Lattice-valued matrix game with mixed strategies for intelligent decision support

Knowledge-Based Systems

Volumn 32, Issue , 2012, Pages 56-64

  Xu, Yang ^a   Liu, Jun ^b   Zhong, Xiaomei ^a   Chen, Shuwei ^b,c  

^a SOUTHWEST JIAOTONG UNIVERSITY   (China)

^b UNIVERSITY OF ULSTER   (United Kingdom)

^c ZHENGZHOU UNIVERSITY   (China)

Author keywords

Decision support system; Knowledge based system; l * Module; Lattice; Lattice valued matrix game; Mixed strategy; Multi agent system

Indexed keywords

ALGEBRA STRUCTURES; BASIC PROPERTIES; CONFLICT SITUATION; DECISION PROBLEMS; EXISTENCE OF A SOLUTIONS; FUNDAMENTAL RESEARCH; GAME APPROACH; INTELLIGENT DECISION SUPPORT; LATTICE; MATRIX GAME; MIXED STRATEGY; MULTI AGENT SYSTEM (MAS); REAL-WORLD PRACTICE; RESEARCH APPROACH; RESEARCH DIRECTIONS; SUFFICIENT CONDITIONS;

DECISION MAKING; DECISION SUPPORT SYSTEMS; KNOWLEDGE BASED SYSTEMS; MULTI AGENT SYSTEMS; RESEARCH;

GAME THEORY;

EID: 84861625588     PISSN: 09507051     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.knosys.2011.08.019     Document Type: Article

References (52)

