Parameterization of Multi-Decisive Hypersoft Set Under Fuzzy Environment With Application in Multi-Attribute Decision Making
Abstract
Fuzzy parameterized hypersoft expert set (FPHSE-set) is the generalisation of fuzzy parameterized soft expert set (FPSE-set). The FPHSE-set overcomes the shortcomings of FPSE-set for the examination of multi-argument approximate function. The FPHSE-set takes on the real-world situation where each attribute is actually supposed to be further categorised. Each category contains non matching sub-attribute valued disjoint set with the use of multi-argument approximate function. The FPHSE-set is more adaptable and dependable in the decision-support system with the comprehensive analysis of attributes. As a result, the primary goal of this paper is to describe how to characterise the FPHSE-set using set-theoretic, axiomatic, and algorithmic approaches. Two algorithms are suggested to investigate the proposed model’s function in decision-making while coping with a real-world event of computer system selection for a bank office in order to validate it. A comparative comparison between the suggested approach and a few relevant, current methods is used to assess the advantages of the proposed strategy.
References
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L. A. Zadeh, ”Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338-353, 1965.
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M. A. D. D. O. Ferreira, L. C. Ribeiro, H. S. Schuffner, M. P. Lib´ orio, & P. I. Ekel, ”Fuzzyset-based multi-attribute decision-making, its computing implementation, and applications”, Axioms, vol. 13, no. 3, pp. 142, 2024.
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D. Andalib Ardakani, M. Kiani, A. Saffari Darberazi, F. Zamzam, & E. Mofatehzadeh, ”An Interval Type-2 Fuzzy AHP Approach for Success Factors of Green Supply Chain Management”, International Journal of Research in Industrial Engineering, vol. 13, no. 3 pp. 237-256, 2024.
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V. Uluc¸ay, & M. S ¸ahin, ”Intuitionistic fuzzy soft expert graphs with application”, Uncertainty discourse and applications, vol. 1, no. 1, pp. 1-10, 2024.
X. Li, Y. Zhang, A. Sorourkhah, & S. A. Edalatpanah, ”Introducing antifragility analysis algorithm for assessing digitalization strategies of the agricultural economy in the small farming section”. Journal of the Knowledge Economy, pp. 1-25, 2023.
T. N. Chusi, S. Qian, S. A. Edalatpanah, Y. Qiu, M. Bayane Bouraima, & A. B. Ajayi, ”Interval-valued spherical fuzzy extension of SWARA for prioritizing strategies to unlock Africa’s potential in the carbon credit market”, Computational Algorithms and Numerical Dimensions, vol. 3, no. 3, pp. 217-227, 2024.
A. Sezgin, & E. Yavuz, ”Soft Binary Piecewise Plus Operation: A New Type of Operation For Soft Sets”, Uncertainty Discourse and Applications, vol. 1, no. 1, pp. 79-100, 2024.
R. Vellapandi, & S. Gunasekaran, ”A new decision making approach for winning strategy based on muti soft set logic”, Journal of fuzzy extension and applications, vol. 1, no. 2, pp. 112-121, 2020.
F. Smarandache, ”Soft set product extended to hypersoft set and indetermsoft set cartesian product extended to indetermhypersoft set”, Journal of fuzzy extension and applications, vol. 3, no. 4, pp. 313-316, 2022.
M. Pethaperumal, V. Jayakumar, S. A. Edalatpanah, A. B.K. Mohideen, & S. Annamalai, ”An enhanced MADMwithq-Rungorthopairmulti-fuzzysoft set in healthcare supplier selection”, Journal of Intelligent & Fuzzy Systems, (Preprint), pp. 1-12, 2024.
D. Molodtsov, ”Soft set theory firrst results”, Computers and mathematics with applications, vol. 4, no. 37, pp. 19-31, 1999.
P. K. Maji, R. Biswas, & A. R. Roy, ”Soft set theory”, Computers & Mathematics with applications, vol. 45, no. 4-5, pp. 555-562, 2003.
M. I. Ali, F. Feng, X. Liu, W. K. Min, & M. Shabir, ”On some new operations in soft set theory”, Computers & mathematics with applications, vol. 57, no. 9, pp. 1547-1553, 2009.
