MORE ON INTUITIONISTIC FUZZY SUBLATTICES AND THEIR IDEALS

In this paper, we study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals with respect to an intuitionistic fuzzy t-norm on an adequate lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to intuitionistic fuzzy t-norm are established

CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals

Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established

On generalized interval valued fuzzy quasi-ideals of semigroups

In this paper, we give the concepts of generalized interval valued fuzzy subsemigroups, which are generalizations of the notion of interval valued fuzzy subsemigroups and of (ᾱ, β)-interval valued fuzzy subsemigroups, where ᾱ ≺ β. Also we prove some of related properties of generalized interval valued fuzzy quasi-ideals on semigroups. In the main results, we characterize regular and intra-regular semigroups in terms of generalized interval valued fuzzy ideal and quasi-ideals.Publisher's Versio

An (α,β)-Hesitant Fuzzy Set Approach to Ideal Theory in Semigroups

The aim of this manuscript is to introduce the $(\alpha,\beta)$-hesitant fuzzy set and apply it to semigroups. In this paper, as a generalization of the concept of hesitant fuzzy sets to semigroup theory, the concept of $(\alpha,\beta)$-hesitant fuzzy subsemigroups of semigroups is introduced, and related properties are discussed. Furthermore, we define and study $(\alpha,\beta)$-hesitant fuzzy ideals on semigroups. In particular, we investigate the structure of $(\alpha,\beta)$-hesitant fuzzy ideal generated by a hesitant fuzzy ideal in a semigroup. In addition, we also introduce the concepts of $(\alpha,\beta)$-hesitant fuzzy semiprime sets of semigroups, and characterize regular semigroups in terms of $(\alpha,\beta)$-hesitant fuzzy left ideals and $(\alpha,\beta)$-hesitant fuzzy right ideals. Finally, several characterizations of regular and intra-regular semigroups by the properties of $(\alpha,\beta)$-hesitant ideals are given

Doubt fuzzy BCI-algebras

The aim of this note is to introduce the notion of doubt fuzzy p-ideals in BCI-algebras and to study their properties. We also solve the problem of classifying doubt fuzzy p-ideals and study fuzzy relations on BCI-algebras

Bipolar Valued Fuzzy SA-subalgebras and Fuzzy SA-ideals of SA- algebra.

In this paper, the notions of bipolar valued fuzzy SA-subalgebras and bipolar valued fuzzy SA-ideals on SA-algebras with their properties are familiarized. Several theorems are stated and proved with their examples. After that we introduced  new notion which is negative anti-fuzzy SA-subalgebra(SA-ideal) of SA-algebra  . The image and inverse image of bipolar valued fuzzy SA-subalgebras and bipolar valued fuzzy SA-ideals are defined and how the homomorphic images and inverse images of bipolar valued become bipolar valued fuzzy on SA-algebras is studied as well

Zariski topology on the spectrum of fuzzy classical primary submodules

[EN] Let R be a commutative ring with identity and M a unitary R-module. The fuzzy classical primary spectrum F cp.spec(M) is the collection of all fuzzy classical primary submodules A of M, the recent generalization of fuzzy primary ideals and fuzzy classical prime submodules. In this paper, we topologize FM(M) with a topology having the fuzzy primary Zariski topology on the fuzzy classical primary spectrum F cp.spec(M) as a subspace topology, and investigate the properties of this topological space.This work (Grant No. RGNS 64-189) was financially supported by Office of the Permanent Secretary, Ministry of Higher Education, Science, Research and Innovation.Panpho, P.; Yiarayong, P. (2022). Zariski topology on the spectrum of fuzzy classical primary submodules. Applied General Topology. 23(2):333-343. https://doi.org/10.4995/agt.2022.1742733334323

Intuitionistic fuzzy ideals of BCK-algebras

We consider the intuitionistic fuzzification of the concept of subalgebras and ideals in BCK-algebras, and investigate some of their properties. We introduce the notion of equivalence relations on the family of all intuitionistic fuzzy ideals of a BCK-algebra and investigate some related properties