Characterizations of fuzzy ideals of a pseudo-BCH-algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. The homomorphic properties of fuzzy ideals are provided. Finally, characterizations of Noetherian pseudo-BCH-algebras and Artinian pseudoBCH-algebras via fuzzy ideals are obtained. Mathematics Subject Classi…cation: 03G25, 06F35.

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

We develope a construction of an L-fuzzy valued measure by extending a measure defined on a σ-algebra of crisp sets to an L-fuzzy valued TM-countably additive measure defined on a TMclan of L-fuzzy sets in the case when operations for L-fuzzy sets and L-fuzzy real numbers are based on the minimum t-norm TM. Keywords— L-fuzzy set, L-fuzzy real number, L-fuzzy valued measure.

the paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. motivated by an open question of s. e. rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of l. a. zadeh. on the next step, w...

In this paper, some types of fuzzy filters a strong Sheffer stroke non-associative MV-algebra (for short, NMV-algebra) are introduced. By presenting new properties filters, we define prime filter in algebraic structure. Then (prime) NMV-algebra determined and features proved. Finally, built quotient by filter.

This paper proposes a logical reconstruction of the classical fuzzy relational database model to accommodate fuzzy disjunctive information. In query processing, we use two supplementary measurements, matching information and extra information, to model the concepts of imprecision and uncertainty, respectively. We also use these two supplementary measurements to determine the quality of answers ...

The aim of this article is to study the concept of unique solvability of max-min fuzzy neutrosophic soft matrix equation and strong regularity of fuzzy neutrosophic soft matrices over Fuzzy Neutrosophic Soft Algebra (FNSA). A Fuzzy Neutrosophic Soft Matrix (FNSM) is said to have Strong, Linear Independent (SLI) column (or, in the case of fuzzy neutrosophic soft square matrices, to be strongly r...

The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...

The aim of this paper is to introduce the notion of intuitionistic fuzzy implicative ideals with thresholds (λ, μ) of BCI-algebras and to investigate its properties and characterizations. Keywords—BCI-algebra, intuitionistic fuzzy set, intuitionistic fuzzy ideal with thresholds (λ,μ), intuitionistic fuzzy implicative ideal with thresholds (λ,μ).

In this paper, we introduce Interpolative Boolean algebra (IBA) as a suitable algebra for intuitionistic fuzzy sets (IFSs). IBA is [0,1]-valued realization of Boolean algebra, consistent with Boolean axioms and theorems. IFS theory takes into account both membership and non-membership function, so it can be viewed as a generalization of the traditional fuzzy set theory. We propose a realization...