Fuzzy soft Hilbert spaces
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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
Keywords
- Fuzzy set
- fuzzy soft Hilbert space
- fuzzy soft inner product space
- fuzzy soft linear space
- fuzzy soft set
- soft set
MSC
References
-
[1]
S. Bayramov, C. Gunduz, Soft locally compact spaces and soft paracompact spaces, J. Math. Sys. Sci., 3 (2013), 122--130
-
[2]
T. Beaula, C. Gunaseeli, On fuzzy soft metric spaces, Malaya J. Mat., 2 (2014), 197--202
-
[3]
T. Beaula, M. M. Priyanga, A new notion for fuzzy soft normed linear space, Int. J. Fuzzy Math. Arch., 9 (2015), 81--90
-
[4]
T. Beaula, M. M. Priyanga, Fuzzy soft linear operator on fuzzy soft normed linear spaces, Int. J. App. Fuzzy Sets Art. Intell., 6 (2020), 73--92
-
[5]
S. Das, S. K. Samanta, On soft inner product spaces, Ann. Fuzzy Math. Inform., 6 (2013), 151--170
-
[6]
S. Das, S. K. Samanta, Soft Metric, Ann. Fuzzy Math. Inform., 6 (2013), 77--94
-
[7]
N. Faried, M. S. S. Ali, H. H. Sakr, Fuzzy soft inner product spaces, Appl. Math. Inf. Sci., 14 (2020), 709--720
-
[8]
C. Gunaseeli, Some Contributions to Special Fuzzy Topological Spaces, Ph.D. Thesis (Bharathidasan University), India (2012)
-
[9]
K. Hayat, M. I. Ali, J. C. R. Alcantud, B.-Y. Cao, K. U. Tariq, Best concept selection in design process: An application of generalized intuitionistic fuzzy soft sets, J. Intell. Fuzzy Syst., 35 (2018), 5707--5720
-
[10]
A. Z. Khameneh, A. Kiliçman, A. R. Salleh, Parameterized norm and parameterized fixed-point theorem by using fuzzy soft set theory, arXiv, 2013 (2013), 15 pages
-
[11]
J. Mahanta, P. K. Das, Fuzzy soft topological spaces, J. Intell. Fuzzy Syst., 32 (2017), 443--450
-
[12]
T. Mahmood, M. I. Ali, M. A. Malik, W. Ahmed, On lattice ordered intuitionistic fuzzy soft sets, Int. J. Algebra Stat., 7 (2018), 46--61
-
[13]
P. K. Maji, R. Biswas, A. R. Roy, Intuitionistic fuzzy soft sets, J. Fuzzy Math., 9 (2001), 677--692
-
[14]
P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555--562
-
[15]
D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19--31
-
[16]
T. J. Neog, D. K. Sut, G. C. Hazarika, Fuzzy soft topological spaces, Int. J. Latest Trend Math., 2 (2012), 54--67
-
[17]
N. Sultana, N. Rani, M. I. Ali, A. Hussain, Soft translations and soft extensions of BCI/BCK-algebras, Sci. World J., 2014 (2014), 6 pages
-
[18]
M. I. Yazar, C. G. Aras, S. Bayramov, Results on soft Hilbert spaces, TWMS J. App. Eng. Math., 9 (2019), 159--164
-
[19]
M. I. Yazar, T. Bilgin, S. Bayramov, C. Gunduz, A new view on soft normed spaces, Int. Math. For., 9 (2014), 1149--1159
-
[20]
L. A. Zadeh, Fuzzy set, Information and Control, 8 (1965), 338--53