A multi-attribute group decision-making algorithm based on soft intervals that considers the priority rankings of group members on attributes of objects, along with some applications

Gözde Yaylalı Umul; Gözde Yaylalı Umul

doi:10.3934/math.2025217

AIMS Mathematics

2025, Volume 10, Issue 3: 4709-4746. doi: 10.3934/math.2025217

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Research article

A multi-attribute group decision-making algorithm based on soft intervals that considers the priority rankings of group members on attributes of objects, along with some applications

Gözde Yaylalı Umul ^,

Department of Mathematics, Muğla Sıtkı Koçman University, Muğla, Turkey

Received: 29 December 2024 Revised: 19 February 2025 Accepted: 20 February 2025 Published: 05 March 2025
MSC : 06A99, 91B06

There are a considerable number of studies involving soft sets, the most significant ones focusing on decision-making. In this study, we have developed decision-making algorithms using soft intervals on soft sets, which accounted for the priority order of individuals in situations where multiple people were involved. Soft sets can be considered as a parameterized family of subsets of the universal set; for this reason, soft sets provide an effective tool for evaluating the multiple attributes of objects in decision-making problems. In this study, the parameter set of the soft set was used for the attributes of the objects, while the universal set of the soft set was used for the objects being selected. A soft interval can be considered as a soft set that includes all parameterized subsets of the universal set within the specified boundaries determined by the order on the soft set. In this study, soft intervals were generated from the orderings on a soft set which were based on the users rankings of object attributes. The first algorithm enabled us to obtain the choice object based on the ranking of decision makers with equal influence on the decision, while the second algorithm achieved this for rankings of those with different influences. Both of these seeked to find the most appropriate object by considering the priority rankings of users in scenarios where a joint decision was required and the optimal decision objects were subsequently ranked. The novelty of the proposed algorithm lied in utilizing the new theory of soft sets to select the most suitable object for a group from multi-attribute objects, considering each member's ranking of attributes of objects.
- soft set,
- soft set relation,
- decision-making,
- multi-attribute group decision-making
Citation: Gözde Yaylalı Umul. A multi-attribute group decision-making algorithm based on soft intervals that considers the priority rankings of group members on attributes of objects, along with some applications[J]. AIMS Mathematics, 2025, 10(3): 4709-4746. doi: 10.3934/math.2025217

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Abstract

There are a considerable number of studies involving soft sets, the most significant ones focusing on decision-making. In this study, we have developed decision-making algorithms using soft intervals on soft sets, which accounted for the priority order of individuals in situations where multiple people were involved. Soft sets can be considered as a parameterized family of subsets of the universal set; for this reason, soft sets provide an effective tool for evaluating the multiple attributes of objects in decision-making problems. In this study, the parameter set of the soft set was used for the attributes of the objects, while the universal set of the soft set was used for the objects being selected. A soft interval can be considered as a soft set that includes all parameterized subsets of the universal set within the specified boundaries determined by the order on the soft set. In this study, soft intervals were generated from the orderings on a soft set which were based on the users rankings of object attributes. The first algorithm enabled us to obtain the choice object based on the ranking of decision makers with equal influence on the decision, while the second algorithm achieved this for rankings of those with different influences. Both of these seeked to find the most appropriate object by considering the priority rankings of users in scenarios where a joint decision was required and the optimal decision objects were subsequently ranked. The novelty of the proposed algorithm lied in utilizing the new theory of soft sets to select the most suitable object for a group from multi-attribute objects, considering each member's ranking of attributes of objects.

