Afrika Matematika

, Volume 25, Issue 3, pp 501–518

Characterization of regular LA-semigroups by interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy ideals


DOI: 10.1007/s13370-012-0130-6

Cite this article as:
Aslam, M., Abdullah, S. & Aslam, S. Afr. Mat. (2014) 25: 501. doi:10.1007/s13370-012-0130-6


The concept of interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy ideals, interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Also regular LA-semigroups are characterized by the properties of the upper part of interval-valued \((\overline{\in }, \overline{\in }\vee \overline{q})\)-fuzzy left ideals, interval-valued \(( \overline{\in },\overline{\in }\vee \overline{q})\)-fuzzy quasi-ideals and interval-valued \((\overline{\in },\overline{\in }\vee \overline{q})\)-fuzzy generalized bi-ideals.


Interval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy sub LA-semigroupsInterval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy idealsInterval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzyInterval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy quasi-ideals

Mathematics Subject Classification (2000)


Copyright information

© African Mathematical Union and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Muhammad Aslam
    • 1
  • Saleem Abdullah
    • 1
  • Samreen Aslam
    • 1
  1. 1.Department of MathematicsQuaid-i-Azam UniversityIslamabadPaksitan