Full Fuzzy parameterized Soft Expert Set with Application to Decision Making
Keywords:
Fuzzy Set, Soft Set, Fuzzy Soft Set, Fuzzy Parameterized Soft Set, Full Fuzzy parameterized Soft Set, Basic Operations, Algebraic Properties
Abstract
In this work, the authors consider a generalization of fuzzy parameterized soft expert set introducing the concept of full fuzzy parameterized soft expert set and study their properties. We define its basic operations and develop an algorithm to demonstrate its application in decision making. We also define the optimal choice object, developing and proving propositions relating to it. Finally, we use a concrete example to illustrate our algorithm.
References
[1] Zadeh L. A.: Fuzzy Set, Information and Control, 8(3), 338-353, (1965),
https://doi.org/10.1016/S0019-9958(65)90241-X.
[2] Alkhazaleh S., Salleh A.R. , Hassan N.: Soft Expert Set, Advances in Decision Sciences Article ID 757868 (2011), https://doi.org/10.1155/2011/757868.
[3] Alkhazaleh, S., Salleh, A.: Fuzzy Soft Expert and its Application, Applied Mathematics, 5 (09), 1349-1368 (2014), https://doi.org/10.4236/am.2014.59127.
[4] Molodtsov, D.A.: Soft Set Theory-First Results, Computers and Mathematics with Applications, 37, 19-31, (1999), https://doi.org/10.1016/S0898-1221(99)00056-5.
[5] Maji, P.K., Biswas, R., Roy, A.R.: Soft Set Theory, Computers and Mathematics with Applications, 45, 555-562, (2003), https://doi.org/10.1016/S0898-1221(03)00016-6.
[6] Maji, R., Roy, A.R.: An Application of Soft Sets in a Decision Making Problem, Comput. Math. Appli., 44, 1077-1083, (2002), https://doi.org/10.1016/S0898-1221(02)00216-X.
[7] Nasef, A.A., El-Maghrabi, A.I., Elfeky, A.M., Jafari, S.: Soft Set Theory and Its Applications, Selected papers of the 2018 International Conferenceon Topology and its Applications, 211-222 (2020)
[8] Cheng, D., Tsang, E.C.C., Yeung, D.S., Wang, X.: The Parameterization Reduction Soft Sets and its Applications. Computers and Mathematics with Appliacations, 49, 757-763, (2005), https://doi.org/10.1016/j.camwa.2004.10.036.
[9] Ihsan, M., Saed, Khalifa, A.: An intelligent Fuzzy parameterized Multi-criteria Decision-support System Based on Intuitionistic Fuzzy Hyper Soft Expert Set For Automobile Evaluation, Advances in Mechanical Engineering, 14(7), (2022), https://doi.org/10.1177/16878132221110005.
[10] Kong, Z., Gao, L., Wang, L., Li, S.:The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications, 56(12), 3029-3037, (2008), https://doi.org/10.1016/j.camwa.2008.07.013
[11] Elijah, E. E., Muhammad, U. F.: A Novel Approach for Normal Parameter Reduction Algorithm of Soft Set Using Unit Similarity Matrix. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1), 43-58, (2023), https://doi.org/10.6084/zenodo.8218007.
[12] Akram, M., Ali, G., Carlos,J. A. R., Riaz, A.: Group Decision-making with Fermatean Fuzzy Soft Expert Knowledge, Artificial Intelligence Review, 55, 5349–5389, (2022), https://doi.org/10.1007/s10462-021-10119-8.
[13] Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy Soft Sets, Journal of Fuzzy Mathematics, 9(3), 677-691, (2001).
[14] Thammajitr, K., Visit, P., Suebsan, P.: Fuzzy Parameterized Relative Fuzzy Soft Set in Decision Making Problems, International Journal of Innovative Computing Information and Control, 18(3), 867–881, (2022).
[15] Cagman, N., Enginoglu, S., Citak, F.: Fuzzy Soft Set Theory and its Applications, Iranian Journal of Fuzzy Systems, 8(3), 137-147, (2011), https://doi.org/10.22111/IJFS.2011.292.
[16] Cagman, N., Citak, F., Enginoglu, S.: Fuzzy Parameterized Soft Set Theory and its Applications, Annals of Fuzzy Mathematics and Informatics, 2(2), 219-226, (2011).
[17] Cagman, N., Citak, F., Enginoglu, S.: Fuzzy Parameterized Fuzzy Soft Set Theory and its Applications, Turkish Journal of Fuzzy Systems, 1(1), 21-35,( 2010).
[18] Majumdar, P., Samanta, S.K.: Generalised Fuzzy Soft Set , Computers and Mathematics with Application 59(2010) 1425-1432.
[19] Triphathy, B. K.,Sooraj T. R., Mohanty R. K.: A New Approach to Fuzzy Soft Set Theory and its Application in Decision Making, Computational Intelligence in Data Mining, 2, 305–313, (2016), https://doi.org/10.1007/978-81-322-2731-128
[20] Bashir, M., Salleh, A.: Possibility Fuzzy Soft Expert Set, 2, 208-211, (2012), https://doi.org/ 10.236/ojapps.2012.24B047 https://doi.org/10.1504/IJADS.2017.084310
[22] Edeghagba,E., E., Muhammad, F.: On Full Fuzzy Prametrized Soft Set, International Journal of Mthematical Sciences and Optimization Theory and Application, 7(2), 76-87, (2022), https://doi.org/10.52968/28302774.
https://doi.org/10.1016/S0019-9958(65)90241-X.
