzy predicate logic is determined or at least estimated .

Department of Mathematics, Jadavpur University Kolkata-700032, India manasi−[email protected] Abstract The notion of intuitionistic fuzzy set was introduced by Atanassov as a generalization of the notion of fuzzy set. In this paper we apply this concept of Atanassov to ideals, prime ideals and semiprime ideals of Γsemigroups in order to obtain some characterization theorems. We also introduce the not...

In Boolean logic, a Karnaugh map may be regarded either as a pictorial form of a trugh table, or as an extension of the Venn diagram. However, when fuzzy logic is concerned another minimization method is required, and therefore an extension of a Karnaugh map is investigated. In this paper a new minimization algorithm is developed in order to remove the existing disadvantage of simplifying fuzzy...

Let R be a Noetherian ring, F := Rr and M ⊆ F a submodule of rank r. Let A∗(M) denote the stable value of Ass(Fn/Mn), for n large, where Fn is the nth symmetric power of Fn and Mn is the image of the nth symmetric power of M in Fn. We provide a number of characterizations for a prime ideal to belong to A∗(M). We also show that A∗(M) ⊆ A∗(M), where A∗(M) denotes the stable value of Ass(Fn/Mn).

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...

Abstract: In this paper, we compute number of fuzzy subgroups of some dihedral groups such as D2pn where p is a prime number and D2p1×p2×···×pn where p1, p2, ..., pn are distinct prime numbers. We use their chain diagram to determine the number of their fuzzy subgroups and present an explicit recursive formula to D2pn and at the result in specially case D2n and finally a formula to count number...

In this paper the concept of soft fuzzy filter on X, soft fuzzy prime filter on X, soft fuzzy ultrafilter on X, soft fuzzy minimal prime filter collections are introduced. The concept of soft fuzzy limit space (X, ltτ ) and the related properties are discussed. The functor ι from the collection of soft fuzzy filters F(X) to the collection of filters on X and the functor ω defined from the colle...

A pseudo-addition in BL-algebras is a binary operation that is associative and non commutative. The aim of this paper is to use the notion of pseudo-addition to study the notion of ideal and fuzzy ideal as a natural generalization of that of ideal and fuzzy ideal in MV-algebras. Using a pseudo-addition, we characterize fuzzy ideals and also obtain a concrete description of the fuzzy ideals gene...

In this paper we introduce the notion of intuitionistic fuzzy prime, strongly prime, semiprime bi-ideals in ternary semigroup and look for some of their related characteristics. Also here we introduce irreducible and strongly irreducible intuitionistic fuzzy bi-ideals in a ternary semigroup. AMS subject classification: 20N10, 20M12, 04A72.