Introducing hesitant fuzzy equations and determining market equilibrium price

• Autorzy: Babakordi Fatemeh , Taghi-Nezhad N. A.
• Języki publikacji: EN

Abstrakty

EN

A vast majority of research has been performed in the field of hesitant fuzzy sets (HFSs), involving the introduction of some properties, operations, relations and modifications of such sets or considering the application of HFSs in MCDM (multicriteria decision making). On the other hand, no research has been performed in the field of fully hesitant fuzzy equations. Therefore, in this paper, fully hesitant fuzzy equations and dual hesitant fuzzy equations are introduced. First, a method is proposed to solve one-element hesitant fuzzy equations. Then, the proposed method is extended to solve n-element hesitant fuzzy equations effectively. Moreover, to show the applicability of the proposed method, it is used to solve a real world problem. Thus, the proposed method is applied to determine market equilibrium price. Also, some other numerical examples are presented to better show the performance of the proposed method.

Słowa kluczowe

EN

hesitant fuzzy set; hesitant fuzzy equations; dual hesitant fuzzy equations; membership degree

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2021
• Tom: Vol. 50, No. 3
• Strony: 363--382
• Opis fizyczny: Bibliogr. 43 poz., rys.

Twórcy

autor

Babakordi Fatemeh

• Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran

autor

Taghi-Nezhad N. A.

• Department of Mathematics, Faculty of Science, Gonbad Kavous University, Gonbad Kavous, Iran

