Volume 20 , Issue 2 , PP: 135-161, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Muhammad Saeed 1 * , Florentin Smarandache 2 , Muhammad Arshad 3 , Atiqe Ur Rahman 4
Doi: https://doi.org/10.54216/IJNS.200209
When compared to its extension, hypersoft set, a soft set only deals with a single set of attributes, while a hypersoft set deals with several attribute-valued disjoint sets that correspond to various attributes. Several researchers have developed models based on soft sets, but the majority of these models suffer from limitations since they are inappropriate for interval-type data or uncertain data. In order to address these issues, a novel model interval-valued fuzzy hypersoft set (IV F HS -set) is presented in this research article. This model not only resolves the inadequacy of soft set for distinct attributes for non-overlapping attribute-valued sets, but also addresses the limitations of soft set-like models with having data in interval environment. This work modifies the current fuzzy hypersoft set concept and introduces certain fundamental ideas, such as subset, not set, whole set, and absolute relative null set, relative absolute set and aggregation operations e.g. intersection, union, extended intersection, restricted union, complement, OR, AND, difference, restricted difference are discussed under IV F HS -set environment with illustrated examples. Some new hybrids of fuzzy hypersoft set under interval-valued settings are also discussed. Moreover, some extensions of IV F HS -set are presented along with different operations.
interval-valued fuzzy set , interval-valued fuzzy soft set , hypersoft set , set-theoretic operations
[1] P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics, vol. 9, no. 3, pp. 589-602, 2001.
[2] L. A. Zadeh, Fuzzy sets, Information and Control, vol. 8, pp. 338-353, 1965.
[3] D. Molodtsov, Soft set theory, first results, Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31, 1999.
[4] A. U. Rahman, M. Saeed, M. Ihsan, M. Arshad, S. Ayaz, A conceptual framework of m-convex and m-concave sets under soft set environment with properties, Transactions in Mathematical and Computational Sciences, vol. 1, no. 1, pp. 49-60, 2021.
[5] A. U. Rahman, M. Saeed, M. Arshad, M. Ihsan, M. R. Ahmad, (m; n)-Convexity-cum-Concavity on Fuzzy Soft Set with Applications in First and Second Sense, Punjab University Journal of Mathematics,
vol. 53, no. 1, 2021.
[6] A. U. Rahman, M. Arshad, M. Saeed, A Conceptual Framework of Convex and Concave Sets under Refined Intuitionistic Fuzzy Set Environment, Journal of Prime Research in Mathematics, vol. 17, no. 2, pp. 122-137, 2021.
[7] X. Yang, T. Y. Lin, J. Yang, Y. Li, D. Yu, Combination of interval-valued fuzzy set and soft set. Computers and Mathematics with Applications, vol. 58, no. 3, pp. 521-527, 2009.
[8] M. B. Gorzałczany, A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy sets and systems, vol. 21, no. 1, pp. 1-17, 1987.
[9] X. Peng, H. Garg, Algorithms for interval-valued fuzzy soft sets in emergency decision making based on WDBA and CODAS with new information measure, Computers and Industrial Engineering, vol. 119,
pp. 439-452, 2018.
[10] B. Chetia, P. K. Das, An Application of Interval-Valued Fuzzy Soft Sets in Medical Diagnosis, Int. J. Contemp. math. sciences, vol. 5, no. 38, pp. 1887-1894, 2010.
[11] X. D. Peng, Y. Yang. Information measures for interval-valued fuzzy soft sets and their clustering algorithm. Journal of Computer Applications, vol. 35, no. 8, pp. 2350-2354, 2015. doi:10.11772/j.issn.1001-9081.2015.08.2350
[12] X. Ma, Q. Fei, H. Qin, H. Li, W. Chen, A new efficient decision making algorithm based on intervalvalued fuzzy soft set, Applied Intelligence, vol. 51, no. 6, pp. 3226-3240, 2021.
[13] X. Ma, H. Qin, N. Sulaiman, T. Herawan, J. H. Abawajy, The parameter reduction of the interval-valued fuzzy soft sets and its related algorithms, IEEE Transactions on Fuzzy Systems, vol. 22, no. 1, pp. 57-71, 2013.
[14] H. Qin, X. Ma, A complete model for evaluation system based on interval-valued fuzzy soft set, IEEE Access, vol. 6, pp. 35012-35028, 2018.
