Citation: Ting Xie, Dapeng Li. On the stability of projected dynamical system for generalized variational inequality with hesitant fuzzy relation[J]. AIMS Mathematics, 2020, 5(6): 7107-7121. doi: 10.3934/math.2020455
[1] | B. H. Ahn, Computation of Market Equilibria for Policy Analysis: The Project Independence Evaluation Study (PIES) Approach, Garland Press, New York, 1979. |
[2] | J. C. R. Alcantud, V. Torra, Decomposition theorems and extension principles for hesitant fuzzy set, Inform. Fusion, 41 (2018), 48-56. doi: 10.1016/j.inffus.2017.08.005 |
[3] | B. Bedregal, R. Reiser, H. Bustince, et al., Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms, Inform. Sciences, 255 (2014), 82-99. doi: 10.1016/j.ins.2013.08.024 |
[4] | R. Bellman, L. A. Zadeh, Decision making in a fuzzy environment, Manage. Sci., 17 (1970), 141- 164. |
[5] | S. Boyd, L. Vandenberghe, Convex Optimization, Cambridge University Press, Cambridge, 2004. |
[6] | T. R. Ding, C. Z. Li, Course of Ordinary Differential Equations (2nd ed.), Higher Education Press, Beijing, 2004. |
[7] | B. C. Eaves, On the basic theorem of complementarity, Math. Program., 1 (1971), 68-75. doi: 10.1007/BF01584073 |
[8] | F. Facchinei, J. S. Pang, Finite-Dimensional Variational Inequalities and Complementarity Problems I (1st ed.), Springer, New York, 2003. |
[9] | S. C. Fang, E. L. Peterson, Generalized variational inequalities, J. Optimiza. Theory Appl., 38 (1982), 363-383. doi: 10.1007/BF00935344 |
[10] | T. L. Friesz, D. H. Bernstein, N. J. Mehta, et al., Day-to-day dynamic network disequilibria and idealized traveler information systems, Oper. Res., 42 (1994), 1120-1136. doi: 10.1287/opre.42.6.1120 |
[11] | P. T. Harker, J. S. Pang, Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications, Math. Program., 48 (1990), 161-220. doi: 10.1007/BF01582255 |
[12] | P. Hartman, G. Stampacchia, On some nonlinear elliptic differential functional equations, Acta Math., 115 (1966), 271-310. doi: 10.1007/BF02392210 |
[13] | C. F. Hu, Solving fuzzy variational inequalities over a compact set, J. Comput. Appl. Math., 129 (2001), 185-193. doi: 10.1016/S0377-0427(00)00549-5 |
[14] | C. F. Hu, Generalized variational inequalities with fuzzy relation, J. Comput. Appl. Math., 146 (2002), 47-56. doi: 10.1016/S0377-0427(02)00417-X |
[15] | C. F. Hu, F. B. Liu, Solving mathematical programs with fuzzy equilibrium constraints, Comput. Math. Appl., 58 (2009), 1844-1851. doi: 10.1016/j.camwa.2009.08.037 |
[16] | A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Academic Press, New York, 1975. |
[17] | D. Kinderlehrer, G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York and London, 1980. |
[18] | E. Klein, A. Thompson, Theory of Correspondences, Wiley-Interscience, New York, 1984. |
[19] | J. LaSalle, Some extensions of Liapunov's second method, Ire Transactions on Circuit Theory, 7 (1960), 520-527. doi: 10.1109/TCT.1960.1086720 |
[20] | L. W. Liu, Y. Q. Li, On Generalized set-valued variational inclusions, J. Math. Anal. Appl., 261 (2001), 231-240. doi: 10.1006/jmaa.2001.7493 |
[21] | L. Mathiesen, Computational experience in solving equilibrium models by a sequence of linear complementarity problems, Oper. Res., 33 (1985), 1225-1250. doi: 10.1287/opre.33.6.1225 |
[22] | L. Mathiesen, An algorithm based on a sequence of linear complementarity problems applied to a Walrasian equilibrium model: an example, Math. Program., 37 (1987), 1-18. doi: 10.1007/BF02591680 |
[23] | M. A. Noor, Variational inequalities for fuzzy mappings (I), Fuzzy Set. Syst., 55 (1993), 309-312. doi: 10.1016/0165-0114(93)90257-I |
[24] | M. A. Noor, Implicit dynamical systems and quasi variational inequalities, Appl. Math. Comput., 134 (2003), 69-81. |
[25] | M. J. Smith, The existence, uniqueness and stability of traffic equilibria, Transport. Res. B-Meth, 13 (1979), 295-304. |
[26] | V. Torra, Hesitant fuzzy sets, Int. J. Intell. Syst., 25 (2010), 529-539. |
[27] | T. Xie, Z. T. Gong, A hesitant soft fuzzy rough set and its applications, IEEE Access, 7 (2019), 167766-167783. doi: 10.1109/ACCESS.2019.2954179 |
[28] | T. Xie, Z. T. Gong, Variational-like inequalities for n-dimensional fuzzy-vector-valued functions and fuzzy optimization, Open Math., 17 (2019), 627-645. doi: 10.1515/math-2019-0050 |
[29] | X. B. Yang, X. N. Song, Y. S. Qi, et al., Constructive and axiomatic approaches to hesitant fuzzy rough set, Soft Comput., 18 (2014), 1067-1077. doi: 10.1007/s00500-013-1127-2 |
[30] | L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X |