IJPAM: Volume 56, No. 1 (2009)

FUZZY, ROUGH AND ROUGH FUZZY
IDEALS IN TERNARY SEMIGROUPS

Pattarawan Petchkhaew$^1$, Ronnason Chinram$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Prince of Songkla University
Hat Yai, Songkhla, 90112, THAILAND
$^2$e-mail: [email protected]


Abstract.The formal definition of a ternary semigroup was given by Lehmer in 1932, but earlier such structures was studied by Kasner and Prüfer. Any semigroup can be reduced to a ternary semigroup but a ternary semigroup does not necessarily reduce to a semigroup. The notion of fuzzy sets was introduced by Zadeh in 1965 and that of rough sets by Pawlak in 1982. In this paper, we study fuzzy, rough and rough fuzzy ternary subsemigroups (left ideals, right ideals, lateral ideals, ideals) of ternary semigroups.

Received: August 27, 2008

AMS Subject Classification: 20N10, 08A72, 03E72, 20M12

Key Words and Phrases: fuzzy sets, rough sets, ternary semigroups, ternary subsemigroups, left ideals, right ideals, lateral ideals, ideals

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 56
Issue: 1