Soft order topology and graph comparison based on soft order

Kemal Taşköprü; Kemal Taşköprü

doi:10.3934/math.2023492

AIMS Mathematics

2023, Volume 8, Issue 4: 9761-9781. doi: 10.3934/math.2023492

Previous Article Next Article

Research article

Soft order topology and graph comparison based on soft order

Kemal Taşköprü ^,

Department of Mathematics, Faculty of Science, Bilecik Şeyh Edebali University, Bilecik 11100, Turkey

Received: 11 December 2022 Revised: 07 February 2023 Accepted: 15 February 2023 Published: 21 February 2023
MSC : 03E72, 06F30, 05C90

Soft sets provide a suitable framework for representing and dealing with vagueness. A scenario for vagueness can be that alternatives are composed of specific factors and these factors have specific attributes. Towards this scenario, this paper introduces soft order and its associated order topology on the soft sets with a novel approach. We first present the definitions and properties of the soft order relations on the soft sets via soft elements. Next, we define soft order topology on any soft set and provide some properties of this topology. In order to implement what we introduced about the soft orders, we describe soft preference and soft utility mapping on the soft sets and we finally demonstrate a decision-making application over the soft orders intended for comparing graphs.
- soft order,
- soft order topology,
- soft preference,
- soft utility,
- graph comparison
Citation: Kemal Taşköprü. Soft order topology and graph comparison based on soft order[J]. AIMS Mathematics, 2023, 8(4): 9761-9781. doi: 10.3934/math.2023492

Related Papers:

Abstract

Soft sets provide a suitable framework for representing and dealing with vagueness. A scenario for vagueness can be that alternatives are composed of specific factors and these factors have specific attributes. Towards this scenario, this paper introduces soft order and its associated order topology on the soft sets with a novel approach. We first present the definitions and properties of the soft order relations on the soft sets via soft elements. Next, we define soft order topology on any soft set and provide some properties of this topology. In order to implement what we introduced about the soft orders, we describe soft preference and soft utility mapping on the soft sets and we finally demonstrate a decision-making application over the soft orders intended for comparing graphs.

