Fuzzy near best approximation as a generalization of fuzzy best approximation

Khoddami, Ali Reza; Tourani, Rasoul

doi:10.22103/jmmr.2024.23101.1594

Fuzzy near best approximation as a generalization of fuzzy best approximation

Document Type : Research Paper

Authors

Ali Reza Khoddami

Rasoul Tourani

Faculty of Mathematical Sciences, Shahrood University of Technology, P. O. Box 3619995161-316, Shahrood, Iran

10.22103/jmmr.2024.23101.1594

Abstract

‎‎‎Given a fuzzy normed space, we will introduce the notion of fuzzy near best approximation as a generalization of the notion of fuzzy best approximation. Some basic properties are characterized and also many examples for illustration are presented. Also, the hereditary properties of the fuzzy near best approximation on direct sum and tensor product of linear spaces are discussed.

Keywords

‎Fuzzy near best approximation

Direct sum

Tensor product

Fuzzy norm‎

Subjects

Fuzzy Mathematics and Soft Computing

[1] Belton, Alexander C. R. (2004). Functional Analysis. Hyperlinked and revised edition.

[2] Abbasi, N., & Mottaghi Golshan, H. (2015). On best approximation in fuzzy metric spaces. Kybernetika, 51, (2), 374-386. https://doi.org/10.14736/kyb-2015-2-0374.

[3] Bonsall, F.F., & Duncan, J. (1973). Complete Normed Algebras. Springer-Verlag, Berlin Heidelberg New York.

[4] Bag, T., & Samanta, S. K. (2003). Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math., 11, (3), 687-705.

[5] Cheng, S. C., & Mordeson, J. N. (1994). Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc., 86, 429-436.

[6] Deutschi., F. (2000). Best Approximation in Inner Product Spaces. Canad. Math. Soc.

[7] Kovac, F. D., & Levis, F. E. (2022). Extended best Lp-approximation is near-best approximation in Lq, p 􀀀 1 q < p. J. Approx. Theory, 284, 105819. https://doi.org/10.1016/j.jat.2022.105819.

[8] Mazaheri, H., & Bizhanzadeh, Z., & Moosavi, S. M., & Dehghan, M. A. (2019). Fuzzy farthest points and fuzzy best approximation points in fuzzy normed spaces. Theory Approx. Appl., 13, (1), 11-25.

[9] Sadeqi, I., & Solaty Kia, F. (2009). Fuzzy normed linear space and its topological structure. Chaos Solit. Fractals, 40, 2576-2589. https://doi.org/10.1016/j.chaos.2007.10.051.

[10] Shams, M., & Vaezpour, S.M. (2009). Best approximation on probabilistic normed spaces. Chaos Solit. Fractals, 41, (4), 1661-1667. https://doi.org/10.1016/j.chaos.2008.07.009.

[11] Veeramani, P. (2001). Best approximation in fuzzy metric spaces. J. Fuzzy Math., 9, (1), 75-80.

[12] Vaezpour, S. M., & Karimi, F. (2008). t􀀀best approximation in fuzzy normed spaces. Iran. J. Fuzzy Syst., 5, (2), 93-99. https://doi.org/10.22111/ijfs.2008.338.

[13] Zadeh, L. A. (1965). Fuzzy sets. Inform. and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241.