Certain properties of soft multi-set topology with applications in multi-criteria decision making

Muhammad  Riaz; Naim Çagman; Nabeela Wali; Amna Mushtaq

doi:10.31181/dmame2003070r

Authors

Muhammad Riaz Department of Mathematics, University of the Punjab, Lahore, Pakistan
Naim Çagman Department of Mathematics, Tokat Gaziosmanpasa University, Tokat, Turkey
Nabeela Wali Department of Mathematics, University of the Punjab, Lahore, Pakistan
Amna Mushtaq Department of Mathematics, University of the Punjab, Lahore, Pakistan

DOI:

https://doi.org/10.31181/dmame2003070r

Keywords:

Soft multi-sets; soft multi-set topology; aggregation operators, algorithms; MCDM

Abstract

The aim of this paper is to introduce the notion of soft multi-set topology (SMS-topology) defined on a soft multi-set (SMS). Soft multi-set and soft multi-set topology are fundamental tools in computational intelligence, which have a large number of applications in soft computing, fuzzy modeling and decision-making under uncertainty. The idea of power whole multi-subsets of a SMS is defined to explore various rudimentary properties of SMS-topology. Certain properties of SMS-topology like SMS-basis, MS-subspace, SMS-interior, SMS-closure and boundary of SMS are explored. Furthermore, the multi-criteria decision-making (MCDM) algorithms with aggregation operators based on SMS-topology are established. Algorithm i (i = 1, 2, 3) are developed for the selection of best alternative for biopesticides, for the selection of best textile company, for the award of performance, respectively. Some real life applications of the proposed algorithms in MCDM problems are illustrated by numerical examples. The the reliability and feasibility of proposed MCDM techniques is shown by comparison analysis with some existing techniques.

Downloads

Download data is not yet available.

References

Ali M.I. (2011). A note on soft sets, rough soft sets and fuzzy soft sets, Applied Soft Computing, 11, 3329-3332.

Ali M.I., Feng F., Liu X. Y., Min W. K. & Shabir M. (2009). On some new operations in soft set theory, Computers and Mathematics with Applications, 57, 1547-1553.

Alkhazaleh S., Salleh A. R., & Hassan N., Soft Multisets Theory, Applied Mathematical Sciences, 5(72), 3561-3573.

Atanassov K.T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96.

Babitha K.V. & John S.J. (2013). On soft multi-set, Annals of Fuzzy Mathematics and Informatics, 5(1), 35-44.

Balami H.M. & Ibrahim A.M. (2013). Soft multiset and its application in information system, International Journal of scientific research and management, 1(9), 471-481.

Blizard W.D. (1989). Multiset theory, Notre Dame Journal of Formal Logic, 30, 36-65.

C¸ a˘gman N., Karata¸s S. & Enginoglu S. (2011) Soft topology, Computers and Mathematics with Applications, 62, 351-358.

C¸ a˘gman N., Enginoglu S & C¸ itak F. (2011). Fuzzy soft set theory and its applications, Iranian Journal of Fuzzy Systems, 8(8), 137-147.

C¸ a˘gman N., C¸ itak F. & Enginoglu S. (2011), FP-soft set theory and its applications, Annals of Fuzzy Mathematics and Informatics, 2(2), 219-226.

Chen D. (2005). The parametrization reduction of soft sets and its applications, Computers and Mathematics with Applications, 49, 757-763.

Feng F., Li C., Davvaz B. & Ali M.I. (2010), Soft sets combined with fuzzy sets and rough sets, a tentative approach, Soft Computing, 14(9), 899-911.

Feng F., Liu X.Y., Leoreanu-Fotea V. & Jun Y.B. (2011). Soft sets and soft rough sets, Information Sciences, 181(6), 1125-1137.

Feng F., Fujita H., Ali M. I. & Yager R.R., Life Fellow IEEE. & X.Y. Liu (2018). Another view on generalized intuitionistic fuzzy soft sets and related multiattribute decision making methods IEEE Transactions On Fuzzy Systems, 1-15.

Garg H. & Rani D. (2019). A robust correlation coefficient measure of complex intuitionistic fuzzy sets and their applications in decision-making, Applied Intelligence, 49, 496-512.

K. P. Girish and S. J. John, General relations between partially ordered multi-sets and their chains and antichains, Math. Commun. 14(2)(2009), 193-206.

Girish K.P. & John S.J. (2012), On multi-set topologies, Theory and Applications of Mathematics and Computer Science, 2(1), 37-52.

Gorzalzany M. B. (1987). A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21, 1-17.

Hashmi M.R., Riaz M. & Smarandache F. (2020), m-polar neutrosophic topology with applications to multi-criteria decision-making in medical diagnosis and clustering analysis, International Journal of Fuzzy Systems, 22(1), 273-292.

Karaaslan F. & Hunu F. (2020). Type-2 single-valued neutrosophic sets and their applications in multi-criteria group decision making based on TOPSIS method. Journal of Ambient Intelligence Humanized Computing, Doi.org/10.1007/s12652-020-01686-9.

