Characterizations of Ordered Semigroups in Terms of Anti-fuzzy Ideals

• Published in: Fuzzy information and engineering Vol. 11; no. 4; pp. 428 - 445
• Main Authors: Salam, Abdus, Ashraf, Wajih, Mahboob, Ahsan, Khan, Noor Mohammad
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.10.2019; Taylor & Francis Group
• Subjects: antifuzzy bi-ideal; fuzzy bi-ideal; Fuzzy sets; fuzzy subset; k; Ordered semigroup; q; Semigroups
• ISSN: 1616-8658; 1616-8666
• DOI: 10.1080/16168658.2020.1753496

Adopting the notion of a -quasi-coincidence of a fuzzy point with a fuzzy set, the idea of an (∈,∈∨(k ∗ , q k ))-antifuzzy left (right) ideal, (∈,∈∨(k ∗ , q k ))-antifuzzy ideal and (∈,∈∨(k ∗ , q k ))-antifuzzy (generalized) bi-ideal in ordered semigroups are proposed, that are the generalization of the idea of an antifuzzy left (right) ideal, antifuzzy ideal and antifuzzy (generalized) bi-ideal in ordered semigroups and a few fascinating characterizations are obtained. In this paper, we tend to focus to suggest a connection between standard generalized bi-ideals and (∈,∈∨(k ∗ , q k ))-antifuzzy generalized bi-ideals. In addition, different classes of regular ordered semigroups are characterized by the attributes of this new idea. Finally, the -lower part of an (∈,∈∨(k ∗ , q k ))-antifuzzy generalized bi-ideal is outlined and a few characterizations are mentioned.