Document Type : Research Article
Authors
Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran.
10.30473/coam.2023.68208.1240
Abstract
This paper presents the introduction of two novel equation types: the partial hesitant fuzzy equation and the half hesitant fuzzy equation. Additionally, an efficient method is proposed to solve these equations by defining four solution categories: Controllable, Tolerable Solution Set (TSS), Controllable Solution Set (CSS), and Algebraic Solution Set (ASS). Furthermore, the paper establishes eight theorems that explore different types of solutions and lay out the conditions for the existence and non-existence of hesitant fuzzy solutions. The practicality of the proposed method is demonstrated through numerical examples.
Keywords
- Categories of hesitant fuzzy equations
- Partial hesitant fuzzy equation
- Half hesitant fuzzy equation
- Algebraic solution set
Main Subjects
[1] Abbasbandy, S., Asady, B. (2004). “Newton’s method for solving fuzzy nonlinear equations”, Applied Mathematics and Computation, 159, 349-356.
[2] Abuhijleh, E.A. (2023). “Complex hesitant fuzzy graph”, Fuzzy Information and Engineering, 15(2), 149-161.
[3] Alcantud, J.C.R., de Andrés, R., Torrecillas M.J.M. (2016). “Hesitant fuzzy worth: An innovative ranking methodology for hesitant fuzzy subsets”, Applied Soft Computing, 38, 232-243.
[4] Allahviranloo, T., Babakordi, F. (2017). “Algebraic solution of fuzzy linear system as: ÃX +B X =Y AX + BX = Y ”, Soft Computing, 21(24), 7463-7472.
[5] Amirfakhrian, M. (2012). “Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance”, Soft Computing, 16(6), 1035-1041.
[6] Babakordi, F. (2020). “Hesitant fuzzy set and its types”, Journal of Decisions and Operations Research, 4(4), 353-361.
[7] Babakordi, F., Allahviranloo, T. (2022). “Introducing and solving the hesitant fuzzy system AX −B”, Systems Research Institute, Polish Academy of Sciences.
[8] Babakordi, F., Taghi-Nezhad, N.A. (2021). “Introducing hesitant fuzzy equations and determining market equilibrium price”, Control and Cybernetics, 50.
[9] Babakordi, F., Allahviranloo, T., Adabitabarfirozja, T. (2016). “An efficient method for solving LR fuzzy dual matrix system”, Journal of Intelligent & Fuzzy Systems, 30, 575-581.
[10] Baker kearfott, R. (1996). “Rigorous global search: Continues problems”, Kluwer Academic Publishers, The Netherlands.
[11] Buckley, J. (1991). “Solving fuzzy equations: A new solution concept”, Fuzzy Sets and Systems, 39(3), 291-301.
[12] Buckley, J.J., Feuring, T., Hayashi, Y. (2002). “Solving fuzzy equations using evolutionary algorithms and neural nets”, Soft Computing, 6, 116-123.
[13] Farahani, H., Nehi, H., Paripour, M. (2016). “Solving fuzzy complex system of linear equations using eigenvalue method”, Journal of Intelligent & Fuzzy Systems, 31(3), 1689-1699.
[14] Jeon, J., Krishnan, S., Manirathinam, T., Narayanamoorthy, S., Nazir Ahmad, M., Ferrara, M., Ahmadian, A. (2023). “An innovative probabilistic hesitant fuzzy set MCDM perspective for selecting flexible packaging bags after the prohibition on single-use plastics”, Scientific Reports, 13(1), 1-20.
[15] Khalili Goodarzi, F., Taghinezhad, N.A., Nasseri, S.H. (2014). “A new fuzzy approach to solve a novel model of open shop scheduling problem”, University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, 76(3), 199-210.
[16] Kirişci, M. (2023). “Fermatean hesitant fuzzy sets for multiple criteria decision-making with applications”, Fuzzy Information and Engineering, 15(2), 100-127.
[17] Nasseri, S.H., Khalili, F., Taghi-Nezhad, N., Mortezania, S. (2014). “A novel approach for solving fully fuzzy linear programming problems using membership function concepts”, Annals of Fuzzy Mathematics and Informatics, 7(3), 355-368.
[18] Noor’ani, A., Kavikumar, J., Mustaf, M., Nor, S. (2011). “Solving dual fuzzy polynomial equation by ranking method”, Far East Journal of Mathematical Sciences, 51(2), 151-163.
[19] Taghi-Nezhad, N. (2019). “The p-median problem in fuzzy environment: Proving fuzzy vertex optimality theorem and its application”, Soft Computing.
[20] Taghi-Nezhad, N.A., Babakordi, F. (2023). “Fully hesitant parametric fuzzy equation”, Soft Computing, 1-12.
[21] Taleshian, F., Fathali, J., Taghi-Nezhad, N.A. (2018). “Fuzzy majority algorithms for the 1-median and 2-median problems on a fuzzy tree”, Fuzzy Information and Engineering, 1-24.
[22] Torra, V. (2010). “Hesitant Fuzzy Sets”, International Journal of Intelligent Systems, 25(6), 529-539.
[23] Torra, V., Narukawa, Y. (2009). “On hesitant fuzzy sets and decision”, In: 18-th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea.
[24] Wang, K., Lee, H. (1965). “First course on fuzzy theory and applications”, Advances in Soft Computing.
[25] Xia, M.M., Xu, Z.S. (2011). “Hesitant fuzzy information aggregation in decision making”, International Journal of Approximate Reasoning, 52(3), 395-407.
[26] Xia, M., Xu, Z., Chen, N. (2013).“Some hesitant fuzzy aggregation operators with their application in group decision making”, Group Decision and Negotiation, 22(2), 259-279.
[27] Xu, Y. (2023). “On uncertainty measures of the interval-valued hesitant fuzzy set”, Advance in Fuzzy System, Volume 2023, Article ID: 3228324, doi:10.1155/2023/3228324.
[28] Zhang, Z., Wang, C., Tian, D., Li, K. (2014). “Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making”, Computers & Industrial Engineering, 67, 116-138.
[29] Zhao, J., Xie, W. (2023). “Interval grey hesitant fuzzy set and its applications in decision-making”, Journal of Mathematics, Volume 2023, Article ID: 7694396, doi:10.1155/2023/7694396.
[30] Zhu, B., Xu, Z., Xia, M. (2011). “Hesitant fuzzy information aggregation in decision making”, International Journal of Approximate Reasoning, 52(3), 395-407.
)