K. V. Babitha, & J. Sunil, ”Soft set relations and functions”, Computers & Mathematics with applications, vol. 60, no. 7, pp. 1840-1849, 2010.
N. C¸a˘ gman, & S. Enginoˆ glu, ”Soft set theory and uni-int decision making”, European journal of operational research, vol. 207, no. 2, pp. 848-855, 2010.
T. Herawan, & M. M. Deris, ”A soft set approach for association rules mining”, Knowledgebased systems, vol. 24, no. 1, pp. 186-195, 2011.
T.Som,”Onthetheoryofsoftset, softrelation and fuzzy soft relation”, in Proc. of the National Conference on Uncertainty: A Mathematical Approach, UAMA-06, Burdwan, pp. 1-9, 2006.
H. Aktac ¸, and N. C¸a˘ gman, ”Soft sets and soft groups”, Information sciences, vol. 177, pp. 2726- 2735, 2007.
Y. Zou and Z. Xiao, ”Data analysis approaches of soft sets under incomplete information”, Knowledge base system, vol. 21, pp. 941-945, 2008.
S. Alkhazaleh, & A. R. Salleh, ”Soft expert sets”, Advances in decision sciences, vol. 2011, pp.1-12, 2011.
M. Ihsan, M. Saeed, & A. U. Rahman, ”A Rudimentary approach to develop context for convexity cum concavity on soft expert set with some generalized results”, Punjab university journal of mathematics, vol. 53, no. 9, pp. 621-629, 2021.
M. Ihsan, A. U. Rahman, M. Saeed, & H. A. E. W. Khalifa, ”Convexity-cum-concavity on fuzzy soft expert set with certain properties”, International journal of fuzzy logic and intelligent systems, vol. 21, no. 3, pp. 233-242, 2021.
S. Alkhazaleh, & A. R. Salleh, ”Fuzzy soft expert set and its application”, Applied mathematics, vol. 5, no. 9, pp. 1349-1368, 2014.
F. Smarandache, ”Extension of soft set to hypersoft set and then to plithogenic hypersoft set”, Neutrosophic sets and systems, vol. 22, pp. 168-170, 2018.
M. Abbas, G. Murtaza, & F. Smarandache, ”Basic operations on hypersoft sets and hypersoft point”, Neutrosophic sets and systems, vol. 35, pp. 407-422, 2020.
S. Y. Musa, & B. A. Asaad, ”Hypersoft topological spaces”, Neutrosophic sets and systems, vol. 49, no. 1, pp. 26, 2022.
H. Kamac¨ı, ”On hybrid structures of hypersoft sets and rough sets”, International journal of modern science and technology, vol. 6, no. 4, pp. 69-82, 2021.
D. Ajay, & J. J. Charisma, ”An mcdm based on alpha open hypersoft sets and its application”, in International Conference on Intelligent and Fuzzy Systems, Springer, Cham, pp. 333-341, 2021.
O. Dalklc¸, ”Determining the membership degrees in the range (0, 1) for hypersoft sets independently of the decision-maker”, International journal of systems science, pp. 1-11, 2022.
N. C¸a˘ gman, F. C¸itak, & S. Enginoˆ glu, ”FP-soft set theory and its applications”, Annals of fuzzy mathe- matics and informatics, vol. 2, no. 2, pp. 219-226, 2011.
S. Alkhazaleh, & A. R. Salleh, ”Fuzzy soft expert set and its application”, Applied mathematics, vol. 5, no. 9, pp. 1349-1368, 2014.
Y. Tella, A. Peter, & S. B. Hosea, ”Fuzzy parameterized fuzzy soft set for multiple criteria decision process under multiple expert assessments”, International journal of engineering sciences & management, vol. 5, no. 1, pp.180-185, 2015.
M. Bashir, & A. R. Salleh, ”Fuzzy parameterized soft expert set”, Abstract and applied analysis, vol. 2012, pp.1-15, 2012.
A. U. Rahman, M. Saeed, & S. Zahid, ”Application in decision making based on fuzzy parameterized hypersoft set theory”, Asia mathematika, vol. 5, no. 1, pp.19-27, 2021.
M. Ihsan, A. U.Rahman, & M. Saeed, ”Hypersoft expert set with application in decision making for recruitment process”, Neutrosophic sets and systems, vol. 42, pp. 191-207, 2021.
