Characterization of Ordered Semigroups in Terms of Fuzzy Soft Ideals

Malaysian Mathematical · Yunqiang Yin · Jianming Zhan

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Fuzzy and Soft Set Theory Advanced Algebra and Logic Fuzzy Systems and Optimization

Abstract

In this paper, we apply the concept of fuzzy soft sets to ordered semigroup the- ory. The concepts of (2g;2g_qd)-fuzzy left (right) ideals, (2g;2g_qd)-fuzzy bi-ideals and (2g;2g_qd)-fuzzy quasi-ideals are introduced and some related properties are obtained. Three kinds of lattice structures of the set of all (2g;2g_qd)-fuzzy soft left (right) ideals of an ordered semigroup are derived. The characterization of left quasi-regular ordered semigroups and ordered semigroups that are left quasi-regular and intra-regular in terms of (2g;2g_qd)-fuzzy left (right) ideals, (2g;2g_qd)-fuzzy bi-ideals and (2g;2g_qd)-fuzzy quasi-ideals is discussed.

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References

1999Soft set theory—First results 2003Soft set theory 2009On some new operations in soft set theory 2007A fuzzy soft set theoretic approach to decision making problems 2001FUZZY SOFT SETS 2008Soft semirings 2010Soft sets and soft rings 2008Soft BCK/BCI-algebras

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