References

[1]	D. Molodtsov, Soft set theory-first results, Comput. Math. Appl., 37 (1999), 19–31. http://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
[2]	M. I. Ali, M. Shabir, F. Feng, Representation of graphs based on neighborhoods and soft sets, Int. J. Mach. Learn. Cyber., 8 (2017), 1525–1535. http://doi.org/10.1007/s13042-016-0525-z doi: 10.1007/s13042-016-0525-z
[3]	M. B. Kandemir, The concept of $\sigma$-algebraic soft set, Soft Comput., 22 (2018), 4353–43607. http://doi.org/10.1007/s00500-017-2901-3 doi: 10.1007/s00500-017-2901-3
[4]	E. Aygün, H. Kamacı, Some generalized operations in soft set theory and their role in similarity and decision making, J. Intell. Fuzzy Syst., 36 (2019), 6537–6547. http://doi.org/10.3233/JIFS-182924 doi: 10.3233/JIFS-182924
[5]	V. Çetkin, E. Güner, H. Aygün, On 2S-metric spaces, Soft Comput., 24 (2020), 12731–12742. http://doi.org/10.1007/s00500-020-05134-w doi: 10.1007/s00500-020-05134-w
[6]	S. A. Ghour, W. Hamed, On two classes of soft sets in soft topological spaces, Symmetry, 12 (2020), 265. http://doi.org/10.3390/sym12020265 doi: 10.3390/sym12020265
[7]	J. C. R. Alcantud, Soft open bases and a novel construction of soft topologies from bases for topologies, Mathematics, 8 (2020), 672. http://doi.org/10.3390/math8050672 doi: 10.3390/math8050672
[8]	J. C. R. Alcantud, An operational characterization of soft topologies by crisp topologies, Mathematics, 9 (2021), 1656. http://doi.org/10.3390/math9141656 doi: 10.3390/math9141656
[9]	G. Muhiuddin, D. Al-Kadi, K. P. Shum, A. M. Alanazi, Generalized ideals of BCK/BCI-algebras based on fuzzy soft set theory, Adv. Fuzzy Syst., 2021 (2021), 8869931. http://doi.org/10.1155/2021/8869931 doi: 10.1155/2021/8869931
[10]	İ. Zorlutuna, Soft set-valued mappings and their application in decision making problems, Filomat, 35 (2021), 1725–1733. http://doi.org/10.2298/FIL2105725Z doi: 10.2298/FIL2105725Z
[11]	T. M. Al-shami, E. A. Abo-Tabl, Soft $\alpha$-separation axioms and $\alpha$-fixed soft points, AIMS Math., 6 (2021), 5675–5694. http://doi.org/10.3934/math.2021335 doi: 10.3934/math.2021335
[12]	S. A. Ghour, On soft generalized $\omega$-closed sets and soft $T_{1/2}$ spaces in soft topological spaces, Axioms, 11 (2022), 194. http://doi.org/10.3390/axioms11050194 doi: 10.3390/axioms11050194
[13]	G. Ali, M. N. Ansari, Multiattribute decision-making under Fermatean fuzzy bipolar soft framework, Granular Comput., 7 (2022), 337–352. http://doi.org/10.1007/s41066-021-00270-6 doi: 10.1007/s41066-021-00270-6
[14]	T. M. Al-shami, J. C. R. Alcantud, A. Mhemdi, New generalization of fuzzy soft sets: $(a, b)$-fuzzy soft sets, AIMS Math., 8 (2023), 2995–3025. http://doi.org/10.3934/math.2023155 doi: 10.3934/math.2023155
[15]	S. Das, S. K. Samanta, Soft real sets, soft real numbers and their properties, J. Fuzzy Math., 20 (2012), 551–576.
[16]	S. Das, S. K. Samanta, On soft metric spaces, J. Fuzzy Math., 21 (2013), 707–734.
[17]	A. Ç. Güler, E. D. Yıldırım, O. B. Özbakır, A fixed point theorem on soft $G$-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 885–894. http://doi.org/10.22436/jnsa.009.03.18 doi: 10.22436/jnsa.009.03.18
[18]	M. Chiney, S. K. Samanta, Soft topology redefined, J. Fuzzy Math., 27 (2019), 459–486.
[19]	İ. Altıntaş, K. Taşköprü, Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping, Turk. J. Math., 44 (2020), 2199–2216. http://doi.org/10.3906/mat-2004-63 doi: 10.3906/mat-2004-63
[20]	K. Taşköprü, İ. Altıntaş, A new approach for soft topology and soft function via soft element, Math. Meth. Appl. Sci., 44 (2021), 7556–7570. http://doi.org/10.1002/mma.6354 doi: 10.1002/mma.6354
[21]	İ. Altıntaş, K. Taşköprü, B. Selvi, Countable and separable elementary soft topological space, Math. Meth. Appl. Sci., 44 (2021), 7811–7819. http://doi.org/10.1002/mma.6976 doi: 10.1002/mma.6976
[22]	İ. Demir, Some soft topological properties and fixed soft element results in soft complex valued metric spaces, Turk. J. Math., 45 (2021), 971–987. http://doi.org/10.3906/mat-2101-15 doi: 10.3906/mat-2101-15