References

[1]	D. Abuzaid, S. Al Ghour, Three new soft separation axioms in soft topological spaces, AIMS Mathematics, 9 (2024), 4632–4648. https://doi.org/10.3934/math.2024223 doi: 10.3934/math.2024223
[2]	U. Acar, F. Koyuncu, B. Tanay, Soft sets and soft rings, Comput. Math. Appl., 59 (2010), 3458–3463. https://doi.org/10.1016/j.camwa.2010.03.034 doi: 10.1016/j.camwa.2010.03.034
[3]	T. M. Al-shami, Soft somewhat open sets: soft separation axioms and medical application to nutrition, Comp. Appl. Math., 41 (2022), 216. https://doi.org/10.1007/s40314-022-01919-x doi: 10.1007/s40314-022-01919-x
[4]	F. Al-Sharqi, A. G. Ahmad, A. Al-Quran, Similarity measures on interval-complex neutrosophic soft sets with applications to decision making and medical diagnosis under uncertainty, Neutrosophic Sets Sy., 51 (2022), 495–515.
[5]	F. Al-Shargi, Y. Al-Qudah, N. Alotaibi, Decision-making techniques based on similarity measures of possibility neutrosophic soft expert sets, Neutrosophic Sets Sy., 55 (2023), 358–382.
[6]	A. O. Atagün, H. Kamacı, Decompositions of soft sets and soft matrices with applications in group decision making, Sci. Iran., 31 (2024), 518–534. https://doi.org/10.24200/SCI.2021.58119.5575 doi: 10.24200/SCI.2021.58119.5575
[7]	K. V. Babitha, J. J. Sunil, Soft set relations and functions, Comput. Math. Appl., 60 (2010), 1840–1849. https://doi.org/10.1016/j.camwa.2010.07.014 doi: 10.1016/j.camwa.2010.07.014
[8]	K. V. Babitha, J. J. Sunil, Transitive closures and ordering on soft sets, Comput. Math. Appl., 62 (2011), 2235–2239. https://doi.org/10.1016/j.camwa.2011.07.010 doi: 10.1016/j.camwa.2011.07.010
[9]	Z. Baser, V. Ulucay, Energy of a neutrosophic soft set and its applications to multi-criteria decision-making problems, Neutrosophic Sets Sy., 79 (2025), 479–492.
[10]	N. Çağman, S. Enginoğlu, Soft matrix theory and its decision making, Comput. Math. Appl., 59 (2010), 3308–3314. https://doi.org/10.1016/j.camwa.2010.03.015 doi: 10.1016/j.camwa.2010.03.015
[11]	N. Çağman, S. Karataş, S. Enginoğlu, Soft topology, Comput. Math. Appl., 62 (2011), 351–358. https://doi.org/10.1016/j.camwa.2011.05.016 doi: 10.1016/j.camwa.2011.05.016
[12]	N. Ç. Polat, G. Yaylalı, B. Tanay, A method for Decision Making Problems by Using Graph Representation of Soft Set Relations, Intell. Autom. Soft Co., 25 (2019), 305–311. https://doi.org/10.31209/2018.100000006 doi: 10.31209/2018.100000006
[13]	O. Dalkılıç, N. Demirtaş, Decision analysis review on the concept of class for bipolar soft set theory, Comp. Appl. Math., 41 (2022), 205. https://doi.org/10.1007/s40314-022-01922-2 doi: 10.1007/s40314-022-01922-2
[14]	F. Feng, X. Y. Liu, V. Leoreanu-Fotea, Y. B. Jun, Soft sets and soft rough sets, Inform. Sciences, 118 (2011), 1125–1137. https://doi.org/10.1016/j.ins.2010.11.004 doi: 10.1016/j.ins.2010.11.004
[15]	D. Gifu, Soft sets extensions: innovating healthcare claims analysis, Appl. Sci., 14 (2024), 8799. https://doi.org/10.3390/app14198799 doi: 10.3390/app14198799
[16]	H. H. Sakr, B. S. Alanazi, Effective vague soft environment-based decision-making, AIMS Mathematics, 9 (2024), 9556–9586. https://doi.org/10.3934/math.2024467 doi: 10.3934/math.2024467
[17]	Z. Kong, G. D. Zhang, L. F. Wang, Z. X. Wu, S. Q. Qi, H. F. Wang, An efficient decision making approach in incomplete soft set, Appl. Math. Model., 38 (2014), 2141–2150. https://doi.org/10.1016/j.apm.2013.10.009 doi: 10.1016/j.apm.2013.10.009
[18]	H. Li, M. Yazdi, Stochastic game theory approach to solve system safety and reliability decision-making problem under uncertainty, In: Advanced decision-making methods and applications in system safety and reliability problems, Cham: Springer, 2022,127–151. https://doi.org/10.1007/978-3-031-07430-1_8
[19]	X. L. Ma, J. M. Zhan, M. I. Ali, N. Mehmood, A survey of decision making methods based on two classes of hybrid soft set models, Artif. Intell. Rev., 49 (2018), 511–529. https://doi.org/10.1007/s10462-016-9534-2 doi: 10.1007/s10462-016-9534-2