1. J.P. Aubin Mathematical methods in economics and game theory 1979 North-Holland Amsterdam
2. I. Bárány, J. Lee, and M. Shubik Classification of two-person ordinal bimatrix games International Journal of Game Theory 21 3 1992 267 290
3. G. Birkhoff Lattice Theory third ed. 1967 American Mathematical Society Providence, RL
4. C.F. Camerer Progress in behavioral game theory Journal of Economic Perspective 11 1997 167 188
5. S. Cebi, and C. Kahraman Developing a group decision support system based on fuzzy information axiom Knowledge-Based Systems 23 1 2010 3 16
6. H.K.H. Chow, K.L. Choy, and W.B. Lee A dynamic logistics process knowledge-based system - an RFID multi-agent approach Knowledge-Based Systems 20 2007 357 372
7. R. Cignoli, I. D'Ottaviano, and D. Mundici Algebraic Foundations of Many-Valued Reasoning 2000 Kluwer Dordrecht
8. B.A. Davey, and H.A. Priestley Introduction to Lattices and Order third ed. 2002 Cambridge University Press Cambridge
9. A. Day The lattice theory of functional dependencies and normal decompositions International Journal of Algebra and Computation 2 1990 409 431
10. Düntsch Rough relation algebras Fundamenta Informaticae 21 1994 321 331
11. B. Ganter, G. Stumme, R. Wille (Eds.), Formal Concept Analysis: Foundations and Applications, Lecture Notes in Artificial Intelligence, No. 3626, Springer-Verlag, 2005.
12. G. Gierz, K. Hofmann, K. Keimel, J. Lawson, M. Mislove, and D. Scott Continuous Lattices and Domains 2003 Cambridge University Press Cambridge
13. P. Gmytrasiewicz, and S. Parsons Editorial: decision theory and game theory in agent design Decision Support Systems 39 2005 151 152
14. E. Goles, M. Morvan, and H.D. Phan Lattice structure and convergence of a game of cards Annals of Combinatorics 6 3-4 2002 327 335
15. S. Gottwald A Treatise on Many-Valued Logics Studies in Logic and Computation vol. 9 2001 Research Studies Press Ltd. Baldock
16. M. Grabisch The lattice of embedded subsets Discrete Applied Mathematics 158 2010 479 488
17. G. Grätzer General Lattice Theory second ed. 2003 Birkhäuser Verlag Basel
18. Y.H. Guo, and Y. Xu Determining solution of lattice-valued matrix games Journal of System Engineering 10 4 1995 63 72 (in Chinese)
19. A. Guo, and E. Miller Lattice point methods for combinatorial games Advances in Applied Mathematics 46 2011 363 378
20. P. Hajek Metamathematics of Fuzzy Logic 1998 Kluwer Academic Publishers Dordrecht
21. E. Harzheim Ordered Sets 2005 Springer New York
22. He L.P., Huang H.Z., Du L., Zhang X.D., and Miao Q. (2007), A review of possibilistic approaches to reliability analysis and optimization in engineering design, Human-Computer Interaction. HCI Applications and Services, Lecture Notes in Computer Science, 2007, Volume 4553/2007, 1075-1084.
23. J. Järvinen, Lattice theory for rough sets, Transactions on Rough Sets VI, Lecture Notes in Computer Science, vol. 4374, 2007, pp. 400-498.
24. A.J. Jones, Game Theory - Mathematical Model of Conflict, New York, 1980.
25. V.G. Kaburlasos Towards a Unified Modeling and Knowledge-Representation Based on Lattice Theory - Computational Intelligence and Soft Computing Applications Studies in Computational Intelligence vol. 27 2006 Springer Heidelberg, Germany
26. V.G. Kaburlasos, G.X. Ritter, Computational Intelligence Based on Lattice Theory, Studies in Computational Intelligence, vol. 67, Springer, Heidelberg, Germany, 2007.
27. K. Leyton-Brown, and Y. Shoham Essentials of Game Theory: A Concise Multidisciplinary Introduction 2008 Morgan & Claypool Publishers
28. D.F. Li Linear programming approach to solve interval-valued matrix games Omega 39 2011 655 666
29. Y.M. Li, and W. Pedrycz Minimization of lattice finite automata and its application to the decomposition of lattice languages Fuzzy Sets and Systems 158 13 2007
30. Q. Liu, X. Sun, H.Q. Wang, and J. Zhao A multi-agent based system for e-procurement exception management Knowledge-Based Systems 24 1 2011 49 57
31. F. Llerena, and C. Rafels The vector lattice structure of the n-person TU games Games and Economic Behavior 54 2 2006 373 379
32. J. Lu, D. Ruan, and G.Q. Zhang A special issue on intelligent decision support and warning systems Knowledge-Based Systems 23 1 2010 1 2
33. J. Ma, J. Lu, and G.Q. Zhang Decider: a fuzzy multi-criteria group decision support system Knowledge-Based Systems 23 1 2010 23 31
34. J. Montero, B. Cappelle, and E.E. Kerre The usefulness of complete lattices in reliability theory T. Onisawa, J. Kacprzyck, Reliability and Safety Analyses under Fuzziness 1995 Physica Verlag Heidelberg 95 110
35. V. Novak, I. Perfilieva, and J. Mojckojr Mathematical Principles of Fuzzy Logic 1999 Kluwer Academic Publishers Dordrecht
36. A. Ortmann, and R. Squire A game-theoretic explanation of the administrative lattice in institutions of higher learning Journal of Economic Behavior & Organization 43 3 2000 377 391
37. M.J. Osborne An Introduction to Game Theory 2004 OUP Oxford
38. J. Pavelka On fuzzy logic II: many-valued rules of inference, II: enriched residuated lattices and semantics of propositional calculi, III: semantical completeness of some many-valued propositional calculi Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 25 1979 45 52 119-134, 447-464
39. E. Rasmusen Games and Information fourth ed. 2007 Blackwell Oxford
40. S.N. Ravi, K.B. Ravi, and T. Srikanth Rough set model using lattice theory International Journal of Machine Intelligence 0975-2927 2 1 2010 89 92
41. O. Roozmand, N. Ghasem-Aghaee, G. Jan Hofstede, M.A. Nematbakhsh, A. Baraani, and T. Verwaart Agent-based modeling of consumer decision making process based on power distance and personality Knowledge-Based Systems 24 7 2011 1075 1095
42. M. Sotomayor The lattice structure of the set of stable outcomes of the multiple partners assignment game International Journal of Game Theory 28 4 1999 567 583
43. P.D. Straffin Game Theory and Strategy 1993 Mathematical Association of American Washington, DC
44. T. Sueyoshi An agent-based approach equipped with game theory: strategic collaboration among learning agents during a dynamic market change in the California electricity crisis Energy Economics 32 2010 1009 1024
45. L.C. Thomas, Game Theory and Applications, New York, 1985.
46. M. Wang, H. Wang, and D. Xu The design of intelligent workXow monitoring with agent technology Knowledge-based Systems 18 6 2005 257 266
47. R. Wille Restructuring lattice theory: an approach based on hierarchies of concepts I. Rival, Ordered Sets 1982 Reidel Dordrecht, Boston 445 470
48. *-modules and Theory of Lattice-valued Games, Ph.D. Thesis, Southwest Jiaotong University, Sichuan, China, 1996 (in Chinese).
49. Y. Xu, K.Y. Qin, and l-module Chinese Quarterly Journal of Mathematics 10 Suppl. 1995 1 8 (in Chinese)
50. Y. Xu, J. Liu, J. Ma, On the solutions of lattice-valued matrix game with fuzziness, in: The Joint 9th IFSA World Congress and 20th NAFIPS International Conference: Fuzziness and Soft Computing in the New Millenium, July 25-28, Canada, 2001, pp. 2301-2304.
51. Y. Xu, D. Ruan, K.Y. Qin, and J. Liu Lattice-Valued Logic: An Alternative Approach to Treat Fuzziness and Incomparability 2003 Springer-Verlag Berlin
52. L. Zhou The set of Nash equilibria of a supermodular game is a complete lattice Games and Economic Behaviour 7 1994 295 300