Gradation of continuity for mappings between L-soft topological spaces

Year 2022, , 781 - 792, 15.07.2022

Vildan Çetkin

https://doi.org/10.17714/gumusfenbil.847795

Abstract

In this article, we aim to present the degrees of continuity, closedness and openness for a soft mapping which is defined between L-soft topological spaces, where L is a complete DeMorgan algebra. We propose the gradation of continuity for a soft mapping with the help of the soft closure operators and by considering the fuzzy soft inclusion which depends on the lattice implication. We also observe many characterizations and properties of the degree of the continuity. Then, we present the degree of openness for a soft mapping with help of the soft interior operators. At the end, we investigate the relations among the proposed concepts; the degree of continuity, closedness and openness in a natural way.

Keywords

Closure, Continuity, Fuzzy soft set, L-soft topology, Openness, Soft maping

L-esnek topolojik uzaylar arasındaki dönüşümler için sürekliliğin derecelendirmesi

Abstract

Bu çalışmada, L bir tam DeMorgan cebiri olmak üzere, L-esnek topolojik uzaylar arasında tanımlanan esnek dönüşümler için süreklilik, kapalılık ve açıklığın derecelendirmesini sunmayı amaçladık. Esnek kapanış operatörleri yardımıyla ve kafes gerektirme işlemine dayanan bulanık esnek içerme bağıntısının da dikkate alınmasıyla esnek bir dönüşüm için sürekliliğin derecelendirmesini ifade ettik. Ayrıca sürekliliğin bu derecelendirmesinin birçok karakterizasyonunu ve özelliğini gözlemledik. Daha sonra, esnek iç operatörlerinin yardımıyla esnek dönüşümler için açıklığın derecelendirmesini verdik. En sonunda, ifade edilen yapılar olan sürekliliğin, kapalılığın ve açıklığın derecelendirmeleri arasındaki ilişkileri doğal bir yolla inceledik.

Keywords

Kapanış, Süreklilik, Bulanık esnek küme, L-esnek topoloji, Açıklık, Esnek dönüşüm

References

• Ahmad, B., & Kharal, A. (2009). On fuzzy soft sets. Advances in Fuzzy Systems, 586507. https://doi.org/10.1155/2009/586507
• Al-jarrah, H. H., Rawshdeh, A., & Al-shami, T. M. (2022). On soft compact and soft Lindelöf spaces via soft regular closed sets. Afrika Mathematika, 33 (23) https://doi.org/10.1007/s13370-021-00952-z
• Aygünoğlu, A., & Aygün, H. (2009). Introduction to fuzzy soft group. Computers and Mathematics with Applications, 58, 1279-1286. https://doi.org/10.1016/j.camwa.2009.07.047
• Çetkin, V. (2014). Bulanık esnek topolojik yapılar [Doktora Tezi, Kocaeli Üniversitesi Fen Bilimleri Enstitüsü]. Çetkin, V., & Aygün, H. (2014). On fuzzy soft topogenous structure. Journal of Intelligent and Fuzzy Ssytems, 27, 247-255. https://doi.org/10.3233/IFS-130993
• Çetkin, V., & Aygün, H. (2016). On L-soft merotopies. Soft Computing, 20, 4779-4790. https://doi.org/10.1007/s00500-016-2037-x
• Çetkin, V. (2019). Parameterized degree of semi-precompactness in the fuzzy soft universe. Journal of Intelligent and Fuzzy Ssytems, 36, 3661–3670. https://doi.org/ 10.3233/JIFS-181830
• Çetkin, V. (2022). Bornological spaces in the context of fuzzy soft sets. Filomat, 36(4), 1341-1350. https://doi.org/10.2298/FIL2204341C
• Georgiou, D. N., Megaritis, A. C., & Petropoulos, V. I. (2013). On soft topological spaces, Applied Mathematics and Information Sciences, 7(5), 1889–1901. https://doi.org/10.12785/amis/070527
• Gierz, G. et al., (1980). A compendium of continuous lattices, Springer-Verlag, New York Heidelberg Berlin.
• Kharal, A., & Ahmad, B. (2009). Mappings on fuzzy soft classes. Advances in Fuzzy Systems, 407890. https://doi.org/10.1155/2009/407890
• Kocinac, Lj.D.R., Al-shami, T., & Çetkin, V. (2021). Selection principles in the context of soft sets: Menger spaces. Soft Computing, 25, 12693-12702. https://doi.org/10.1007/s00500-021-06069-6
• Liang, C.Y., & Shi, F. G. (2014). Degree of continuity for mappings of (L,M)-fuzzy topological spaces. Journal of Intelligent and Fuzzy Systems, 27, 2665–2677. https://doi.org/10.3233/IFS-141238
• Liu, Y. M., & Luo, M. K. (1997). Fuzzy topology, World Scientific Publication, Singapore.
• Maji, P. K., Biswas, R., & Roy, A. R. (2001). Fuzzy soft sets. Journal of Fuzzy Mathematics, 9(3), 589-602.
• Molodtsov, D. (1999). Soft set theory-first results. Computers and Mathematics with Applications, 37 (4/5), 19-31.
• Pang, B. (2014). Degrees of continuous mappings, open mappings, and closed mappings in L-fuzzifying topological spaces. Journal of Intelligent and .Fuzzy Systems, 27, 805–816. https: doi.org/10.3233/IFS-131038
• Roy, A. R., & Maji, P. K. (2007). A fuzzy soft set theoretic approach to decision making problems. Jourmal of Computational and Applied Mathematics, 203, 412–418. https.//doi.org/10.1016/j.cam.2006.04.008
• Tanay, B., & Kandemir, M. B. (2011). Topological structure of fuzzy soft sets, Computers and Mathematics with Applications, 61, 2952-2957. https://doi.org/10.1016/j.camwa.2011.03.056
• Terepeta, M. (2019). On separating axioms and similarity of soft topological spaces. Soft Computing, 23, 1049-1057. https://doi.org/10.1007/s00500-017-2824-z
• Varol, B. P., & Aygün, H. (2012). Fuzzy soft topology. Hacettepe Journal of Mathematics and Statistics, 41 (3). 407–419.
• Xiu, Z., & Li, Q. (2019). Degrees of L-continuity for mappings between L-topological spaces. Mathematics, 7, 1013; https://doi.org./10.3390/math7111013
• Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X