Abstract
Fuzzy hypersoft set (FHS-set) is an effective and flexible model as it not only minimizes the complexities of fuzzy set for dealing uncertainties, but also fulfills the parameterization requirements of soft set and fuzzy soft set. FHS-set is projected to address the limitations of these models regarding the entitlement of multi-argument approximate function. This kind of function maps the sub-parametric tuples to power set of universe. It emphasizes the partitioning of each attribute into its attribute-valued set that is missing in existing soft set-like structures. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. As convexity has an essential function in optimization and control, pattern classification and recognition, image processing and in different fields of operation research, numerical analysis, etc. In order to tackle the various features of classical convexity (concavity) with uncertain environment of multi-argument approximate function, an articulate cum mathematical technique is utilized to develop a theoretical framework of convexity cum concavity on fuzzy hypersoft set which is more generalized and effective concept to deal with optimization relating problems. Moreover, some generalized properties like strictly convex (concave), strongly convex (concave), \(\delta \)-inclusion and aggregation operations are established. The proposed study is authenticated with the provision of daily-life application based on proposed decision-making algorithm. Lastly, the features of proposed study are compared with the some existing relevant models to show its meritorious impact.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
This study has no associated data.
References
Abbas M, Murtaza G, Smarandache F (2020) Basic operations on hypersoft sets and hypersoft point. Neutrosophic Sets Syst 35:407–421. https://doi.org/10.5281/zenodo.3951694
Ahsan M, Saeed M, Rahman AU (2021) A theoretical and analytical approach for fundamental framework of composite mappings on fuzzy hypersoft classes. Neutrosophic Sets and Syst 45:268–285. https://doi.org/10.5281/zenodo.5486295
Alcantud JCR, Rambaud SC, Torrecillas MJM (2017) Valuation fuzzy soft sets: a flexible fuzzy soft set based decision making procedure for the valuation of assets. Symmetry 9(11):253. https://doi.org/10.3390/sym9110253
Ali MI, Feng F, Liu X, Min WK, Sabir M (2009) On some new operations in soft set theory. Comput Math Appl 57:1547–1553. https://doi.org/10.1016/j.camwa.2008.11.009
Babitha KV, Sunil JJ (2010) Soft set relations and functions. Comput Math Appl 60:1840–1849. https://doi.org/10.1016/j.camwa.2010.07.014
Babitha KV, Sunil JJ (2011) Transitive closure and ordering in soft set. Comput Math Appl 61:2235–2239. https://doi.org/10.1016/j.camwa.2011.07.010
Debnath S (2021) Fuzzy hypersoft sets and its weightage operator for decision making. J Fuzzy Ext Appl 2(2):163–170. https://doi.org/10.22105/jfea.2021.275132.1083
Deli I (2019) Convex and concave sets based on soft sets and fuzzy soft sets. J New Theory 29:101–110
Feng F, Li C, Davvaz B, Ali MI (2010) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14(9):899–911. https://doi.org/10.1007/s00500-009-0465-6
Ge X, Yang S (2011) Investigations on some operations of soft sets. World Acad Sci Eng Technol 75:1113–1116
Guan X, Li Y, Feng F (2013) A new order relation on fuzzy soft sets and its application. Soft Comput 17(1):63–70. https://doi.org/10.1007/s00500-012-0903-8
Hassan N, Sayed OR, Khalil AM, Ghany MA (2017) Fuzzy soft expert system in prediction of coronary artery disease. Int J Fuzzy Syst 19(5):1546–1559. https://doi.org/10.1007/s40815-016-0255-0
Ihsan M, Rahman AU, Saeed M (2021) Hypersoft expert set with application in decision making for recruitment process. Neutrosophic Sets Syst 42:191–207. https://doi.org/10.5281/zenodo.4711524
Ihsan M, Rahman AU, Saeed M (2021) Fuzzy hypersoft expert set with application in decision making for the best selection of product. Neutrosophic Sets and Syst 46:318. https://doi.org/10.5281/zenodo.5553534
Kamacı H, Saqlain M (2021) n-ary fuzzy hypersoft expert sets. Neutrosophic Sets Syst 43:180–211. https://doi.org/10.5281/zenodo.4914849
Khameneh AZ, Kılıçman A (2018) Parameter reduction of fuzzy soft sets: an adjustable approach based on the three-way decision. Int J Fuzzy Syst 20(3):928–942. https://doi.org/10.1007/s40815-017-0409-8
Li F (2011) Notes on soft set operations. ARPN J Syst softw 1(6):205–208