[15] X. Peng, Y. Yang, Information measures for interval-valued fuzzy soft sets and their clustering algorithm, J. Comput. Appl., vol. 35, pp. 23-50, 2015.
[16] K. T. Atanassov, Intuitionistic fuzzy sets, In Intuitionistic fuzzy sets, Physica, Heidelberg, pp. 1-137, 1999.
[17] F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic, Analytic Synthesis and Synthetic Analysis, American Research Press, Rehoboth, 1998.
[18] B. C. Cuong, Picture fuzzy sets, Journal of Computer Science and Cybernetics, vol. 30, pp. 409-420, 2014.
[19] F. Smarandache, Extension of soft set of hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets Syst., vol. 22, pp. 168-170, 2018. http://doi.org/10.5281/zenodo.2838716
[20] M. Saeed, A. U. Rahman, M. Ahsan, F. Smarandache, An inclusive study on fundamentals of hypersoft set, Theory and Application of Hypersoft Set, vol. 1, pp. 1-23, 2021.
[21] F. Abbas, G. Murtaza, F. Smarandache, Basic operations on hypersoft sets and hypersoft points, Neutrosophic Sets Syst., vol. 35, pp. 407-421, 2020. [CrossRef]
[22] A. U. Rahman, M. Saeed, F. Smarandache, Convex and Concave Hypersoft Sets with Some Properties, Neutrosophic Sets Syst., vol. 38, pp. 497-508, 2020.
[23] A. U. Rahman, A. Hafeez, M. Saeed, M. R. Ahmad, U. Farwa, Development of Rough Hypersoft Set with Application in Decision Making for the Best Choice of Chemical Material, In Theory and Application of Hypersoft Set, Pons Publishing House, Brussel, pp. 192-202, 2021.
[24] H. Kamacı, On hybrid structures of hypersoft sets and rough sets, International Journal of Modern Science and Technology, vol. 6, no. 4, pp. 69-82, 2021.
[25] N. Martin, F. Smarandache, Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft Sets, A Novel Outlook, Neutrosophic Sets Syst., vol. 33, pp. 78–91, 2020.
[26] A. Yolcu, T.Y. Ozturk, Fuzzy Hypersoft Sets and Its Application to Decision-Making, In Theory and Application of Hypersoft Set; Pons Publishing House: Brussel, Belgium, pp. 50–64, 2021.
[27] M. Arshad, M. Saeed, A. U. Rahman, D. A. Zebari, M. A. Mohammed, A. S. Al-Waisy, M. Albahar, M. Thanoon, The Assessment of Medication Effects in Omicron Patients through MADM Approach Based on Distance Measures of Interval-Valued Fuzzy Hypersoft Set, Bioengineering, vol. 9, no. 11, 2022.
[28] A.U. Rahman, M. Saeed, S. Zahid, Application in Decision Making Based on Fuzzy Parameterized Hypersoft Set Theory, Asia Math., vol. 5, pp. 19–27, 2021.
[29] A. U. Rahman, M. Saeed, M. Arshad, S. El-Morsy, Multi-Attribute Decision-Support System Based on Aggregations of Interval-Valued Complex Neutrosophic Hypersoft Set, Applied Computational Intelligence and Soft Computing, 2021.
[30] M. Arshad, M. Saeed, A. U. Rahman, A novel intelligent multi-attributes decision-making approach based on generalized neutrosophic vague hybrid computing, Neutrosophic Sets and Systems, vol. 50, no.
1, 2022.
[31] M. Saeed, A. U. Rahman, M. Arshad, A. Dhital, A novel approach to neutrosophic hypersoft graphs with properties, Neutrosophic Sets and Systems, vol. 46, pp. 336-355, 2021.
[32] M. Saeed, A. U. Rahman, M. Arshad, A study on some operations and products of neutrosophic hypersoft graphs, Journal of Applied Mathematics and Computing, vol. 68, no. 4, pp. 2187-2214, 2022.
[33] 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.
[34] F. Smarandache, Practical Applications of IndetermSoft Set and IndetermHyperSoft Set and Introduction to TreeSoft Set as an extension of the MultiSoft Set. Neutrosophic Sets and Systems, vol. 51, pp. 939-947, 2022.
[35] F. Smarandache, Introduction to the IndetermSoft Set and IndetermHyperSoft Set. Neutrosophic Sets and Systems, vol. 50, 629-650, 2022.
