ON $(ALPHA ,BETA)$-FUZZY IDEALS OF TERNARY SEMIGROUPS

Bijan Davvaz

Abstract


In this paper, we introduce the concept of generalized
fuzzy ideals in ternary semigroups, which is a generalization of the fuzzy
ideals of semigroups. In this regard, we define ($\alpha ,\beta $)-fuzzy
left (right, lateral) ideals, ($\alpha ,\beta $)-fuzzy quasi-ideals and ($
\alpha ,\beta $)-fuzzy bi-ideals and invetigate some related properties of
ternary semigroups. Special concentration is paid to ($\in ,\in \vee q$
)-fuzzy left (right, lateral) ideals, ($\in ,\in \vee q$)-fuzzy quasi-ideals
and ($\in ,\in \vee q$)-fuzzy bi-ideals. Finally, we
characterize regular ternary semigroups in terms of these notions.

DOI : http://dx.doi.org/10.22342/jims.19.2.120.123-138


Keywords


Fuzzy subset; ($\in ,\in \vee q$)-fuzzy left (right,

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References


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DOI: https://doi.org/10.22342/jims.19.2.120.123-138

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