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Year 2023, Volume: 11 Issue: 1, 1 - 13, 28.03.2023
https://doi.org/10.36753/mathenot.1172408

Abstract

References

  • [1] Molodtsov, D.: Soft set theory–First results. Comput. Math. Appl. 37, 19-31 (1999).
  • [2] John, S.: Soft Sets-Theory and Applications. Springer Nature. Switzerland (2021).
  • [3] Maji, P. K., Roy, A. R., Biswas, R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077-1083 (2002).
  • [4] Chen, D., Tsang, E. C. C., Yeung, D. S., Wang, X.: The parameterization reduction of soft sets and its applications. Comput. Math. Appl. 49, 757-763 (2005).
  • [5] Pei, D.; Miao, D.: From soft sets to information systems. In: IEEE International Conference on Granular Computing. 2, 617-621 (2005).
  • [6] Feng, F., Li, C., Davvaz, B., Ali, M. I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 899-911 (2010).
  • [7] Alcantud, J. C. R.: Some formal relationships among soft sets, fuzzy sets, and their extensions. Internat. J. Approx. Reason. 68, 45-53 (2016).
  • [8] Deli, I.: Interval-valued neutrosophic soft sets and its decision making. Int. J. Mach. Learn. Cyber. 8, 665-676 (2017).
  • [9] Çetkin, V., Güner, E., Aygün, H.: On 2S-metric spaces. Soft Comput. 24, 12731-12742 (2020).
  • [10] Akgüller, Ö.: Discrete Ricci curvature-based statistics for soft sets. Soft Comput. 25, 599-612 (2021).
  • [11] Maji, P. K., Biswas, R., Roy, A. R.: Soft set theory. Comput. Math. Appl. 45, 555-562 (2003).
  • [12] Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547-1553 (2009).
  • [13] Akta¸s, H., Ça˘gman, N.: Soft sets and soft groups. Inform. Sci. 177, 2726-2735 (2007).
  • [14] Ça˘gman, N., Engino˘ glu, S.: Soft set theory and uni–int decision making. Eur. J. Oper. Res. 207 (2), 848-855 (2010).
  • [15] Sezgin, A., Atagün, A. O.: On operations of soft sets. Comput. Math. Appl. 61, 1457-1467 (2011).
  • [16] Abbas, M., Ali, B., Romaguera, S.: On generalized soft equality and soft lattice structure. Filomat. 28, 1191-1203 (2014).
  • [17] Ali, M. I., Shabir, M., Feng, F.: Representation of graphs based on neighborhoods and soft sets. Int. J. Mach. Learn. Cyber. 8, 1525-1535 (2017).
  • [18] Kandemir, M. B.: The concept of σ-algebraic soft set. Soft Comput. 22, 4353-4360 (2018).
  • [19] Aygün, E., Kamacı, H.: Some generalized operations in soft set theory and their role in similarity and decision making. J. Intell. Fuzzy Syst. 36, 6537-6547 (2019).
  • [20] Das, S., Samanta, S. K.: Soft real sets, soft real numbers and their properties. J. Fuzzy Math. 20, 551-576 (2012).
  • [21] Das, S., Samanta, S. K.: On soft metric spaces. J. Fuzzy Math. 21, 707-734 (2013).
  • [22] Güler, A. Ç., Yıldırım, E. D., Özbakır, O. B.: A fixed point theorem on soft G-metric spaces. J. Nonlinear Sci. Appl. 9, 885-894 (2016).
  • [23] Chiney, M., Samanta, S.: Soft topology redefined. J. Fuzzy Math. 27, 459-486 (2019).
  • [24] Altınta¸s, I., Ta¸sköprü, K.: Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping. Turkish J. Math. 44, 2199-2216 (2020).
  • [25] Ta¸sköprü, K., Altınta¸s, I.: A new approach for soft topology and soft function via soft element. Math. Meth. Appl. Sci. 44, 7556-7570 (2021).
  • [26] Altınta¸s, I., Ta¸sköprü, K., Selvi, B.: Countable and separable elementary soft topological space. Math. Meth. Appl. Sci. 44, 7811-7819 (2021).
  • [27] Altınta¸s, I., Ta¸sköprü, K., Esengul kyzy, P.: Soft partial metric spaces. Soft Comput. 26, 8997-9010 (2022).
  • [28] Babitha, K. V., Sunil, J. J.: Soft set relations and functions. Comput. Math. Appl. 60, 1840-1849 (2010).
  • [29] Babitha, K. V., Sunil, J. J.: Transitive closures and orderings on soft sets. Comput. Math. Appl. 62, 2235-2239 (2011).
  • [30] Yang, H. L., Guo, Z. L.: Kernels and closures of soft set relations, and soft set relation mappings. Comput. Math. Appl. 61, 651-662 (2011).
  • [31] Park, J. H., Kim, O. H., Kwun, Y. C.: Some properties of equivalence soft set relations. Comput. Math. Appl. 63, 1079-1088 (2012).
  • [32] Feng, F., Ali, M. I., Shabir, M.: Soft relations applied to semigroups. Filomat. 27, 1183-1196 (2013).
  • [33] Qin, K., Liu, Q., Xu, Y.: Redefined soft relations and soft functions. Int. J. Comput. Int. Sys. 8, 819-828 (2015).
  • [34] Kanwal, R. S., Qurashi, S. M., Shabir, M.: Generalized approximation of substructures in quantales by soft relations. Comp. Appl. Math. 39, 1-22 (2020).
  • [35] Yaylalı, G., Polat, N., Tanay, B.: Soft intervals and soft ordered topology. CBU J. of Sci. 13, 81-89 (2017).
  • [36] Al-Shami, T. M., El-Shafei, M. E., Abo-Elhamayel, M.: On soft topological ordered spaces. J. King Saud Univ. Sci. 31, 556 566 (2019).
  • [37] Al-Shami, T. M., El-Shafei, M. E.: Two new forms of ordered soft separation axioms. Demonstr. Math. 53, 8-26 (2020).
  • [38] Alcantud, J. C. R.: Softarisons: theory and practice. Neural. Comput. Appl. 33, 16759-16771 (2021).
  • [39] Alhazaymeh, K., Hassan, N.: Vague soft set relations and functions. J. Intell. Fuzzy Syst. 28, 1205-1212 (2015).
  • [40] Karaaslan, F.: Bipolar soft rough relations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 65, 105-126 (2016).
  • [41] Qamar, M. A., Hassan, N.: Q-Neutrosophic soft relation and its application in decision making. Entropy 20, 1-14 (2018).
  • [42] Kanwal, R. S., Shabir, M.: Rough approximation of a fuzzy set in semigroups based on soft relations. Comp. Appl. Math. 38, 1-23 (2019).
  • [43] El-Shafei, M. E., Al-shami, T. M.: Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Comp. Appl. Math. 39, 1-17 (2020).
  • [44] Dalkılıç, O.: Relations on neutrosophic soft set and their application in decision making. J. Appl. Math. Comput. 67, 257-273 (2021).
  • [45] Dalkılıç, O., Demirta¸s, N.: A novel perspective for Q-neutrosophic soft relations and their application in decision making. Artif. Intell. Rev. 1-21 (2022).
  • [46] Munkres, J. R.: Topology. Pearson. London (2014).
  • [47] Beardon, A.F.: Topology and Preference Relations. In: Mathematical Topics on Representations of Ordered Structures and Utility Theory: Essays in Honor of Professor Ghanshyam B. Mehta. Springer International Publishing. 3-21, Cham (2020).

