S-Fuzzy Left h-Ideal of Hemirings

The notion of S-fuzzy left h-ideals in a hemiring is introduced and it's basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finite-valued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuzzy relations on hemirings are discussed.The notion of direct product and S-product are introduced and some properties of the direct product and S-product of S-fuzzy left h-ideal of hemiring are also discussed.

• D.R Prince Williams

• hemiring
• left h-ideal
• anti fuzzy h-ideal
• S-fuzzy left hideal
• t-conorm
• homomorphism.

[1] M.T. Abu Osman, On some product of fuzzy subgroups,Fuzzy Sets and Systems 24 (1987), pp. 79-86.[2] M. Akram and J. Zhan,On sensible fuzzy ideals of BCK-algebras withrespect to a t-conorm Int. J. Math. Math. Sci. (2006), pp. 1-12.[3] Y.U Cho,Y.B Jun and E.H. Roh,On sensible fuzzy subalgebra of BCK-algebras with respect to s-norm SCMJ Online (e-2005), pp. 11-18.[4] Y.B Jun,M.A Öztürk and S.Z. Song,On fuzzy h-ideals of hemirings Inform. Sci. 162(3-4) (2004), pp. 211-226.[5] B. Schweizer and A.Sklar,Statistical metric spaces Pacific J. Math. 10(1960), pp. 313-334.[6] B. Schweizer and A.Sklar,Associative functions and abstract semigroups Statistical metric spaces Publ. Math.Debrecen 10 (1963), pp. 69-81.[7] D.R. La Torre,On h-ideals and k-ideals in hemirings Publ.Math.Debrecen 12 (1965), pp. 219-226.[8] L.A Zadeh,Fuzzy sets Information Control 8 (1965), pp. 338-353.[9] J.Zhan,On properties of fuzzy left h-ideals in hemirings with t-norms Int.J. Math. Math. Sci. 19 (2005), pp. 3127-3144.[10] J.Zhan,On properties of fuzzy hyperideals in hypernear-rings with t-norms J. APPl. Math. Computing 20(1-2) (2006), pp. 255-277