TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Analysis of operation on spherical fuzzy soft topology and its application

, * , ,

* Corresponding author · click or hover a name for details

pp. 2707–2732Vol. 28Issue 7October 2025DOI: 10.47974/JIM-2329XML
Received:
07 Jan 2025
Published Online:
06 Oct 2025
Article type:
Research Article
Language:
EN
Article no.:
JIM-2329
Pages:
2707–2732

Abstract

In this manuscript, we introduce the idea of operation approach on on spherical fuzzy soft topology (𝒮𝓕𝒮 𝒯) and analyse its characteristics in spherical fuzzy soft topological space. Also, we define 𝒮𝓕𝒮 g~-regular space and 𝒮𝓕𝒮 g~ regular operation in 𝒮𝓕𝒮 𝒯𝒮 and study certain results using 𝒮𝓕𝒮 g~-regular space and 𝒮𝓕𝒮 g~-regular operation. Using operation on 𝒮𝓕𝒮  topology, we bring forth the topological operators like 𝒮𝓕𝒮 g~-closure and 𝒮𝓕𝒮 g~-interior and analyse their characteristics. As an application of operation approach on 𝒮𝓕𝒮  topology, we present a decision making algorithm and provide an illustration. We also develop a python program for the proposed algorithm.

Keywords

Subject Classifications

54-0454A4054A0503E75

References

[1] L. A. Zadeh, “Fuzzy sets,” Inf. Control, vol. 8, no. 3, pp. 338–353 (1965).
[2] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets Syst., vol. 20, no. 1, pp. 87–96 (1986).
[3] R. R. Yager, “Pythagorean fuzzy subsets,” in Proc. 2013 Joint IFSA World Congr. NAFIPS Annu. Meet. (IFSA/NAFIPS), Edmonton, AB, Canada, pp. 57–61 (2023).
[4] B. C. Cuong and V. Kreinovich, “Picture fuzzy sets—a new concept for computational intelligence problems,” in Proc. Int. Conf. Fuzzy Syst. (FUZZ-IEEE), Hyderabad, India, pp. 1–6 (2023).
[5] F. K. Gundogdu and C. Kahraman, “Spherical fuzzy sets and spherical fuzzy TOPSIS method,” J. Intell. Fuzzy Syst., vol. 36, no. 1, pp. 337–352 (2019).
[6] D. Molodtsov, “Soft set theory—first results,” Comput. Math. Appl., vol. 37, pp. 19–31 (1999).
[7] P. K. Maji, R. Biswas, and A. R. Roy, “An application of soft sets in a decision making problem,” Comput. Math. Appl., vol. 44, pp. 1077–1083 (2002).
[8] P. K. Maji, R. Biswas, and A. R. Roy, “Fuzzy soft sets,” J. Fuzzy Math., vol. 9, no. 3, pp. 589–602 (2001).
[9] P. K. Maji, R. Biswas, and A. R. Roy, “Intuitionistic fuzzy soft sets,” J. Fuzzy Math., vol. 9, no. 3, pp. 677–692 (2001).
[10] X. Peng, Y. Yang, J. Song, and Y. Jiang, “Pythagorean fuzzy soft set and its application,” Comput. Eng., vol. 41, no. 7, pp. 224–229 (2015).
[11] Y. Yang, C. Liang, S. Ji, and T. Liu, “Adjustable soft discernibility matrix based on picture fuzzy soft sets and its applications in decision making,” J. Intell. Fuzzy Syst., vol. 29, no. 4, pp. 1711–1722 (2015).
[12] F. Perveen, J. J. Sunil, K. V. Babitha, and H. Garg, “Spherical fuzzy soft sets and its applications in decision-making problem,” J. Intell. Fuzzy Syst., vol. 37, no. 6, pp. 8237–8250 (2019).
[13] C. L. Chang, “Fuzzy topological spaces,” J. Math. Anal. Appl., vol. 24, no. 1, pp. 182–190 (1968).
[14] R. Lowen, “Fuzzy topological spaces and fuzzy compactness,” J. Math. Anal. Appl., vol. 56, no. 3, pp. 621–633 (1976).