[23]	İ. Altıntaş, K. Taşköprü, P. Esengul kyzy, Soft partial metric spaces, Soft Comput., 26 (2022), 8997–9010. http://doi.org/10.1007/s00500-022-07313-3 doi: 10.1007/s00500-022-07313-3
[24]	D. S. Bridges, G. B. Mehta, Representations of preferences orderings, Springer, 1995. http://dx.doi.org/10.1007/978-3-642-51495-1
[25]	S. Barberà, P. J. Hammond, C. Seidl, Handbook of utility theory, Springer, 1999.
[26]	G. Herden, G. B. Mehta, The Debreu Gap Lemma and some generalizations, J. Math. Econ., 40 (2004), 747–769. http://doi.org/10.1016/j.jmateco.2003.06.002 doi: 10.1016/j.jmateco.2003.06.002
[27]	M. J. Campión, J. C. Candeal, E. Induráin, Preorderable topologies and order-representability of topological spaces, Topol. Appl., 156 (2009), 2971–2978. http://doi.org/10.1016/j.topol.2009.01.018 doi: 10.1016/j.topol.2009.01.018
[28]	Ö. Evren, E. A. Ok, On the multi-utility representation of preference relations, J. Math. Econ., 47 (2011), 554–563. http://doi.org/10.1016/j.jmateco.2011.07.003 doi: 10.1016/j.jmateco.2011.07.003
[29]	J. C. R. Alcantud, G. Bosi, M. Zuanon, Richter-Peleg multi-utility representations of preorders, Theory Decis., 80 (2016), 443–450. http://doi.org/10.1007/s11238-015-9506-z doi: 10.1007/s11238-015-9506-z
[30]	A. F. Beardon, Topology and preference relations, Springer, 2020. http://doi.org/10.1007/978-3-030-34226-5-1
[31]	M. I. Ali, T. Mahmood, M. M. U. Rehman, M. F. Aslam, On lattice ordered soft sets, Appl. Soft Comput., 36 (2015), 499–505. http://doi.org/10.1016/j.asoc.2015.05.052 doi: 10.1016/j.asoc.2015.05.052
[32]	A. Ali, M. I. Ali, N. Rehman, A more efficient conflict analysis based on soft preference relation, J. Intell. Fuzzy Syst., 34 (2018), 283–293. http://doi.org/10.3233/JIFS-171172 doi: 10.3233/JIFS-171172
[33]	M. A. Qamar, N. Hassan, $Q$-neutrosophic soft relation and its application in decision making, Entropy, 20 (2018), 1–14. http://doi.org/10.3390/e20030172 doi: 10.3390/e20030172
[34]	R. S. Kanwal, M. Shabir, Rough approximation of a fuzzy set in semigroups based on soft relations, Comput. Appl. Math., 38 (2019), 89. http://doi.org/10.1007/s40314-019-0851-3 doi: 10.1007/s40314-019-0851-3
[35]	M. E. El-Shafei, T. M. Al-shami, Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem, Comput. Appl. Math., 39 (2020), 138. http://doi.org/10.1007/s40314-020-01161-3 doi: 10.1007/s40314-020-01161-3
[36]	O. Dalkılıç, Relations on neutrosophic soft set and their application in decision making, J. Appl. Math. Comput., 67 (2021), 257–273. http://doi.org/10.1007/s12190-020-01495-5 doi: 10.1007/s12190-020-01495-5
[37]	O. Dalkılıç, N. Demirtaş, A novel perspective for $Q$-neutrosophic soft relations and their application in decision making, Artif. Intell. Rev., 56 (2022), 1493–1513. http://doi.org/10.1007/s10462-022-10207-3 doi: 10.1007/s10462-022-10207-3
[38]	G. Yaylalı, N. Ç. Polat, B. Tanay, Soft intervals and soft ordered topology, CBU Fen Derg., 13 (2017), 81–89. http://doi.org/10.18466/cbayarfbe.302645 doi: 10.18466/cbayarfbe.302645
[39]	T. M. Al-Shami, M. E. El-Shafei, M. Abo-Elhamayel, On soft topological ordered spaces, J. King Saud Univ. Sci., 31 (2019), 556–566. http://doi.org/10.1016/j.jksus.2018.06.005 doi: 10.1016/j.jksus.2018.06.005
[40]	T. M. Al-Shami, M. E. El-Shafei, Two new forms of ordered soft separation axioms, Demonstr. Math., 53 (2020), 8–26. http://doi.org/10.1515/dema-2020-0002 doi: 10.1515/dema-2020-0002
[41]	S. Jafari, A. E. F. El-Atik, R. M. Latif, M. K. El-Bably, Soft topological spaces induced via soft relations, WSEAS Trans. Math., 20 (2021), 1–8. http://doi.org/10.37394/23206.2021.20.1 doi: 10.37394/23206.2021.20.1
[42]	K. Taşköprü, E. Karaköse, A soft set approach to relations and its application to decision making, Math. Sci. Appl. E-Notes, 11 (2023), 1–13. http://doi.org/10.36753/mathenot.1172408 doi: 10.36753/mathenot.1172408
[43]	N. M. Kriege, F. D. Johansson, C. Morris, A survey on graph kernels, Appl. Network Sci., 5 (2020), 1–42. http://doi.org/10.1007/s41109-019-0195-3 doi: 10.1007/s41109-019-0195-3

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)