Fuzzy L\(^P\) -Spaces

Marzieh Shams Yousef\(^{a,*}\), Forouzan Farahrooz\(^b\)

\(^a\)Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
\(^b\)Department of Mathematics, Payame Noor University, Tehran, Iran.

Correspondence should be addressed to: mmaths@gmail.com

Copyright © 2022 Shams Yousef, Forouzan Farahrooz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: : 20 April 2021; Accepted: 3 May 2022; Published Online: 7 June 2022.

Abstract

The purpose of this paper is to introduce the fuzzy L\(^P\)-Spaces. We give some basic definitions and main properties of fuzzy spaces. The fuzzy Holder’s inequality will be proved. Also we show that the dual offuzzy L\(^P\)-spaces is fuzzy L\(^q\)-spaces, where the scalars p and q are conjugate exponents.

Keywords:

α-cut, Fuzzy functions, Hausdorff distance, Fuzzy L\(^P\)-Spaces.