Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi‐Ideals

Jian Tang, Xiangyun Xie and Yanfeng Luo

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: The concept of non‐k‐quasi‐coincidence of an interval valued ordered fuzzy point with an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the non‐k‐quasi‐coincidence of a fuzzy point with a fuzzy set. By using this new concept, we introduce the notion of interval valued (∈¯,∈¯∨qk~¯)‐fuzzy quasi‐ideals of ordered semigroups and study their related properties. In addition, we also introduce the concepts of prime and completely semiprime interval valued (∈¯,∈¯∨qk~¯)‐fuzzy quasi‐ideals of ordered semigroups and characterize bi‐regular ordered semigroups in terms of completely semiprime interval valued (∈¯,∈¯∨qk~¯)‐fuzzy quasi‐ideals. Furthermore, some new characterizations of regular and intra‐regular ordered semigroups by the properties of interval valued (∈¯,∈¯∨qk~¯)‐fuzzy quasi‐ideals are given.

Date: 2014
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https://doi.org/10.1155/2014/867459

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:867459

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