Kumar K. & Garg H. (2018). TOPSIS method based on the connection number of set pair analysis under interval-valued intuitionistic fuzzy set environment, Computational & Applied Mathematics, 37(2), 1319-1329.

Kumar K.R. & Naisal S.A. (2016). Interior exterior and boundary of fuzzy soft multi topology in decision making, International Conference on Control, Instrumentation, Communication and Computational Technologies, (ICCICCT 2016).

Mahanta J. & D. Das. (2015). Boundary and exterior of a multiset topology, Math.GM, arXiv:1501.07193v1.

Maji P.K. Roy A.R. & Biswas R. (2002). An application of soft sets in a decision making problem, Computers and Mathematics with Applications, 44(8-9), 1077-1083.

Maji P.K. Roy A.R. & Biswas R. (2003). Soft set theory, Computers and Mathematics with Applications, 45(4-5), 555-562.

Molodtsov D. (1999). Soft set theory-first results, Computers and Mathematics with Applications, 37(4-5), 19-31.

Mukherjee A., Das A. K. & Saha A. (2014). Topological structure formed by soft multi sets and soft multi compact space, Annals of Fuzzy Mathematics and Informatics, 7(6), 919-933.

Naeem K., Riaz M., Peng X.D. & Afzal D. (2019). Pythagorean fuzzy soft MCGDM methods based on TOPSIS, VIKOR and aggregation operators, Journal of Intelligent & Fuzzy Systems, 37(5), 6937-6957.

Pawlak Z. (1982). Rough sets, International Journal of Computer & Information Sciences, 11, 341-356.

Peng X.D. & Yang Y. (2015). Some results for Pythagorean fuzzy sets, International Journal of Intelligent Systems, 30(11), 1133-1160.

Peng X.D., Yuan H.Y. & Yang Y. (2017). Pythagorean fuzzy information measures and their applications, International Journal of Intelligent Systems, 32(10), 991-1029.

Pie D. & Miao D. (2005). From soft sets to information system, Granular Computing 2005 IEEE Inter. Conf. 2, 617-621.

Riaz M., C¸ a˘gman N., Zareef I. & Aslam M. (2019). N-soft topology and its applications to multi-criteria group decision making, Journal of Intelligent & Fuzzy Systems, 36(6), 6521-6536.

Riaz M., Davvaz B., Fakhar A. & Firdous F. (2020). Hesitant fuzzy soft topology and its applications to multi-attribute group decision-making, Soft Computing, DOI:10.1007/s00500-020-04938-0.

Riaz M. & Hashmi M.R. (2019). Linear Diophantine fuzzy set and its applications towards multi-attribute decision making problems, Journal of Intelligent & Fuzzy Systems, 37(4), 5417-5439.

Riaz M. & Tehrim S.T. (2019), Bipolar fuzzy soft mappings with application to bipolar disorder, International Journal of Biomathematics, 12(7), 1-31.

Riaz N. & Tehrim S.T. (2020), Cubic bipolar fuzzy set with application to multi-criteria group decision making using geometric aggregation operators, Soft Computing, DOI.10.1007/s00500-020-04927-3.

Roy R. & Maji P. K. (2007). A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics 203(2), 412-418.

Shabir M. & Naz M. (2011). On soft topological spaces, Computers and Mathematics with Applications, 61, 1786-1799.

Syropoulos A. (2001). Mathematics of Multisets, GR-671 00 Xanith, GREECE 347-358.

Tokat D. & Osmanoglu I. (2011). Soft multi set and soft multi topology, Nevsehir Universitesi Fen Bilimleri Enstitusu Dergisi Cilt, 2, 109-118.

Tokat D. & Osmanoglu I. (2013). Connectedness on Soft multi topological spaces, Journal of New Results in Sciences, 2, 8-18.

Yager R.R. & Abbasov A. M. (2013). Pythagorean membership grades, complex numbers, and decision making, International Journal of Intelligent Systems, 28(5), 436-452.

Yager R.R. (2014). Pythagorean membership grades in multi-criteria decision making, IEEE Transactions on Fuzzy Systems, 22(4), 958-965.

Yager R.R. (2017). Generalized Orthopair Fuzzy sets, IEEE Transactions on Fuzzy Systems, 25(5), 1220-1230.

Zadeh L.A. (1965), Fuzzy sets, Information and Control, 8, 338-353.

Zhang X. L. & Xu Z. S. (2014). Extension of TOPSIS to multiple criteria decision making with pythagorean fuzzy sets, International Journal of Intelligent Systems, 29(12), 1061-1078.

Zhan J., Liu Q. & Davvaz B. (2015). A new rough set theory: rough soft hemirings, Journal of Intelligent and Fuzzy Systems, 28(4)(2015), 1687-1697.

Zhan J. & Alcantud J.C.R. (2019). A novel type of soft rough covering and its application to multi-criteria group decision-making, Artificial Intelligence Review, 52, 2381-2410.

Zhang W. R. (1994). Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference, 305-309.