semigroup

Pythagorean Q-anti neutrosophic ideals in gamma semigroup
Annals of Communications in Mathematics 2022
, 5 (2)
, 88-96
DOI: https://doi.org/10.62072/acm.2022.050203
AbstractIn this article, we define the concept of Pythagorean Q-anti neutrosophic ideal in gamma semigroup, Pythagorean Q-anti neutrosophic bi-ideal in gamma semigroup, and Pythagorean Q-anti neutrosophic interior ideal in gamma semigroup. We have illustrated the definition with an example. We have shown that Pythagorean Q- anti neutrosophic bi-ideal is a fuzzy bi-ideal and Pythagorean Q-anti neutrosophic ideal is a Pythagorean Q-anti neutrosophic interior ideal. Also, we have established some of its properties in detail.

Pythagorean cubic ideal of semigroup
Annals of Communications in Mathematics 2021
, 4 (2)
, 196-206
DOI: https://doi.org/10.62072/acm.2021.040213
AbstractIn this paper, we introduce the notion of Pythagorean cubic ideal in semigroup. Also, we discuss some of their properties with examples.

On Pythagorean fuzzy ideal of subtraction semigroup and near subtraction
Annals of Communications in Mathematics 2020
, 3 (4)
, 261-272
DOI: https://doi.org/10.62072/acm.2020.030403
AbstractIn this paper, we define the notions of Pythagorean fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.

On some relative weakly hyperideals and relative prime bi-hyperideals in ordered hypersemigroups and in involution ordered hypersemigroups
Annals of Communications in Mathematics 2020
, 3 (1)
, 63-79
DOI: https://doi.org/10.62072/acm.2020.030107
AbstractThe aim of the present paper is to define and bring together the fundamental definitions such as relative hyperideals, relative bi-hyperideals, relative quasi-hyperideals, relative prime hyperideals, relative weakly prime hyperideals, relative semiprime hyperideals, relative prime and relative semiprime bi-hyperideals, and hyper relative regularity of dynamic algebraic character to develop the theory of hypersemigroups, and obtain the results relating to and connecting these hyperideal-theoretic definitions of this vast theory to the larger framework of the algebraic area of ordered hypersemigroups as well as of involution ordered hypersemigroups.

Applications of an Anti-fuzzy Semigroup
Annals of Communications in Mathematics 2024
, 7 (4)
, 430-438
DOI: https://doi.org/10.62072/acm.2024.070409
AbstractThis paper introduces the ”anti fuzzy semigroup,” a novel algebraic structure that integrates the concepts of semigroups and anti fuzzy sets. We demonstrate, through a specific example, how a Kinship system can be represented as an anti fuzzy semigroup, effectively capturing the relationships between managers and subordinates. This appli- cation underscores the potential of anti fuzzy semigroups to model complex hierarchical structures and relationships within organizational settings. Furthermore, we investigate the representation of DNA sequences using this framework. We delve into the algebraic properties of anti fuzzy semigroups, proving that the union of two such semigroups always results in another anti fuzzy semigroup. However, we provide a counterexample to demon- strate that the intersection of two anti fuzzy semigroups may not necessarily preserve the anti fuzzy semigroup property. Finally, the Cartesian product of two anti fuzzy semigroups forms an anti fuzzy semigroup.