Different Approximation to Fuzzy Ring Homomorphisms

Year 2019, Volume: 23 Issue: 6, 1163 - 1172, 01.12.2019

Ümit Deniz

https://doi.org/10.16984/saufenbilder.379634

Cited By: 3

Abstract

Bu
çalışmada TL-halka homomorfizmaları tanımı verildi. Literatürde fuzzy halka
homomorfizma tanımını Malik ve Mordeson kendi tanımladıkları fuzzy fonksiyon
tanımını kullanarak vermişlerdir. Bu çalışmada biz fuzzy halka homomorfizması
tanımını Demirci’nin Fuzzy Fonksiyon tanımını kullanarak verdik. Klasik
cebirdeki halka homomorfizmaları ile ilgili bazı tanım ve teoremleri fuzzy
cebirine taşıdık ve ispatladık.

Keywords

Fuzzy sets, Fuzzy Relations, Fuzzy Functions, Fuzzy Ring Homomorphims

References

• 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.
• 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.
• Klement E.P., Mesiar R. and Pap E., Triangular Norms. Position Paper III: Continuous t-Norms, Fuzzy Sets and Systems 145 (2004) 439-454.
• Demirci M. and Recasens J., Fuzzy Groups, Fuzzy Functions and Fuzzy Equivalence Relations, Fuzzy Sets and Systems 144 (2004) 441-458.
• Demirci M., Fuzzy Functions and Their Applications, Journal of .Mathematical Analysis and Applications 252 (2000) 495-517.
• Demirci M., Fundamentals of M-vague Algebra and M-Vague Arithmetic Operations, Int. J. Uncertainly, Fuzziness Knowledge-Based Systems 10, 1 (2002) 25-75.
• ostak A. P., Fuzzy Functions and an Extension of the Category L-Top of Chang-Goguen L-Topological Spaces, Proceedings of the Ninth Prague Symposium, pp. 271-294, Topology Atlas, Toronto, 2002
• 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.
• Wang Z. D. and Yu Y. D., ТL-subrings and ТL-ideals, Part 1: Basic concepts, Fuzzy Sets and Systems 68 (1994) 93-103.
• Zadeh L. A., Fuzzy Sets, Information and Control, 8 (1965) 338-353.
• Karaçal F. and Khadjiev D, ∨-Distributive and infinetly ∨-distributive t-norms on complete lattice, Fuzzy Sets and Systems 151 (2005) 341-352
• Baets B. De, Mesiar R., Triangular norms on product lattices, Fuzzy Sets and Systems 104 (1999) 61-75
• A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517
• W.J. Liu, Fuzzy Invariant supgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982) 133-139
• W.J. Liu, Operations on fuzzy ideals, Fuzzy Sets and Systems 11 (1983) 31-41
• D.S. Malik, J.N. Mordeson, Fuzzy homomorphisms of rings, Fuzzy Sets and Systems, 46 (1992) 139-146
• Yamak, S., Fuzzy Algebraic Structure and Fuzzy Representations, Postgraduate Thesis, Karadeniz Technical University, Institute of Science and Technology, 1995.