On the Pasting Lemma on a Fuzzy Soft Topological Space with Mixed Structure

Year 2020, Volume: 8 Issue: 2, 15 - 20, 15.10.2020

Nihal Taş

https://doi.org/10.36753/mathenot.647458

Cited By: 1

Abstract

In this paper, we define the notion of a $(\upsilon _{1},\upsilon _{2})$-$g$-closed fuzzy soft set on a fuzzy soft topological space. Using this notion, we investigate some properties of a $(\upsilon _{1},\upsilon _{2})$-$g$-closed fuzzy soft set and prove a new version of the "Pasting Lemma" with mixed structure.                                                                                                                                                                                                                                                                                                           

Keywords

Pasting lemma, Fuzzy soft topological space, $(\upsilon _{1},\upsilon _{2})$-$g$-closed fuzzy soft set, Mixed structure

References

• [1] Açıkgöz, A., Ta¸s, N.: Some new mixed soft sets. Mathematical Sciences and Applications E-Notes. 2 (2), 105-118 (2014).
• [2] Açıkgöz, A., Ta¸s, N. A., Noiri, T.: A decomposition of some types of mixed soft continuity in soft topological spaces. Filomat. 30 (2), 379-385 (2016).
• [3] Ahmad, B., Kharal, A.: On fuzzy soft sets. Advances in Fuzzy Systems. 2009, 6 pages, Article ID 586507 (2009).
• [4] Alcantud, J. C. R., Rambaud, S. C., Torrecillas, M. J. M.: Valuation fuzzy soft sets: a flexible fuzzy soft set based decision making procedure for the valuation of assets. Symmetry 9 (11), 253 (2017).
• [5] Anitha, M., Selvi, R., Thangavelu, P.: Pasting lemmas for g-continuous functions. Missouri Journal of Mathematical Sciences. 21 (1), 28-33 (2009).
• [6] Björn, A. Martio, O.: Pasting lemmas and characterizations of boundary regularity for quasiminimizers. Results in Mathematics. 55, 265-279 (2009).
• [7] Csaszar, A.: Mixed constructions for generalized topologies. Acta Mathematica Hungarica. 122 (1-2), 153-159 (2009).
• [8] Demir, İ., Özbakır, O. B.: Some properties of fuzzy soft proximity spaces. The Scientific World Journal. 2015, 10 pages, Article ID 752634 (2015).
• [9] Demir. İ., Özbakır, O. B.: An extension of Lowen’s uniformity to the fuzzy soft sets. Konuralp Journal of Mathematics. 6 (2), 321-331 (2018).
• [10] Ergül, Z. G., Yüksel, ¸S.: A new type of soft covering based rough sets applied to multicriteria group decision making for medical diagnosis. Mathematical Sciences and Applications E-Notes. 7 (1), 28-38 (2019).
• [11] Gnanambal, Y., Balachandran, K.: On gpr-continuous functions in topological spaces. Indian Journal of Pure and Applied Mathematics. 30 (6), 581-593 (1999).
• [12] İrkin, R., Özgür, N. Y., Taş, N.: Optimization of lactic acid bacteria viability using fuzzy soft set modelling. An International Journal of Optimization and Control: Theories and Applications (IJOCTA). 8 (2), 266-275 (2018).
• [13] Kalaichelvi, Dr. A., Malini, P. H.: Application of fuzzy soft sets to investment decision making problem. International Journal of Mathematical Sciences and Applications. 1 (3), 1583-1586 (2011).
• [14] Kannan, K., Rao, K. C.: Pasting lemmas for some continuous functions. Thai Journal of Mathematics. 12 (1), 245-249 (2014).
• [15] Karaca, F., Taş, N.: Decision making problem for life and non-life insurances. Journal of Balıkesir University Institute of Science and Technology. 20 (1), 572-588 (2018).
• [16] Mahanta, J., Das, P. K.: Results on fuzzy soft topological spaces. arXiv:1203.0634v1, (2012).
• [17] Maji, P. K., Biswas, R., Roy, A. R.: Fuzzy soft sets. The Journal of Fuzzy Mathematics. 9 (3), 589-602 (2001).
• [18] Molodtsov, D.: Soft set theory - first results. Computer Mathematics and its Applications. 37 (4-5), 19-31 (1999).
• [19] Mukherjee, P., Park, C.: On fuzzy soft Bitopological spaces. Mathematics and Computer Sciences Journal. 10 (7), 1-8 (2015).
• [20] Nazmul, S., Samanta, S. K.: Soft topological soft groups. Mathematical Sciences. 6 (1), 66 (2012).
• [21] Özgür, N. Y., Taş, N.: A note on “application of fuzzy soft sets to investment decision making problem”. Journal of New Theory 7, 1-10 (2015).
• [22] Tanay, B., Kandemir, M. B.: Topological structure of fuzzy soft sets. Computer Mathematics and its Applications 61 (10), 2952-2957 (2011).
• [23] Tas, N. A., Özbakır, O. B.: On some mixed types of continuity on generalized neighborhood systems. Journal of Advanced Studies in Topology. 5 (2), 32-43 (2014).
• [24] Taş, N., Özgür, N. Y., Demir, P.: An application of soft set and fuzzy soft set theories to stock management, Süleyman Demirel University Journal of Natural and Applied Sciences. 21 (2), 791-196 (2017).
• [25] Taş, N.: Two new versions of the pasting lemma via soft mixed structure (submitted).
• [26] Tozlu, N., Yüksel, Ş.: Soft A-sets and soft B-sets in soft topological spaces. Mathematical Sciences and Applications E-Notes. 5 (2), 17-25 (2017).
• [27] Varol, B. P., Aygün, H.: Fuzzy soft topology. Hacettepe Journal of Mathematics and Statistics. 41 (3), 407-419 (2012).
• [28] Zadeh, L. A.: Fuzzy sets. Information and Control. 8, 338-353 (1965).