Bibliografia

• Abbasbandy, S. and Asady, B. (2004) Newton’s method for solving fuzzy nonlinear equations. Appl Math Comput, 159, 349–356.
• Allahviranloo, T. and Babakordi, F. (2017) Algebraic solution of fuzzy linear system as: $$\widetilde {A}\widetilde {X}+\widetilde {B}\widetilde {X}= \widetilde {Y}$$ A˜X˜+ B˜X˜= Y˜. Soft Computing, 21(24), 7463-7472.
• Amirfakhrian, M. (2012) Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance. Soft Comput, 16(6), 1035–1041.
• Babakordi, F. and Firozja, A. (2020) Solving Fully Fuzzy Dual Matrix System With Optimization Problem. International Journal of Industrial Mathematics, 12(2), 109-119.
• Babakordi, F., Allahviranloo, T. and Adabitabarrozja, T. (2016) An efficient method for solving LR fuzzy dual matrix system. Journal of Intelligent & Fuzzy Systems, 30, 575–581.
• Baumol, W. J. (1972). Economic Theory and Operations Analysis. Prentice-Hall, Inc., Englewood Cliffs, New Jersey.
• Begnini, M., Bertol, W. and Martins, N. A. (2018). Design of an adaptive fuzzy variable structure compensator for the nonholonomic mobile robot in trajectory tracking task. Control and Cybernetics, 47(3), 239-275.
• Boyacı, A. Ç. (2020) Selection of eco-friendly cities in Turkey via a hybrid hesitant fuzzy decision making approach. Applied Soft Computing, 89.
• Buckley, J. (1991) Solving fuzzy equations: a new solution concept. Fuzzy Sets Syst, 39(3), 291–301.
• Buckley, J., Feuring, T. and Hayashi, Y. (2002) Solving fuzzy equations using evolutionary algorithms and neural nets. Soft Computing, 6(2), 116–123.
• Chen, N., Xu, Z. and Xia, M. (2013) Interval-valued hesitant preference relations and their applications to group decision making. Knowledge Based Systems, 37, 528–540.
• Farahani, H., Nehi, H. and Paripour, M. (2016) Solving fuzzy complex system of linear equations using eigenvalue method. J. Intell. Fuzzy Syst., 31(3), 1689–1699.
• Farhadinia, B. (2014a) Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int. J. Intell. Syst., 29, 184–205.
• Farhadinia, B. (2014b) Distance and similarity measures for higher order hesitant fuzzy sets. Knowledge Based Systems, 55, 43–48.
• Farhadinia, B. and Herrera-Viedma, E. (2018) Sorting of decision-making methods based on their outcomes using dominance-vector hesitant fuzzybased distance. Soft Computing. doi:https://doi.org/10.1007/s00500-018-3143-8
• Fiedler, M., Nedoma, J., Ramik, J., Rohn, J. and Zimmermann, K. (2006) Optimization Problems with Inexact Data. Springer.
• Hesamian, Gh. (2017) Fuzzy similarity measure based on fuzzy sets. Control and Cybernetics, 46 (1), 71-86.
• Kalshetti, S. C. and Dixit, S. K. (2018) Self-adaptive grey wolf optimization based adaptive fuzzy aided sliding mode control for robotic manipulator. Control & Cybernetics, 47(4), 383-409.
• Khalili Goodarzi, F., Taghinezhad, N. A. and 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.
• Liu, P. and Zhang, X. (2020) A new hesitant fuzzy linguistic approach for multiple attribute decision making based on Dempster–Shafer evidence theory. Applied Soft Computing, 86.
• Lodwick, W. (1990) Analysis of structure in fuzzy linear programs. Fuzzy Sets and Systems, 38, 15-26.
• Nasseri, S. H., Khalili, F., Taghi-Nezhad, N. and Mortezania, S. (2014) A novel approach for solving fully fuzzy linear programming problems using membership function concepts. Ann. Fuzzy Math. Inform., 7(3), 355-368.
• Noor’ani, A., Kavikumar, J., Mustaf, M. and Nor, S. (2011) Solving dual fuzzy polynomial equation by ranking method. Far East J Math Sci, 51(2), 151–163.
• Peng, J., Wang, J., Wu, X. and Tian, C. (2017). Hesitant intuitionistic fuzzy aggregation operators based on the archimedean t-norms and tconorms. Int. J. Fuzzy Syst., 19(3), 702–714.
• Ranjbar, M. and Effati, S. (2019) Symmetric and right-hand-side hesitant fuzzy linear programming. IEEE Transactions on Fuzzy Systems, 28(2), 215-227.
• Stolfi, J. and de Figueriredo, L. (1997) Self-Validated Numerical Methods and Applications. IMPA, Brazilian Mathematics Colloquium monograph.
• Taghi-Nezhad, N. (2019) The p-median problem in fuzzy environment: proving fuzzy vertex optimality theorem and its application. Soft Computing. doi:https://doi.org/10.1007/s00500-019-04074-4
• Taleshian, F., Fathali, J., and 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.
• Tang, X., Peng Z, Ding, H., Cheng, M. and Yang, S. (2018) Novel distance and similarity measures for hesitant fuzzy sets and their applications to multiple attribute decision making. J. Intell. Fuzzy Syst., 34, 3903–3916.
• Torra, V. (2010) Hesitant Fuzzy Sets. International Journal of Intelligent Systems, 25(6), 529–539.
• Torra, V. and Narukawa, Y. (2009) On hesitant fuzzy sets and decision. The 18-th IEEE International Conference on Fuzzy Systems, Jeju Island, Korea, 1378-1382.
• Viattchenin, D. A., Owsiński, J. W. and Kacprzyk, J. (2018) New developments in fuzzy clustering with emphasis on special types of tasks. Control and Cybernetics, 47(2), 115-130.
• Wang, J., Wang, D., Zhang, H. and Chen, X. (2014) Multi-criteria outranking approach with hesitant fuzzy sets. OR Spectr, 36, 1001–1019.
• Wei, G. and Zhao, X. (2013) Induced hesitant interval-valued fuzzy Einstein aggregation operators and their application to multiple attribute decision making. J. Intell. Fuzzy Syst., 24(4), 789–803.
• Wu, P., Zhou, L., Chen, H. and Tao, Z. (2020) Multi-stage optimization model for hesitant qualitative decision making with hesitant fuzzy linguistic preference relations. Applied Intelligence, 50(1), 222-240.
• Xia, M., Xu, Z. and Chen, N. (2013) Some Hesitant fuzzy aggregation operators with their application in group decision making. Group Decis. Negot., 22(2), 259–279.
• Xian, S. and Guo, H. (2020) Novel supplier grading approach based on interval probability hesitant fuzzy linguistic TOPSIS. Engineering Applications of Artificial Intelligence, 87.
• Yu, D., Wu, Y. and Zhou, W. (2011) Multi-criteria decision making based on Choquet integral under hesitant fuzzy environment. J. Comput. Inf. Syst., 12(7), 4506–4513.
• Zhang, Z. and Chen, S. M. (2020) Group decision making with hesitant fuzzy linguistic preference relations. Information Sciences, 514, 354-368.
• Zhang, Z., Wang, C., Tian, D. and Li, K. (2014) Induced generalized hesitant fuzzy operators and their application to multiple attribute group decision making. Comput. Ind. Eng., 67, 116–138.
• Zhou, W. (2014) An accurate method for determining hesitant fuzzy aggregation operator weights and its application to project investment. Int. J. Intell. Syst., 29(7), 668–686.
• Zhu, B., Xu, Z. and Xia, M. (2011) Hesitant fuzzy information aggregation in decision making. International Journal of Approximate Reasoning, 52(3), 395–407.
• Zhu, J., Fu, F., Yin, K., Luo, J. and Wei, D. (2014) Approaches to multiple attribute decision making with hesitant interval-valued fuzzy information under correlative environment. J. Intell. Fuzzy Syst., 27, 1057–1065.