Liu Y, Qin K, Martínez L (2018) Improving decision making approaches based on fuzzy soft sets and rough soft sets. Appl Soft Comput 65:320–332. https://doi.org/10.1016/j.asoc.2018.01.012
Majeed SN (2016) Some notions on convex soft sets. Ann Fuzzy Math Inform 12(4):517–526
Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562. https://doi.org/10.1016/S0898-1221(03)00016-6
Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602
Molodtsov D (1999) Soft set theory - first results. Comput Math Appl 37:19–31. https://doi.org/10.1016/S0898-1221(99)00056-5
Martin N, Smarandache F (2020) Introduction to combined plithogenic hypersoft sets. Neutrosophic Sets Syst 35:503–510. https://doi.org/10.5281/zenodo.3951708
Paik B, Mondal SK (2020) A distance-similarity method to solve fuzzy sets and fuzzy soft sets based decision-making problems. Soft Comput 24(7):5217–5229. https://doi.org/10.1007/s00500-019-04273-z
Pei D, Miao D (2005) From soft set to information system. In international conference of granular computing IEEE 2:617–621. https://doi.org/10.1109/GRC.2005.1547365
Rahman AU, Saeed M, Zahid S (2021) Application in decision making based on fuzzy parameterized hypersoft set theory. Asia Mathematika 5(1):19–27. https://doi.org/10.5281/zenodo.4721481
Rahman AU, Saeed M, Smarandache F, Ahmad MR (2020) Development of hybrids of hypersoft set with complex fuzzy set, complex intuitionistic fuzzy set and complex neutrosophic set. Neutrosophic Sets Syst 38:335–354. https://doi.org/10.5281/zenodo.4300520
Rahman AU, Saeed M, Hafeez A (2021) Theory of bijective hypersoft set with application in decision making. Punjab Univ J Math 53(7):511–526. https://doi.org/10.52280/pujm.2021.530705
Salih HM, Sabir PO (2018) Some new properties of convex and concave soft sets. Diyala J Pure Sci 15(9):84–94. https://doi.org/10.24237/djps.1501.471B
Saeed M, Rahman AU, Ahsan M, Smarandache F (2021) An inclusive study on fundamentals of hypersoft set. In: Smarandache F, Saeed M, Abdel-Baset M, Saqlain M (eds) Theory Appl Hypersoft Set. Pons Publishing House, Brussels, pp 1–23
Saeed M, Ahsan M, Abdeljawad T (2021) A development of complex multi-fuzzy hypersoft set with application in MCDM based on entropy and similarity measure. IEEE Access 9:60026–60042. https://doi.org/10.1109/ACCESS.2021.3073206
Sezgin A, Atagün AO (2011) On operations of soft sets. Comput Math Appl 61(5):1457–1467. https://doi.org/10.1016/j.camwa.2011.01.018
Smarandache F (2018) Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic Sets Syst 22:168–170
Xiao F (2018) A hybrid fuzzy soft sets decision making method in medical diagnosis. IEEE Access 6:25300–25312. https://doi.org/10.1109/ACCESS.2018.2820099
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353. https://doi.org/10.1016/S0019-9958(65)90241-X
Zhan J, Zhu K (2017) A novel soft rough fuzzy set: z-soft rough fuzzy ideals of hemirings and corresponding decision making. Soft Comput 21(8):1923–1936. https://doi.org/10.1007/s00500-016-2119-9
Zhang J, Wu X, Lu R (2020) Decision analysis methods combining quantitative logic and fuzzy soft sets. Int J Fuzzy Syst 22(6):1801–1814. https://doi.org/10.1007/s40815-020-00899-6
Acknowledgements
Authors are thankful to referees for improving the quality of this paper their their valuable suggestions.
Funding
The authors received no specific funding for this study.
Author information
Authors and Affiliations
Contributions
Conceptualization was done by A.U.R. and M.S.; methodology was done by A.U.R. and F.S.; software was done by A.U.R.; validation was done by A.U.R., M.S. and F.S.; formal analysis was carried out by A.U.R. and M.S.; investigation was done by M.S. and F.S.; visualization was done by A.U.R., M.S. and F.S.; supervision was done by M.S. and F.S. All authors have read and agreed to the published version of the manuscript.
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethical approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Informed consent
Informed consent was obtained from all individual participants included in the study.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Rahman, A.U., Saeed, M. & Smarandache, F. A theoretical and analytical approach to the conceptual framework of convexity cum concavity on fuzzy hypersoft sets with some generalized properties. Soft Comput 26, 4123–4139 (2022). https://doi.org/10.1007/s00500-022-06857-8
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-022-06857-8