Classifications and Properties of (α,β )-Fuzzy Ideals in Ternary Semigroups

Authors

Noor Rehman, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan\\ Department of Basic Sciences, Riphah Interantional University, Islamabad, PakistanFollow
Muhammd Shabir, Department of Mathematics, Quaid-i-Azam University, Islamabad, PakistanFollow
Young Bae Jun, Department of Mathematics Education, Gyeongsang National University, Jinju 660-701, Republic of KoreaFollow

Author Country (or Countries)

Pakistan

Abstract

Classifications of (a,b )-fuzzy left (right and lateral) ideals of ternary semigroups are discussed. Relations between (∈,∈ ∨q)-fuzzy left (right and lateral) ideals and (q,∈∨q)-fuzzy left (right and lateral) ideals are established. Given special sets, so called t-q-set and t-∈∨q-set, conditions for the t-q-set and t-∈∨q-set to be left (right and lateral) ideals are considered. Conditions for a fuzzy set to be an (∈,q)-fuzzy left (right and lateral) ideals, a (q,∈)-fuzzy left (right and lateral)ideals and a (q,∈∨q)-fuzzy left (right and lateral) ideals are considered. Some new characterizations of weakly regular ternary semigroups are also established. Finally, the implication-based fuzzy ideals are discussed.

Recommended Citation

Rehman, Noor; Shabir, Muhammd; and Bae Jun, Young (2015) "Classifications and Properties of (α,β )-Fuzzy Ideals in Ternary Semigroups," Applied Mathematics & Information Sciences: Vol. 09: Iss. 3, Article 54.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/54