[20]	P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (2001), 589–602.
[21]	P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002), 1077–1083. https://doi.org/10.1016/S0898-1221(02)00216-X doi: 10.1016/S0898-1221(02)00216-X
[22]	P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl., 45 (2003), 555–562. https://doi.org/10.1016/S0898-1221(03)00016-6
[23]	D. Molodtsov, Soft set theory–first results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
[24]	K. F. B. Muhaya, K. M. Alsager, Extending neutrosophic set theory: Cubic bipolar neutrosophic soft sets for decision making, AIMS Mathematics, 9 (2024), 27739–27769. https://doi.org/10.3934/math.20241347 doi: 10.3934/math.20241347
[25]	S. Y. Musa, B. A. Asaad, Bipolar M-parametrized N soft sets: A gateaway to informed decision making, J. Math. Comput. Sci., 36 (2025), 121–141. https://doi.org/10.22436/jmcs.036.01.08 doi: 10.22436/jmcs.036.01.08
[26]	A. Sezgin, N. H. Çam, Soft Theta-product: A new product for soft sets with its decision-making, Multicriteria Algorithms with Applications, 6 (2025), 9–33. https://doi.org/10.61356/j.mawa.2025.6439 doi: 10.61356/j.mawa.2025.6439
[27]	A. Sezgin, E. Şenyiğit, A new product for soft sets with its decision-making: soft star-product, Big. Data. Comp. Vis., 5 (2025) 52–73.
[28]	A. Sezgin, E. Şenyiğit, M. Luzum, A new product for soft sets with its decision-making: soft Gamma-product, Earthline Journal of Mathematical Sciences, 15 (2025), 211–234. https://doi.org/10.34198/ejms.15225.211234 doi: 10.34198/ejms.15225.211234
[29]	S. Yin, Y. D. Zhao, A. Hussain, K. Ullah, Comprehensive evaluation of rural regional integrated clean energy systems considering multi-subject interest coordination with pythagorean fuzzy information, Eng. Appl. Artif. Intel., 138 (2024), 109342. https://doi.org/10.1016/j.engappai.2024.109342 doi: 10.1016/j.engappai.2024.109342
[30]	B. Tanay, G. Yaylalı, New structures on partially ordered soft sets and soft Scott topology, Annals of Fuzzy Mathematics and Informatics, 7 (2014), 89–97.
[31]	P. Wang, X. Donga, J. H. Chena, X. M. Wu, F. Chiclanac, Reliability-driven large group consensus decision-making method with hesitant fuzzy linguistic information for the selection of hydrogen storage technology, Inform. Sciences, 689 (2025), 121457. https://doi.org/10.1016/j.ins.2024.121457 doi: 10.1016/j.ins.2024.121457
[32]	P. Wang, P. D. Liu, Y. Y. Li, F. Tenga, W. Pedrycz, Trust exploration and leadership incubation based opinion dynamics model for social network group decision-making: A quantum theory perspective, Eur. J. Oper. Res., 317 (2024), 156–170. https://doi.org/10.1016/j.ejor.2024.03.025 doi: 10.1016/j.ejor.2024.03.025
[33]	G. Yaylalı, N. Çakmak Polat, B. Tanay, Soft intervals and soft ordered topology, Celal Bayar Universitesi Fen Bilimleri Dergisi, 13 (2017), 81–89.
[34]	G. Yaylalı, N. Ç. Polat, B. Tanay, A soft interval based decision making method and its computer application, Found. Comput. Decis. S., 46 (2021), 273–296. https://doi.org/10.2478/fcds-2021-0018 doi: 10.2478/fcds-2021-0018
[35]	M. Yazdi, E. Zarei, S. Adumene, R. Abbassi, P. Rahnamayiezekavat, Uncertainty modeling in risk assessment of digitalized process systems, Methods in Chemical Process Safety 6 (2022), 389–416. https://doi.org/10.1016/bs.mcps.2022.04.005 doi: 10.1016/bs.mcps.2022.04.005
[36]	A. Z. Khameneh, A. Kılıçman, Multi-attribute decision-making based on soft set theory: a systematic review, Soft Comput., 23 (2019), 6899–6920. https://doi.org/10.1007/s00500-018-3330-7 doi: 10.1007/s00500-018-3330-7
[37]	X. H. Zhang, On interval soft sets with applications, Int. J. Comput. Intell. Syst., 7 (2014), 186–196. https://doi.org/10.1080/18756891.2013.862354 doi: 10.1080/18756891.2013.862354

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