IMCS/Publications/QRS/Issues/QRS v.20, n.1 (27), 2012/

On fuzzy ordered semigroups

Authors: N. Kehayopulu, M. Tsingelis


There are two equivalent definitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The first one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the first definition. The present paper serves as an example to show that using the second definition the proofs of the results can be simplified, drastically in some cases, using only the definitions themselves.


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