A Soft Set Approach to Relations and Its Application to Decision Making

Year 2023, Volume: 11 Issue: 1, 1 - 13, 28.03.2023
https://doi.org/10.36753/mathenot.1172408

Abstract

One of the most useful mathematical tools for examining the relationships among objects is the concept of relation. Besides, it can also be necessary to throw light on uncertainties in these relationships. Soft set theory, in which different approaches used in defining the notions bring about different applications in many areas, enables to overcome uncertainties. The purpose of this paper is to define soft relation in a different way and to give a decision making method using the concept of soft relation. For this purpose, firstly, the soft relations are defined on the collection of soft elements, unlike the previous ones. After their basic properties are provided, the correspondence between the soft and classical relations is investigated and some examples are given. Finally, an algorithm is proposed using the soft relation for solving decision making problems, where the decision is related to other circumstances, and given an illustrative example.

References

  • [1] Molodtsov, D.: Soft set theory–First results. Comput. Math. Appl. 37, 19-31 (1999).
  • [2] John, S.: Soft Sets-Theory and Applications. Springer Nature. Switzerland (2021).
  • [3] Maji, P. K., Roy, A. R., Biswas, R.: An application of soft sets in a decision making problem. Comput. Math. Appl. 44, 1077-1083 (2002).
  • [4] Chen, D., Tsang, E. C. C., Yeung, D. S., Wang, X.: The parameterization reduction of soft sets and its applications. Comput. Math. Appl. 49, 757-763 (2005).
  • [5] Pei, D.; Miao, D.: From soft sets to information systems. In: IEEE International Conference on Granular Computing. 2, 617-621 (2005).
  • [6] Feng, F., Li, C., Davvaz, B., Ali, M. I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput. 14, 899-911 (2010).
  • [7] Alcantud, J. C. R.: Some formal relationships among soft sets, fuzzy sets, and their extensions. Internat. J. Approx. Reason. 68, 45-53 (2016).
  • [8] Deli, I.: Interval-valued neutrosophic soft sets and its decision making. Int. J. Mach. Learn. Cyber. 8, 665-676 (2017).
  • [9] Çetkin, V., Güner, E., Aygün, H.: On 2S-metric spaces. Soft Comput. 24, 12731-12742 (2020).
  • [10] Akgüller, Ö.: Discrete Ricci curvature-based statistics for soft sets. Soft Comput. 25, 599-612 (2021).
  • [11] Maji, P. K., Biswas, R., Roy, A. R.: Soft set theory. Comput. Math. Appl. 45, 555-562 (2003).
  • [12] Ali, M. I., Feng, F., Liu, X., Min, W. K., Shabir, M.: On some new operations in soft set theory. Comput. Math. Appl. 57, 1547-1553 (2009).
  • [13] Akta¸s, H., Ça˘gman, N.: Soft sets and soft groups. Inform. Sci. 177, 2726-2735 (2007).
  • [14] Ça˘gman, N., Engino˘ glu, S.: Soft set theory and uni–int decision making. Eur. J. Oper. Res. 207 (2), 848-855 (2010).
  • [15] Sezgin, A., Atagün, A. O.: On operations of soft sets. Comput. Math. Appl. 61, 1457-1467 (2011).
  • [16] Abbas, M., Ali, B., Romaguera, S.: On generalized soft equality and soft lattice structure. Filomat. 28, 1191-1203 (2014).
  • [17] Ali, M. I., Shabir, M., Feng, F.: Representation of graphs based on neighborhoods and soft sets. Int. J. Mach. Learn. Cyber. 8, 1525-1535 (2017).
  • [18] Kandemir, M. B.: The concept of σ-algebraic soft set. Soft Comput. 22, 4353-4360 (2018).
  • [19] Aygün, E., Kamacı, H.: Some generalized operations in soft set theory and their role in similarity and decision making. J. Intell. Fuzzy Syst. 36, 6537-6547 (2019).
  • [20] Das, S., Samanta, S. K.: Soft real sets, soft real numbers and their properties. J. Fuzzy Math. 20, 551-576 (2012).
  • [21] Das, S., Samanta, S. K.: On soft metric spaces. J. Fuzzy Math. 21, 707-734 (2013).