[2] Alkhazaleh S., Salleh A.R. , Hassan N.: Soft Expert Set, Advances in Decision Sciences Article ID 757868 (2011), https://doi.org/10.1155/2011/757868.
[3] Alkhazaleh, S., Salleh, A.: Fuzzy Soft Expert and its Application, Applied Mathematics, 5 (09), 1349-1368 (2014), https://doi.org/10.4236/am.2014.59127.
[4] Molodtsov, D.A.: Soft Set Theory-First Results, Computers and Mathematics with Applications, 37, 19-31, (1999), https://doi.org/10.1016/S0898-1221(99)00056-5.
[5] Maji, P.K., Biswas, R., Roy, A.R.: Soft Set Theory, Computers and Mathematics with Applications, 45, 555-562, (2003), https://doi.org/10.1016/S0898-1221(03)00016-6.
[6] Maji, R., Roy, A.R.: An Application of Soft Sets in a Decision Making Problem, Comput. Math. Appli., 44, 1077-1083, (2002), https://doi.org/10.1016/S0898-1221(02)00216-X.
[7] Nasef, A.A., El-Maghrabi, A.I., Elfeky, A.M., Jafari, S.: Soft Set Theory and Its Applications, Selected papers of the 2018 International Conferenceon Topology and its Applications, 211-222 (2020)
[8] Cheng, D., Tsang, E.C.C., Yeung, D.S., Wang, X.: The Parameterization Reduction Soft Sets and its Applications. Computers and Mathematics with Appliacations, 49, 757-763, (2005), https://doi.org/10.1016/j.camwa.2004.10.036.
[9] Ihsan, M., Saed, Khalifa, A.: An intelligent Fuzzy parameterized Multi-criteria Decision-support System Based on Intuitionistic Fuzzy Hyper Soft Expert Set For Automobile Evaluation, Advances in Mechanical Engineering, 14(7), (2022), https://doi.org/10.1177/16878132221110005.
[10] Kong, Z., Gao, L., Wang, L., Li, S.:The normal parameter reduction of soft sets and its algorithm, Computers and Mathematics with Applications, 56(12), 3029-3037, (2008), https://doi.org/10.1016/j.camwa.2008.07.013
[11] Elijah, E. E., Muhammad, U. F.: A Novel Approach for Normal Parameter Reduction Algorithm of Soft Set Using Unit Similarity Matrix. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 9(1), 43-58, (2023), https://doi.org/10.6084/zenodo.8218007.
[12] Akram, M., Ali, G., Carlos,J. A. R., Riaz, A.: Group Decision-making with Fermatean Fuzzy Soft Expert Knowledge, Artificial Intelligence Review, 55, 5349–5389, (2022), https://doi.org/10.1007/s10462-021-10119-8.
[13] Maji, P.K., Biswas, R., Roy, A.R.: Fuzzy Soft Sets, Journal of Fuzzy Mathematics, 9(3), 677-691, (2001).
[14] Thammajitr, K., Visit, P., Suebsan, P.: Fuzzy Parameterized Relative Fuzzy Soft Set in Decision Making Problems, International Journal of Innovative Computing Information and Control, 18(3), 867–881, (2022).
[15] Cagman, N., Enginoglu, S., Citak, F.: Fuzzy Soft Set Theory and its Applications, Iranian Journal of Fuzzy Systems, 8(3), 137-147, (2011), https://doi.org/10.22111/IJFS.2011.292.
[16] Cagman, N., Citak, F., Enginoglu, S.: Fuzzy Parameterized Soft Set Theory and its Applications, Annals of Fuzzy Mathematics and Informatics, 2(2), 219-226, (2011).
[17] Cagman, N., Citak, F., Enginoglu, S.: Fuzzy Parameterized Fuzzy Soft Set Theory and its Applications, Turkish Journal of Fuzzy Systems, 1(1), 21-35,( 2010).
[18] Majumdar, P., Samanta, S.K.: Generalised Fuzzy Soft Set , Computers and Mathematics with Application 59(2010) 1425-1432.
[19] Triphathy, B. K.,Sooraj T. R., Mohanty R. K.: A New Approach to Fuzzy Soft Set Theory and its Application in Decision Making, Computational Intelligence in Data Mining, 2, 305–313, (2016), https://doi.org/10.1007/978-81-322-2731-128
[20] Bashir, M., Salleh, A.: Possibility Fuzzy Soft Expert Set, 2, 208-211, (2012), https://doi.org/ 10.236/ojapps.2012.24B047 https://doi.org/10.1504/IJADS.2017.084310
[22] Edeghagba,E., E., Muhammad, F.: On Full Fuzzy Prametrized Soft Set, International Journal of Mthematical Sciences and Optimization Theory and Application, 7(2), 76-87, (2022), https://doi.org/10.52968/28302774.
Published
2024-09-30
How to Cite
Edeghagba , E. E., Abubakar , S. I., Umar , F. M., & Abdullahi , M. (2024). Full Fuzzy parameterized Soft Expert Set with Application to Decision Making. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 10(4), 12 - 28. Retrieved from http://ijmso.unilag.edu.ng/article/view/2385
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