Fuzzy Ideals and Fuzzy Filters of Ordered Ternary Semigroups

Ronnason Chinram, Sompob Saelee

Abstract


The notion of ternary semigroups was introduced by Lehmer in 1932 and that of fuzzy sets by Zadeh in 1965. Any
semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup.
A partially ordered semigroup T is called an ordered ternary semigroup if for all x1; x2; x3; x4 2 T; x1 x2 implies
x1x3x4 x2x3x4; x3x1x4 x3x2x4 and x3x4x1 x3x4x2. In this paper, we study fuzzy ternary subsemigroups (left ideals,
right ideals, lateral ideals, ideals) and fuzzy left filters (right filters, lateral filters, filters) of ordered ternary semigroups.


Full Text: PDF DOI: 10.5539/jmr.v2n1p93

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Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

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