  • [22] Güler, A. Ç., Yıldırım, E. D., Özbakır, O. B.: A fixed point theorem on soft G-metric spaces. J. Nonlinear Sci. Appl. 9, 885-894 (2016).
  • [23] Chiney, M., Samanta, S.: Soft topology redefined. J. Fuzzy Math. 27, 459-486 (2019).
  • [24] Altınta¸s, I., Ta¸sköprü, K.: Compactness of soft cone metric space and fixed point theorems related to diametrically contractive mapping. Turkish J. Math. 44, 2199-2216 (2020).
  • [25] Ta¸sköprü, K., Altınta¸s, I.: A new approach for soft topology and soft function via soft element. Math. Meth. Appl. Sci. 44, 7556-7570 (2021).
  • [26] Altınta¸s, I., Ta¸sköprü, K., Selvi, B.: Countable and separable elementary soft topological space. Math. Meth. Appl. Sci. 44, 7811-7819 (2021).
  • [27] Altınta¸s, I., Ta¸sköprü, K., Esengul kyzy, P.: Soft partial metric spaces. Soft Comput. 26, 8997-9010 (2022).
  • [28] Babitha, K. V., Sunil, J. J.: Soft set relations and functions. Comput. Math. Appl. 60, 1840-1849 (2010).
  • [29] Babitha, K. V., Sunil, J. J.: Transitive closures and orderings on soft sets. Comput. Math. Appl. 62, 2235-2239 (2011).
  • [30] Yang, H. L., Guo, Z. L.: Kernels and closures of soft set relations, and soft set relation mappings. Comput. Math. Appl. 61, 651-662 (2011).
  • [31] Park, J. H., Kim, O. H., Kwun, Y. C.: Some properties of equivalence soft set relations. Comput. Math. Appl. 63, 1079-1088 (2012).
  • [32] Feng, F., Ali, M. I., Shabir, M.: Soft relations applied to semigroups. Filomat. 27, 1183-1196 (2013).
  • [33] Qin, K., Liu, Q., Xu, Y.: Redefined soft relations and soft functions. Int. J. Comput. Int. Sys. 8, 819-828 (2015).
  • [34] Kanwal, R. S., Qurashi, S. M., Shabir, M.: Generalized approximation of substructures in quantales by soft relations. Comp. Appl. Math. 39, 1-22 (2020).
  • [35] Yaylalı, G., Polat, N., Tanay, B.: Soft intervals and soft ordered topology. CBU J. of Sci. 13, 81-89 (2017).
  • [36] Al-Shami, T. M., El-Shafei, M. E., Abo-Elhamayel, M.: On soft topological ordered spaces. J. King Saud Univ. Sci. 31, 556 566 (2019).
  • [37] Al-Shami, T. M., El-Shafei, M. E.: Two new forms of ordered soft separation axioms. Demonstr. Math. 53, 8-26 (2020).
  • [38] Alcantud, J. C. R.: Softarisons: theory and practice. Neural. Comput. Appl. 33, 16759-16771 (2021).
  • [39] Alhazaymeh, K., Hassan, N.: Vague soft set relations and functions. J. Intell. Fuzzy Syst. 28, 1205-1212 (2015).
  • [40] Karaaslan, F.: Bipolar soft rough relations. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 65, 105-126 (2016).
  • [41] Qamar, M. A., Hassan, N.: Q-Neutrosophic soft relation and its application in decision making. Entropy 20, 1-14 (2018).
  • [42] Kanwal, R. S., Shabir, M.: Rough approximation of a fuzzy set in semigroups based on soft relations. Comp. Appl. Math. 38, 1-23 (2019).
  • [43] El-Shafei, M. E., Al-shami, T. M.: Applications of partial belong and total non-belong relations on soft separation axioms and decision-making problem. Comp. Appl. Math. 39, 1-17 (2020).
  • [44] Dalkılıç, O.: Relations on neutrosophic soft set and their application in decision making. J. Appl. Math. Comput. 67, 257-273 (2021).
  • [45] Dalkılıç, O., Demirta¸s, N.: A novel perspective for Q-neutrosophic soft relations and their application in decision making. Artif. Intell. Rev. 1-21 (2022).
  • [46] Munkres, J. R.: Topology. Pearson. London (2014).
  • [47] Beardon, A.F.: Topology and Preference Relations. In: Mathematical Topics on Representations of Ordered Structures and Utility Theory: Essays in Honor of Professor Ghanshyam B. Mehta. Springer International Publishing. 3-21, Cham (2020).
There are 47 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Kemal Taşköprü 0000-0002-0760-3782

