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LA-SEMIGROUPS CHARACTERIZED BY THE PROPERTIES OF INTERVAL VALUED (α, β)-FUZZY IDEALS
LA-SEMIGROUPS CHARACTERIZED BY THE PROPERTIES OF INTERVAL VALUED (α, β)-FUZZY IDEALS
Journal of applied mathematics & informatics. 2014. May, 32(3_4): 405-426
  • Received : October 31, 2012
  • Published : May 30, 2014
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Abdullah Saleem
Aslam Samreen
Amin Noor Ul

Abstract
The concept of interval-valued (<TEX>${\alpha},{\beta}$</TEX>)-fuzzy ideals, interval-valued (<TEX>${\alpha},{\beta}$</TEX>)-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 characterized by the properties of the lower part of interval-valued (<TEX>${\in},{\in}{\vee}q$</TEX>)-fuzzy left ideals, interval-valued (<TEX>${\in},{\in}{\vee}q$</TEX>)-fuzzy quasi-ideals and interval-valued (<TEX>${\in},{\in}{\vee}q$</TEX>)-fuzzy generalized bi-ideals. Main Facts.
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