[15] D. Çoker, “An introduction to intuitionistic fuzzy topological spaces,” Fuzzy Sets Syst., vol. 88, no. 1, pp. 81–89 (1997).
[16] D. Coker and A. Haydar Es, “On fuzzy compactness in intuitionistic fuzzy topological spaces,” J. Fuzzy Math., vol. 3, pp. 899–910 (1995).
[17] D. Coker and N. Turanli, “Fuzzy connectedness in intuitionistic fuzzy topological spaces,” Fuzzy Sets Syst., vol. 116, no. 3, pp. 369–375 (2000).
[18] M. Olgun, M. Unver, and S. Yardımcı, “Pythagorean fuzzy topological spaces,” Complex Intell. Syst., vol. 5, no. 2, pp. 177–183 (2019).
[19] M. Shabir and M. Naz, “On soft topological spaces,” Comput. Math. Appl., vol. 61, no. 8, pp. 1786–1799 (2011).
[20] B. Tanay and M. B. Kandemir, “Topological structure of fuzzy soft sets,” Comput. Math. Appl., vol. 61, no. 10, pp. 2952–2957 (2011).
[21] C. Gunduz and S. Bayramov, “Some results on fuzzy soft topological spaces,” Math. Probl. Eng., vol. 2013, Art. no. 835308.
[22] A. Aygunoglu, V. Cetkin, and H. Aygn, “An introduction to fuzzy soft topological spaces,” Hacet. J. Math. Stat., vol. 43, no. 2, pp. 193–204 (2014).
[23] T. Simsekler and S. Yuksel, “Fuzzy soft topological spaces,” Ann. Fuzzy Math. Inform., vol. 5, no. 1, pp. 87–96 (2013).
[24] I. Osmanoglu and D. Tokat, “On intuitionistic fuzzy soft topology,” Gen. Math. Notes, vol. 19, no. 2, pp. 59–70 (2013).
[25] S. Bayramov and C. Gunduz, “On intuitionistic fuzzy soft topological spaces,” TWMS J. Pure Appl. Math., vol. 5, no. 1, pp. 66–79 (2014).
[26] M. Riaz, K. Naeem, M. Aslam, D. Afzal, F. A. A. Almahdi, and S. S. Jamal, “Multi-criteria group decision making with Pythagorean fuzzy soft topology,” J. Intell. Fuzzy Syst., vol. 39, no. 5, pp. 6703–6720 (2020).
[27] H. Garg, F. Perveen PA, S. J. John, and L. Perez-Dominguez, “Spherical fuzzy soft topology and its application in group decision-making problems,” Math. Probl. Eng., vol. 2022, Art. no. 1007133.
[28] M. Riaz,S. Tanveer,D. Pamucar, and D. S. Qin, “Topological data analysis with spherical fuzzy soft AHP-TOPSIS for environmental mitigation system,” Mathematics, vol. 10, no. 11, p. 1826 (2022).
[29] S. Kasahara “Operation compact spaces,” Math. Japonica, vol. 24, no. 1, pp. 97–105 (1979).
[30] D. S. Jankovic, “On functions with α-closed graphs”, Glasnik Matematicki, vol. 18, no. 3, pp. 141–148 (1983).
[31] H. Ogata, “Operation on topological spaces and associated topology,” Math. Japonica, vol. 36, no. 1, pp. 175–184 (1991).
[32] H. Z. Ibrahim, On a class of α_γ-open sets in a topological space, Acta Sci. Technol., vol. 35, no. 3, pp. 539–545 (2013).
[33] B. Ahmad, T. Noiri and S. Hussain, “Properties of bi γ-operations on topological spaces”, Sci. Magna, vol. 4, no. 2, pp. 112–118 (2008).
[34] A. Al-omari and T. Noiri, “Generalizations of Lindelöf spaces via hereditary classes”, Acta Univ. Sapientiae Math., vol. 13, no. 2, pp. 281–291 (2021).
[35] N. Kalaivani, A. I. El-Maghrabi, D. Saravanakumar, and G. Sai Sundara Krishnan, “Operation-compact spaces, regular spaces and normal spaces with α-γ-open sets in topological spaces”, J. Interdiscip. Math., vol. 20, no. 2, pp. 427–441 (2017).
[36] H. Z. Ibrahim, “Weak forms of γ-open sets and new separation axioms”, Int. J. Sci. Eng. Res.,  