Elif Karaköse This is me 0000-0001-6204-0890

Publication Date March 28, 2023
Submission Date September 8, 2022
Acceptance Date November 12, 2022
Published in Issue Year 2023 Volume: 11 Issue: 1

Cite

APA Taşköprü, K., & Karaköse, E. (2023). A Soft Set Approach to Relations and Its Application to Decision Making. Mathematical Sciences and Applications E-Notes, 11(1), 1-13. https://doi.org/10.36753/mathenot.1172408
AMA Taşköprü K, Karaköse E. A Soft Set Approach to Relations and Its Application to Decision Making. Math. Sci. Appl. E-Notes. March 2023;11(1):1-13. doi:10.36753/mathenot.1172408
Chicago Taşköprü, Kemal, and Elif Karaköse. “A Soft Set Approach to Relations and Its Application to Decision Making”. Mathematical Sciences and Applications E-Notes 11, no. 1 (March 2023): 1-13. https://doi.org/10.36753/mathenot.1172408.
EndNote Taşköprü K, Karaköse E (March 1, 2023) A Soft Set Approach to Relations and Its Application to Decision Making. Mathematical Sciences and Applications E-Notes 11 1 1–13.
IEEE K. Taşköprü and E. Karaköse, “A Soft Set Approach to Relations and Its Application to Decision Making”, Math. Sci. Appl. E-Notes, vol. 11, no. 1, pp. 1–13, 2023, doi: 10.36753/mathenot.1172408.
ISNAD Taşköprü, Kemal - Karaköse, Elif. “A Soft Set Approach to Relations and Its Application to Decision Making”. Mathematical Sciences and Applications E-Notes 11/1 (March 2023), 1-13. https://doi.org/10.36753/mathenot.1172408.
JAMA Taşköprü K, Karaköse E. A Soft Set Approach to Relations and Its Application to Decision Making. Math. Sci. Appl. E-Notes. 2023;11:1–13.
MLA Taşköprü, Kemal and Elif Karaköse. “A Soft Set Approach to Relations and Its Application to Decision Making”. Mathematical Sciences and Applications E-Notes, vol. 11, no. 1, 2023, pp. 1-13, doi:10.36753/mathenot.1172408.
Vancouver Taşköprü K, Karaköse E. A Soft Set Approach to Relations and Its Application to Decision Making. Math. Sci. Appl. E-Notes. 2023;11(1):1-13.

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