FUZZY LINEAR MAPPINGS

Öz

In this paper we study fuzzy linear mappings. In literature the fuzzy linear mapping definition was given with classic functions. But we give the definition of fuzzy linear mapping with using the definition of fuzzy function that Demirci was given before. With this definition, we give some definition and theorems that similar to classic algebra about linear mappings and prove them.

Anahtar Kelimeler

• Fuzzy Functions
• Fuzzy Subspaces
• Fuzzy linear Mappings

Kaynakça

1. [1] Kim S. H., Monk B., Neggers J., On pseudo fuzzy linear mappings, Information Sciences, 177, 897-905, (2007).
2. [2] Katsaras A. K., Liu D.B., Fuzzy Vector Spaces and Fuzzy Topological Vector Spaces, Journal of Mathematical Analysis and Applications, 58, 135-146, (1977).
3. [3] Muganda G. C., Fuzzy Linear and Axne Spaces, Fuzzy Sets and Systems, 38, 365-373, (1990).
4. [4] Demirci M., Recasens J., Fuzzy Groups, Fuzzy Functions and Fuzzy Equivalence Relations, Fuzzy Sets and Systems, 144, 441-458,(2004).
5. [5] Demirci M., Fuzzy Functions and Their Applications, Journal of Mathematical Analysis and Applications, 252, 495-517, (2000).
6. [6] Demirci M., Fundamentals of M-vague Algebra and M-vague Arithmetic Operations, Int. J. Uncertainly Fuzziness Knowledge-Based Systems, 10, 1, 25-75, (2002).
7. [7] Sostak 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, Topological Atlas, Toronto, 2002.
8. [8] L. A. Zadeh , Fuzzy sets, Information and Control, 8,338-353, (1965).

9. [9] Abdukhalikov, K. S., The Dual of Fuzzy Subspace, Fuzzy Sets and Systems, 82, 375-381, (1996).
10. [10] Klement E.P., Mesiar R., Pap E., Triangular Norms. Position Paper I: Basic Analytical and Algebraic Properties, Fuzzy Sets and Systems, 145, 411-438, (2004).
11. [11] Klement E.P., Mesiar R., Pap E., Triangular Norms. Position Paper II:General Contructions and Parameterize Families, Fuzzy Sets and Systems, 145, 411-438, (2004).
12. [12] Klement E.P., Mesiar R., Pap E., Triangular Norms. Position Paper III: Continuous t-norms, Fuzzy Sets and Systems, 145, 439-454, (2004).
13. [13] F. Karacal, D. Khadjiev, -Distributive and infinitely -distributive t-norms on complete lattice, Fuzzy Sets and Systems, 151, 341-352, (2005).
14. [14] U. Deniz, Diifferent Approximation to Fuzzy Ring Homomorphisms, Sakarya University Journal of Science, 6,1163-1172,(2019).