We investigate antihomomorphic images and pre images of semiprime, strongly primary, irreducible and strongly irreducible fuzzy ideals of a ring. We also prove that: For a surjective anti-homomorphism f : R → R, if every fuzzy ideal of R is f -invariant and has a fuzzy primary (respectively, strongly primary) decomposition in R, then every fuzzy ideal of R has a fuzzy primary (respectively, str...

this paper consider the   general  forms of $(alpha,beta)$-fuzzyleft ideals (right ideals, bi-ideals, interior ideals) of an orderedsemigroup, where$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedgeq_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneqin_{gamma}wedge q_{delta}$. special attention is paid to$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interiorideals) and some related  pr...

fuzzy bi-ideals play an important role in the study of ordered semigroupstructures. the purpose of this paper is to initiate and study theintiuitionistic fuzzy bi-ideals in ordered semigroups and investigate thebasic theorem of intuitionistic fuzzy bi-ideals. to provide thecharacterizations of regular ordered semigroups in terms of intuitionisticfuzzy bi-ideals and to discuss the relationships ...

let $s$ be an ordered semigroup. a fuzzy subset of $s$ is anarbitrary mapping   from $s$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. in this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $s$ is introduced.regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.finally, two m...

Abstract In this paper, we have introduced anti fuzzy quasi-ideals, anti fuzzy bi-(generalized bi-) ideals and anti fuzzy left (right, two-sided) ideals in LA-semigroup. Further we have characterized an intra-regular LA-semigroup by the properties of their anti fuzzy left (right, two-sided) ideals, anti fuzzy bi(generalized bi-)ideals, anti fuzzy interior ideals and anti fuzzy quasi-ideals. Fur...

in this paper, we introduce the notion of ($epsilon $, $epsilon $ $vee$ q_{k})− fuzzy subnear-ring which is a generalization of ($epsilon $, $epsilon $ $vee$ q)−fuzzy subnear-ring. we have given examples which are ($epsilon $, $epsilon $ $vee$ q_{k})−fuzzy ideals but they are not ($epsilon $, $epsilon $ $vee$ q)−fuzzy ideals. we have also introduced the notions of ($epsilon $, $epsilon $ $vee$ ...

In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal m...

Let $S$ be an ordered semigroup. A fuzzy subset of $S$ is anarbitrary mapping   from $S$ into $[0,1]$, where $[0,1]$ is theusual interval of real numbers. In this paper,  the concept of fuzzygeneralized bi-ideals of an ordered semigroup $S$ is introduced.Regular ordered semigroups are characterized by means of fuzzy leftideals, fuzzy right ideals and fuzzy (generalized) bi-ideals.Finally, two m...

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...