On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups

An ordered AG-groupoid can be referred to as a non-associativeordered semigroup, as the main di¤erence between an ordered semigroup and anordered AG-groupoid is the switching of an associative law. In this paper, wede ne the smallest left (right) ideals in an ordered AG-groupoid and use them tocharacterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with itssemilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the conceptof an ordered A*G**-groupoid and investigate its structural properties by usingthe generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts willverify the existing characterizations and will help in achieving more generalizedresults in future works.

Generalized Ideals of BCK/BCI-Algebras Based on Fuzzy Soft Set Theory

In the present paper, using Lukaswize triple-valued logic, we introduce the notion of α , β -intuitionistic fuzzy soft ideal of BCK / BCI -algebras, where α and β are the membership values between an intuitionistic fuzzy soft point and intuitionistic fuzzy set. Moreover, intuitionistic fuzzy soft ideals with thresholds are introduced, and their related properties are investigated.

Connecting Fuzzifying Topologies and Generalized Ideals by Means of Fuzzy Preorders

The present paper investigates the relations between fuzzifying topologies and generalized ideals of fuzzy subsets, as well as constructing generalized ideals and fuzzifying topologies by means of fuzzy preorders. Furthermore, a construction of generalized ideals from preideals, and vice versa, is obtained. As a particular consequence of the results in this paper, a construction of fuzzifying topology generated by generalized ideals of fuzzy subsets via a givenI-topology is given. The notion ofσ-generalized ideal is introduced and hence everyσ-generalized ideal is shown to be a fuzzifying topology induced by some fuzzy preorder.