J. Appl. Math. & Informatics Vol. 32(2014), No. 3 - 4, pp. 405 - 426 http://dx.doi.org/10.14317/jami.2014.405 LA-SEMIGROUPS CHARACTERIZED BY THE PROPERTIES OF INTERVAL VALUED (α, β)-FUZZY IDEALS SALEEM ABDULLAH * , SAMREEN ASLAM AND NOOR UL AMIN Abstract. The concept of interval-valued (α, β)-fuzzy ideals, interval- valued (α, β)-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. Regular LA-semigroups are character- ized by the properties of the lower part of interval-valued (∈, ∈∨q)-fuzzy left ideals, interval-valued (∈, ∈∨q)-fuzzy quasi-ideals and interval-valued (∈, ∈∨q)-fuzzy generalized bi-ideals. Main Facts. AMS Mathematics Subject Classification : 65H05, 65F10. Key words and phrases : interval-valued (α, β)-fuzzy sub LA-semigroups, interval-valued (α, β)-fuzzy ideals, interval-valued (α, β)-fuzzy bi-ideals, interval-valued (α, β)-fuzzy quasi-ideals. 1. Introduction The concept of fuzzy sets was first introduced by Zadeh [16] and then the fuzzy sets have been used in the reconsideration of classical mathematics. Fuzzy set theory has been shown to be a useful tool to describe situations in which data is imprecise or vague. Fuzzy sets handle such situations by attributing a degree to which a certain object belongs to a set. The fuzzy algebraic structures play a prominent role in mathematics with wide applications in many other branches such as theoratical physics, computer sciences, control engineering, information sciences, coding theory, topological spaces, logic, set theory, group theory, real analysis, measure theory etc. The notion of fuzzy subgroups was defined by Rosenfled [12]. A systematic exposition of fuzzy semigroup was given by Morde- son et. al. [7], and they have find theoratical results on fuzzy semigroups and their use in finite state machine, fuzzy languages and fuzzy coding. Using the Received October 31, 2012. Revised December 28, 2013. Accepted February 8, 2014. * Corresponding author. c ⃝ 2014 Korean SIGCAM and KSCAM. 405