Fuzzy soft Hilbert spaces

Volume 22, Issue 2, pp 142--157 http://dx.doi.org/10.22436/jmcs.022.02.06
Publication Date: July 18, 2020 Submission Date: January 26, 2020 Revision Date: April 10, 2020 Accteptance Date: June 15, 2020

Authors

Nashat Faried - Department of Mathematics, Faculty of Science, Ain Shams University, 11566 Cairo, Egypt. Mohamed S.S. Ali - Department of Mathematics, Faculty of Education, Ain Shams University, 11341 Cairo, Egypt. Hanan H. Sakr - Department of Mathematics, Faculty of Education, Ain Shams University, 11341 Cairo, Egypt.


Abstract

In this work, we define the fuzzy soft Hilbert space \(\tilde{H}\) based on the definition of the fuzzy soft inner product space \((\tilde{U},\widetilde{<\cdot,\cdot>})\), introduced by Faried {et al.} [{N. Faried, M. S. S. Ali, H. H. Sakr, Appl. Math. Inf. Sci., {\bf 14} (2020), 709--720}], in terms of the fuzzy soft vector \(\tilde{v}_{f_{G(e)}}\). Moreover, we show that \(\mathbb{C}^{n}(A)\), \(\mathbb{R}^{n}(A)\) and \(\ell_{2}(A)\) are suitable examples of fuzzy soft Hilbert spaces. In addition, it is proved that the fuzzy soft orthogonal complement of any non-empty fuzzy soft subset of \(\tilde{H}\) is a fuzzy soft closed fuzzy soft subspace of \(\tilde{H}\) and we study some of the fuzzy soft Hilbert spaces properties and some of the fuzzy soft inner product spaces properties. Furthermore, we introduce the definition of the fuzzy soft orthogonal family and the fuzzy soft orthonormal family and introduce examples satisfying them. Moreover, we present the fuzzy soft Bessel's inequality and the fuzzy soft Parseval's formula in this generalized setting.


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ISRP Style

Nashat Faried, Mohamed S.S. Ali, Hanan H. Sakr, Fuzzy soft Hilbert spaces, Journal of Mathematics and Computer Science, 22 (2021), no. 2, 142--157

AMA Style

Faried Nashat, Ali Mohamed S.S., Sakr Hanan H., Fuzzy soft Hilbert spaces. J Math Comput SCI-JM. (2021); 22(2):142--157

Chicago/Turabian Style

Faried, Nashat, Ali, Mohamed S.S., Sakr, Hanan H.. "Fuzzy soft Hilbert spaces." Journal of Mathematics and Computer Science, 22, no. 2 (2021): 142--157


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