[37] C. K. Basu, B. M. Uzzal Afsan, and M. K. Ghosh, “A class of functions and separation axioms with respect to an operation”, Hacet. J. Math. Stat., vol. 38, no. 2, pp. 103–118 (2009).
[38] S. Tahiliani, “Operation approach to β-open sets and applications”, Math. Commun., vol. 16, no. 2, pp. 577–591 (2011).
[39] B. Roy, “Applications of operations on minimal generalized open sets”, Afr. Mat., vol. 29, pp. 1097–1104 (2018).
[40] C. Carpintero, N. Rajesh, and E. Rosas, “Operation approaches on b-open sets and applications”, Bol. Soc. Parana. Mat., vol. 30, no. 1, pp. 21–33 (2012).
[41] S. Hussain and B. Ahmad, “On Minimal gamma-Open Sets”, Eur. J. Pure Appl. Math., vol. 2, no. 3, pp. 338–351 (2009).
[42] A. Al-Omari and T. Noiri, “Properties of γH-compact spaces with hereditary classes”, Atti Accad. Pelor. Pericolanti - Cl. Sci. Fis. Mat. Nat., vol. 98, no. 2, p. 4 (2020).
[43] E. N. Rosas and J. O. Vielma, “Operator-compact and operator-connected spaces”, Sci. Math., vol. 1, no. 2, pp. 203–208 (1998).
[44] B. Ahmad and S. Hussain, “γ-Convergence in topological spaces”, Southeast Asian Bull. Math., vol. 29, no. 5, pp. 835–842 (2005).
[45] N. Kalaivani, D. Saravanakumar, and G. S. S. Krishnan, “On γ-operations in soft topological spaces”, Far East J. Math. Sci., vol. 101, pp. 2067–2077 (2017).
[46] S. S. Benchalli, P. G. Patil, and N. S. Kabbur, “On soft γ-operations in soft topological spaces”, J. New Theory, vol. 6, pp. 20–32 (2015). 
[47] S. A. El-Sheikh and S. El-Sayed, “ γ-operation & decomposition of some forms of fuzzy soft mappings on fuzzy soft ideal topological spaces”, Filomat, vol. 34, no. 1, pp. 187–196 (2020).
[48] B. A. Asaad, T. Al-shami, and E. Abo-Tabl, “Applications of some operators on supra topological spaces”, Demonstr. Math., vol. 53, no. 1, pp. 292–308 (2020).
[49] B. Roy and T. Noiri, “Applications of operations on generalized topological spaces”, Bull. Karaganda Univ., vol. 3, pp. 96–104 (2021).
[50] M. A. Hasan, N. M. Ali Abbas, and S. M. Khalil, “On soft α*-open sets and soft contra α*-continuous mappings in soft topological spaces,” J. Interdiscip. Math., vol. 24, no. 3, pp. 729–734 (2021), doi: 10.1080/09720502.2020.1861786.
[51] Q. H. Imran, K. S. Tanak, and A. H. M. Al-Obaidi, “On new concepts of neutrosophic crisp open sets,” J. Interdiscip. Math., vol. 25, no. 2, pp. 563–572 (2022), doi: 10.1080/09720502.2021.2012900.
[52] B. A. Asaad, T. M Al-shami, and A. Mhemdi, “Bioperators on soft topological spaces”, AIMS Math., vol. 6, no. 11, pp. 12471–12490 (2021).
[53] B. Das, J. Chakraborty, and B. Bhattacharya, “On fuzzy γμ-open sets in generalized fuzzy topological spaces”, Proyecciones (Antofagasta, Online), vol. 41, no. 3, pp. 733–749 (2022).
[54] S. F. Namiq, E. Rosas, and M. Salas-Brown, “New types of connected, component spaces and maximal open set via s-operation,” J. Interdiscip. Math., vol. 27, no. 3, pp. 481–495 (2024), doi: 10.47974/JIM-1723.
[55] W. M. Raoof and L. S. Abdalbaqi, “Supra v-open set and some of its properties,” J. Interdiscip. Math., vol. 27, no. 4, pp. 649–654 (2024), doi: 10.47974/JIM-1736.

Views: 287Downloads: 75Citations: 0