P. Shoval, & Y. Lugasi, ”Models for computer system evaluation and selection”, Information &Management, vol. 12, no. 3, pp. 117-129, 1987.
M. Ihsan, M. Saeed, & A. U. Rahman, ”Neutrosophic hypersoft expert set: Theory and Applications”, Neutrosophic Sets Syst, vol. 50, pp. 431-458, 2022.
M. Ihsan, A. U. Rahman, & M. Saeed, ”Single valued neutrosophic hypersoft expert set with application in decision making”, Neutrosophic Sets and Systems, vol. 47, pp. 451-471, 2021.
P. Eindor, ”Dynamic approach to selecting computers”, Datamation, vol. 23, no. 6, p. 103, 1977.
R. L. Keeney, ”Measurement scales for quantifying attributes”, Behavioral Science, vol. 26, no. 1, pp. 29-36, 1987.
L. A. Zadeh, ”Fuzzy sets”, Information and control, vol. 8, no. 3, pp. 338-353, 1965.
K. Hussain, & k. Ullah, ”An intelligent decision support system for spherical fuzzy sugenoweber aggregation operators and real-life applications”, Spectrum of Mechanical Engineering and Operational Research, vol. 1, no. 1, pp. 177-188, 2024.
M. Asif, U. Ishtiaq, & I. K. Argyros, ”Hamacher aggregation operators for Pythagorean fuzzy set and its application in multi-attribute decision-making problem”, Spectrum of Operational Research, vol. 2, no. 1, pp. 27-40, 2025.
K. H. Gazi, N. Raisa, A. Biswas, F. Azizzadeh, & S. P. Mondal, ”Finding the most important criteria in women’s empowerment for sports sector by pentagonal fuzzy dematel methodology”, Spectrum of Decision Making and Applications, vol. 2, no. 1, pp. 28-52, 2025.
L. Li, & J. Yang, ”Disturbing fuzzy multi-attribute decision-making method with if weight information is disturbing fuzzy number”, Mathematics, vol. 12, no. 8, pp. 1225, 2024.
Q. Yue, J. Ren, B. Hu, & Y. Tao, ”Fermatean fuzzy multi-attribute personnel-position matching group decision-making with unknown weight information”, Expert Systems with Applications, 237, pp. 121451, 2024.
M. A. D. D. O. Ferreira, L. C. Ribeiro, H. S. Schuffner, M. P. Lib´ orio, & P. I. Ekel, ”Fuzzyset-based multi-attribute decision-making, its computing implementation, and applications”, Axioms, vol. 13, no. 3, pp. 142, 2024.
E. Rasool, N. Kausar, S. S. S. Ahmad, N. Aydin, & O. A. Olanrewaju, ”Multi-attribute decision-making based on pythagorean fuzzy numbers and its application in hotel evaluations. decision making”, Applications in management and engineering, vol. 7, no. 2, pp. 559-571, 2024.
V. Uluc¸ay, N. M. S ¸ahin, I. N. Toz, & E. Bozkurt, ”VIKOR Method for Decision-Making Problems Based on Q-Single-Valued Neutrosophic Sets: Law Application” Journal of Fuzzy Extension & Applications, vol. 4, no. 4, pp. 310-326, 2023.
D. Andalib Ardakani, M. Kiani, A. Saffari Darberazi, F. Zamzam, & E. Mofatehzadeh, ”An Interval Type-2 Fuzzy AHP Approach for Success Factors of Green Supply Chain Management”, International Journal of Research in Industrial Engineering, vol. 13, no. 3 pp. 237-256, 2024.
M. Donyavi Rad, E. Sadeh, Z. Amini Sabegh, & R. Ehtesham Rasi. ”Introducing a fuzzy robust integrated model for optimizing humanitarian supply chain processes”, Journal of applied research on industrial engineering, vol. 10, no. 3, pp. 427-453, 2023.
A. Mehmood, A. Ahmad, M. Nawaz, M. M. Saeed, & G. Nordo, ”Discussion on Entropy and Similarity Measures and Their Few Applications Because of Vague Soft Sets”, Systemic Analytics, vol. 2, no. 1, pp. 157-173, 2024.
