Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra...

The notions of an ideal and a fuzzy ideal in BN-algebras are introduced. The properties and characterizations of them are investigated. The concepts of normal ideals and normal congruences of a BN-algebra are also studied, the properties of them are displayed, and a one-to-one correspondence between them is presented. Conditions for a fuzzy set to be a fuzzy ideal are given. The relationships b...

The concept of fuzzy set, which was published by Zadeh in his classic paper [24] of 1965, was applied by many researchers to generalize some of the basic concepts of algebra. The fuzzy algebraic structures play a central role in mathematics with wide applications in many other branches such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, topo...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudo-BCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras in terms of fuzzy...

Characterizations of fuzzy ideals of a pseudo-BCK algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. Given a fuzzy set μ, the least fuzzy ideal containing μ is constructed. The homomorphic properties of fuzzy ideals of a pseudoBCK algebra are provided. Finally, characterizations of Noetherian pseudo-BCK algebras and Artinian pseudo-BCK algebras via fuzzy ideals a...

The commutator of Lie algebra is extended to a product of fuzzy Lie subspaces over fuzzy field. An action of fuzzy field is introduced as an extension of scalar multiplication in Lie algebra. The notion of derived series and descending central series of fuzzy Lie ∼ideal over fuzzy field and the concepts of ∼nilpotent and ∼solvable fuzzy Lie ∼ideals over fuzzy field are studied. Mathematics Subj...

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 we propose and construct fuzzy algebraic additive model, for the estimation of risk in various fields of human activities or nature’s behavior. though the proposed model is useful in a wide range of scientific fields, it was designed for to torrential risk evaluation in the area of river evros. clearly the model’s performance improves when the number of parameters and the actual d...

EQ-algebras introduced by Novák are algebras of truth values for a higher-order fuzzy logic (fuzzy type theory). In this paper, the compatibility of multiplication w.r.t. the fuzzy equality in an arbitrary EQ-algebra is examined. Particularly, an example indicates that the compatibility axiom does not always hold, and then a class of EQ-algebras satisfying the compatibility axiom is characteriz...