Ümit DENİZ

Different Approximation to Fuzzy Ring Homomorphisms

In this study we approach the definition of ?? −ring homomorphism. In the literature, the definition of fuzzy ring homomorphism is given by Malik and Mordeson by using their fuzzy function definition. In this study, we give the definition of fuzzy ring homomorphism by using the definition of Mustafa Demirci’s fuzzy function. Some definition and theorems of ring homomorphism in classic algebra are adapted to fuzzy algebra and proved.

PDF

___

[1] Baets B. De, Mesiar R., Triangular norms on product lattices, Fuzzy Sets and Systems 104 (1999) 61-75

[2] Demirci M. and Recasens J., Fuzzy Groups, Fuzzy Functions and Fuzzy Equivalence Relations, Fuzzy Sets and Systems 144 (2004) 441-458.

[3] Demirci M., Fuzzy Functions and Their Applications, Journal of .Mathematical Analysis and Applications 252 (2000) 495- 517.

[4] Demirci M., Fundamentals of M-vague Algebra and M-Vague Arithmetic Operations, Int. J. Uncertainly, Fuzziness KnowledgeBased Systems 10, 1 (2002) 25-75.

[5] Karaçal F. and Khadjiev D, ∨-Distributive and infinetly ∨-distributive t-norms on complete lattice, Fuzzy Sets and Systems 151 (2005) 341-352

[6] Klement E.P., Mesiar R. and Pap E., Triangular Norms. Position Paper I: Basic Analytical and Algebraic Properties, Fuzzy Sets and Systems 143(2004) 5-26.

[7] Klement E.P., Mesiar R. and Pap E., Triangular Norms. Position Paper II: General Constructions and Parameterized Families, Fuzzy Sets and Systems 145 (2004) 411-438.

[8] Klement E.P., Mesiar R. and Pap E., Triangular Norms. Position Paper III: Continuous t-Norms, Fuzzy Sets and Systems 145 (2004) 439-454.

[9] Liu W.J., Fuzzy Invariant supgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982) 133-139

[10] Liu W.J., Operations on fuzzy ideals, Fuzzy Sets and Systems 11 (1983) 31-41

[11] Malik D.S., Mordeson J.N., Fuzzy homomorphisms of rings, Fuzzy Sets and Systems, 46 (1992) 139-146

[12] Rosenfeld A., Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517

[13] Sostak A. P., Fuzzy Functions and an Extension of the Category L-Top of ChangGoguen L-Topological Spaces, Proceedings of the Ninth Prague Symposium, pp. 271-294, Topology Atlas, Toronto, 2002

[14] Wang Z. D. and Yu Y. D., ТL-subrings and ТL-ideals, Part 2: Generated ТL-ideals, Fuzzy Sets and Systems 87 (1997) 209-217.

[15] Wang Z. D. and Yu Y. D., ТL-subrings and ТL-ideals, Part 1: Basic concepts, Fuzzy Sets and Systems 68 (1994) 93-103.

[16]Yamak, S., Fuzzy Algebraic Structure and Fuzzy Representations, Postgraduate Thesis, Karadeniz Technical University, Institute of Science and Technology, 1995.

[17] Zadeh L. A., Fuzzy Sets, Information and Control, 8 (1965) 338-353.