R. V. Jaikumar, R. Sundareswaran, M. Shanmugapriya, S. Broumi, & T. A. Al-Hawary, ”Vulnerability parameters in picture fuzzy soft graphs and their applications to locate a diagnosis center in cities”, Journal of Fuzzy Extension and Applications, vol. 5, no. 1, pp. 86-99, 2024.
V. Uluc¸ay, & M. S ¸ahin, ”Intuitionistic fuzzy soft expert graphs with application”, Uncertainty discourse and applications, vol. 1, no. 1, pp. 1-10, 2024.
X. Li, Y. Zhang, A. Sorourkhah, & S. A. Edalatpanah, ”Introducing antifragility analysis algorithm for assessing digitalization strategies of the agricultural economy in the small farming section”. Journal of the Knowledge Economy, pp. 1-25, 2023.
T. N. Chusi, S. Qian, S. A. Edalatpanah, Y. Qiu, M. Bayane Bouraima, & A. B. Ajayi, ”Interval-valued spherical fuzzy extension of SWARA for prioritizing strategies to unlock Africa’s potential in the carbon credit market”, Computational Algorithms and Numerical Dimensions, vol. 3, no. 3, pp. 217-227, 2024.
A. Sezgin, & E. Yavuz, ”Soft Binary Piecewise Plus Operation: A New Type of Operation For Soft Sets”, Uncertainty Discourse and Applications, vol. 1, no. 1, pp. 79-100, 2024.
R. Vellapandi, & S. Gunasekaran, ”A new decision making approach for winning strategy based on muti soft set logic”, Journal of fuzzy extension and applications, vol. 1, no. 2, pp. 112-121, 2020.
F. Smarandache, ”Soft set product extended to hypersoft set and indetermsoft set cartesian product extended to indetermhypersoft set”, Journal of fuzzy extension and applications, vol. 3, no. 4, pp. 313-316, 2022.
M. Pethaperumal, V. Jayakumar, S. A. Edalatpanah, A. B.K. Mohideen, & S. Annamalai, ”An enhanced MADMwithq-Rungorthopairmulti-fuzzysoft set in healthcare supplier selection”, Journal of Intelligent & Fuzzy Systems, (Preprint), pp. 1-12, 2024.
D. Molodtsov, ”Soft set theory firrst results”, Computers and mathematics with applications, vol. 4, no. 37, pp. 19-31, 1999.
P. K. Maji, R. Biswas, & A. R. Roy, ”Soft set theory”, Computers & Mathematics with applications, vol. 45, no. 4-5, pp. 555-562, 2003.
M. I. Ali, F. Feng, X. Liu, W. K. Min, & M. Shabir, ”On some new operations in soft set theory”, Computers & mathematics with applications, vol. 57, no. 9, pp. 1547-1553, 2009.
K. V. Babitha, & J. Sunil, ”Soft set relations and functions”, Computers & Mathematics with applications, vol. 60, no. 7, pp. 1840-1849, 2010.
N. C¸a˘ gman, & S. Enginoˆ glu, ”Soft set theory and uni-int decision making”, European journal of operational research, vol. 207, no. 2, pp. 848-855, 2010.
T. Herawan, & M. M. Deris, ”A soft set approach for association rules mining”, Knowledgebased systems, vol. 24, no. 1, pp. 186-195, 2011.
T.Som,”Onthetheoryofsoftset, softrelation and fuzzy soft relation”, in Proc. of the National Conference on Uncertainty: A Mathematical Approach, UAMA-06, Burdwan, pp. 1-9, 2006.
H. Aktac ¸, and N. C¸a˘ gman, ”Soft sets and soft groups”, Information sciences, vol. 177, pp. 2726- 2735, 2007.
Y. Zou and Z. Xiao, ”Data analysis approaches of soft sets under incomplete information”, Knowledge base system, vol. 21, pp. 941-945, 2008.
S. Alkhazaleh, & A. R. Salleh, ”Soft expert sets”, Advances in decision sciences, vol. 2011, pp.1-12, 2011.
M. Ihsan, M. Saeed, & A. U. Rahman, ”A Rudimentary approach to develop context for convexity cum concavity on soft expert set with some generalized results”, Punjab university journal of mathematics, vol. 53, no. 9, pp. 621-629, 2021.
