Fuzzy Farthest Points and Fuzzy Best Approximation Points in Fuzzy Normed Spaces

Subject Areas : Applied Mathematics

Hamid Mazaheri Tehrani ¹ , S. M Mouavi Shams Abad ² , M. A Dehghan ³ , Z. Bizhanzadeh ⁴

1 - Faculty of Mathematics, Yazd University, Yazd, Iran
2 - Faculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan, Iran
3 - Faculty of Mathematics, Vali-e-asr University of Rafsenjan, Rafsenjan, Iran
4 - Faculty of Mathematics, Yazd University, Yazd, Iran

Received: 2018-06-14 Accepted : 2019-02-23 Published : 2019-05-01

Keywords: Fuzzy farthest orthogonality, Fuzzy farthest points, Fuzzy best approximation points, Normed fuzzy space,

Abstract :

In this paper we define fuzzy farthest points, fuzzy best approximation points and farthest orthogonality in fuzzy normed spaces and we will find some results. We prove some existence theorems, also we consider fuzzy Hilbert and show every nonempty closed and convex subset of a fuzzy Hilbert space has an unique fuzzy best approximation.It is well know that the conception of fuzzy sets, firstly defined by Zadeh in 1965. Fuzzy set theory provides us with a framework which is wider than that of classical set theory. Various mathematical structures, whose features emphasize the effects of ordered structure, can be developed on the theory. The theory of fuzzy sets has become an area of active research for the last forty years. On the other hand, the notion of fuzzyness has a wide application in many areas of science and engineering, chaos control, nonlinear dynamical systems, etc. In physics, for example, the fuzzy structure of space time is followed by the fat that in strong quantum gravity regime space time points are determined in a fuzzy manner.

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