M. Ihsan, A. U. Rahman, M. Saeed, & H. A. E. W. Khalifa, ”Convexity-cum-concavity on fuzzy soft expert set with certain properties”, International journal of fuzzy logic and intelligent systems, vol. 21, no. 3, pp. 233-242, 2021.
S. Alkhazaleh, & A. R. Salleh, ”Fuzzy soft expert set and its application”, Applied mathematics, vol. 5, no. 9, pp. 1349-1368, 2014.
F. Smarandache, ”Extension of soft set to hypersoft set and then to plithogenic hypersoft set”, Neutrosophic sets and systems, vol. 22, pp. 168-170, 2018.
M. Abbas, G. Murtaza, & F. Smarandache, ”Basic operations on hypersoft sets and hypersoft point”, Neutrosophic sets and systems, vol. 35, pp. 407-422, 2020.
S. Y. Musa, & B. A. Asaad, ”Hypersoft topological spaces”, Neutrosophic sets and systems, vol. 49, no. 1, pp. 26, 2022.
H. Kamac¨ı, ”On hybrid structures of hypersoft sets and rough sets”, International journal of modern science and technology, vol. 6, no. 4, pp. 69-82, 2021.
D. Ajay, & J. J. Charisma, ”An mcdm based on alpha open hypersoft sets and its application”, in International Conference on Intelligent and Fuzzy Systems, Springer, Cham, pp. 333-341, 2021.
O. Dalklc¸, ”Determining the membership degrees in the range (0, 1) for hypersoft sets independently of the decision-maker”, International journal of systems science, pp. 1-11, 2022.
N. C¸a˘ gman, F. C¸itak, & S. Enginoˆ glu, ”FP-soft set theory and its applications”, Annals of fuzzy mathe- matics and informatics, vol. 2, no. 2, pp. 219-226, 2011.
S. Alkhazaleh, & A. R. Salleh, ”Fuzzy soft expert set and its application”, Applied mathematics, vol. 5, no. 9, pp. 1349-1368, 2014.
Y. Tella, A. Peter, & S. B. Hosea, ”Fuzzy parameterized fuzzy soft set for multiple criteria decision process under multiple expert assessments”, International journal of engineering sciences & management, vol. 5, no. 1, pp.180-185, 2015.
M. Bashir, & A. R. Salleh, ”Fuzzy parameterized soft expert set”, Abstract and applied analysis, vol. 2012, pp.1-15, 2012.
A. U. Rahman, M. Saeed, & S. Zahid, ”Application in decision making based on fuzzy parameterized hypersoft set theory”, Asia mathematika, vol. 5, no. 1, pp.19-27, 2021.
M. Ihsan, A. U.Rahman, & M. Saeed, ”Hypersoft expert set with application in decision making for recruitment process”, Neutrosophic sets and systems, vol. 42, pp. 191-207, 2021.
P. Shoval, & Y. Lugasi, ”Models for computer system evaluation and selection”, Information &Management, vol. 12, no. 3, pp. 117-129, 1987.
M. Ihsan, M. Saeed, & A. U. Rahman, ”Neutrosophic hypersoft expert set: Theory and Applications”, Neutrosophic Sets Syst, vol. 50, pp. 431-458, 2022.
M. Ihsan, A. U. Rahman, & M. Saeed, ”Single valued neutrosophic hypersoft expert set with application in decision making”, Neutrosophic Sets and Systems, vol. 47, pp. 451-471, 2021.
P. Eindor, ”Dynamic approach to selecting computers”, Datamation, vol. 23, no. 6, p. 103, 1977.
R. L. Keeney, ”Measurement scales for quantifying attributes”, Behavioral Science, vol. 26, no. 1, pp. 29-36, 1987.
Published
2025-04-16
How to Cite
IHSAN, Muhammad.
Parameterization of Multi-Decisive Hypersoft Set Under Fuzzy Environment With Application in Multi-Attribute Decision Making.
Yugoslav Journal of Operations Research, [S.l.], apr. 2025.
ISSN 2334-6043.
Available at: <https://yujor.fon.bg.ac.rs/index.php/yujor/article/view/1335>. Date accessed: 21 apr. 2025.
doi: https://doi.org/10.2298/YJOR241115013I.
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Research Articles
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