Ordering based decision making - A survey

Information Fusion

Volumn 14, Issue 4, 2013, Pages 521-531

  Chen, Shuwei ^a,b   Liu, Jun ^a   Wang, Hui ^a   Augusto, Juan Carlos ^a  

^a UNIVERSITY OF ULSTER   (United Kingdom)

^b ZHENGZHOU UNIVERSITY   (China)

Author keywords

Aggregation; Decision making; Lattice; Logic; Ordering relation; Preference

Indexed keywords

AGGLOMERATION; INFORMATION FUSION; SOFTWARE ENGINEERING;

DECISION-MAKING THEORIES; FUTURE RESEARCH DIRECTIONS; LATTICE; LOGIC; ORDER RELATION; ORGANIZATION MANAGEMENT; PREFERENCE; RATIONAL DECISION MAKING;

DECISION MAKING;

EID: 84887820603     PISSN: 15662535     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.inffus.2012.10.005     Document Type: Article

References (120)

1. F. Herrera, S. Alonso, F. Chiclana, E. Herrera-Viedma, Computing with words in decision making: foundations, trends and prospects, Fuzzy Optimization and Decision Making 8 (4) (2009) 337-364.
2. W. Pedrycz, P. Ekel, R. Parreiras, Fuzzy Multicriteria Decision-Making: Models, Methods and Applications, John Wiley and Sons, Chicester, 2011.
3. J. Liu, L. Martínez, H. Wang, R.M. Rodríquez, V. Novozhilov, Computing with words in risk assessment, International Journal of Computational Intelligence Systems 3 (4) (2010) 396-419.
4. D.J. Power, Decision Support Systems: Concepts and Resources for Managers, Greenwood Publishing Group, 2002.
5. Z. Pei, D. Ruan, J. Liu, Y. Xu, Linguistic Values Based Intelligent Information Processing: Theory, Methods, and Applications, Atlantis Press/World Scientific, Paris/Singapore, 2009.
6. R.R. Yager, Aggregation of ordinal information, Fuzzy Optimization and Decision Making 6 (3) (2007) 199-219.
7. Y.H. Chen, T.C. Wang, C.Y. Wu, Multi-criteria decision making with fuzzy linguistic preference relations, Applied Mathematical Modelling 35 (3) (2011) 1322-1330.
8. M. Roubens, Fuzzy sets and decision analysis, Fuzzy Sets and Systems 90 (2) (1997) 199-206.
9. F. Herrera, E. Herrera-Viedma, Linguistic decision analysis: steps for solving decision problems under linguistic information, Fuzzy Sets and Systems 115 (1) (2000) 67-82.
10. F. Herrera, E. Herrera-Viedma, F. Chiclana, Multiperson decision-making based on multiplicative preference relations, European Journal of Operational Research 129 (2) (2001) 372-385.
11. M. Öztürk, A. Tsoukiàs, Bipolar preference modelling and aggregation in decision support, International Journal of Intelligence Systems 23 (9) (2008) 970-984.
12. G. Birkhoff, Lattice Theory, third ed., American Mathematical Society, Providence, RL, 1967.
13. B.A. Davey, H.A. Priestley, Introduction to Lattices and Order, third ed., Cambridge University Press, Cambridge, 2002.
14. V.G. Kaburlasos, G.X. Ritter, Computational Intelligence Based on Lattice Theory, Springer, Heidelberg, 2007.
15. S. Benferhat, S. Lagrue, O. Papini, Reasoning with partially ordered information in a possibilistic logic framework, Fuzzy Sets and Systems 144 (1) (2004) 25-41.
16. S. Benferhat, C. Sossai, Reasoning with multiple-source information in a possibilistic logic framework, Information Fusion 7 (1) (2006) 80-96.
17. B. Malakooti, Ranking and screening multiple criteria alternatives with partial information and use of ordinal and cardinal strength of preferences, IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 30 (3) (2000) 355-368.
18. C. Boutilier, R. Brafman, C. Domshlak, H.H. Hoos, D. Poole, CP-nets: a tool for representing and reasoning with conditional ceteris paribus preference statements, Journal of Artificial Intelligence Research 21 (2004) 135-191.
19. J. Liu, Y. Xu, D. Ruan, L. Martínez, A lattice-valued linguistic-based decision making method, in: The Proceedings of 2005 IEEE Conference on Granular Computing, Beijing, China, 2005, pp. 199-202.
20. T.C. Wang, Y.H. Chen, Incomplete fuzzy linguistic preference relations under uncertain environments, Information Fusion 11 (2) (2010) 201-207.
21. J. Goldsmith, J. Lang, M. Truszczynski, N. Wilson, The computational complexity of dominance and consistency in CP-nets, Journal of Artificial Intelligence Research 33 (2008) 403-432.
22. Z. Xu, Group decision making based on multiple types of linguistic preference relations, Information Sciences 178 (2) (2008) 452-467.
23. M.E. Brown,O.R. Coté Jr., S.M.Lynn-Jones, S.E.Miller, RationalChoiceandSecurity Studies: StephenWalt and His Critics, The MIT Press, Cambridge,MA, 2000.
24. L.A. Zadeh, Fuzzy logic=computing with words, IEEE Transactions on Fuzzy Systems 4 (2) (1996) 103-111.
25. L.A. Zadeh, From computing with numbers to computing with words-from manipulation of measurements to manipulation of perceptions, IEEE Transactions on Circuits and Systems 45 (1) (1999) 105-119.
26. R.R. Yager, A new methodology for ordinal multiobjective decisions based on fuzzy sets, Decision Sciences 12 (4) (1981) 589-600.
27. P.P. Wang, Computing With Words, John Wiley and Sons, Chicester, 2001.
28. F. Herrera, L. Martínez, The 2-tuple linguistic computational model: Advantages of its linguistic description, accuracy and consistency, International Journal of Uncertainty, Fuzziness and Knowledge-based Systems 9 (2001) 33-48.
29. M. Delgado, J.L. Verdegay, M.A. Vila, On aggregation operations of linguistic labels, International Journal of Intelligent Systems 8 (3) (1993) 351-370.
30. L. Martínez, D. Ruan, F. Herrera, Computing with words in decision support systems: an overview on models and applications, International Journal of Computational Intelligence Systems 3 (4) (2010) 382-395.
31. R.R. Yager, An approach to ordinal decision making, International Journal of Approximate Reasoning 12 (3-4) (1995) 237-261.
32. E. Herrera-Viedma, O. Cordón, M. Luque, A.G. Lopez, A.M. Muñoz, A model of fuzzy linguistic IRS based on multi-granular linguistic information, International Journal of Approximate Reasoning 34 (2-3) (2003) 221-239.
33. L. Martínez, Sensory evaluation based on linguistic decision analysis, International Journal of Approximate Reasoning 44 (2) (2007) 148-164.
34. F. Herrera, L. Martínez, A model based on linguistic 2-tuples for dealing with multigranular hierarchical linguistic contexts in multi-expert decisionmaking, IEEE Transactions on Systems, Man and Cybernetics-part B, Cybernetics 31 (2) (2001) 227-234.
35. L. Martínez, F. Herrera, An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Sciences 207 (2012) 1-18.
36. V. Torra, Hesitant fuzzy sets, International Journal of Intelligent Systems 25 (6) (2010) 529-539.
37. R.M. Rodríguez, L. Martínez, F. Herrera, Hesitant fuzzy linguistic term sets for decision making, IEEE Transactions on Fuzzy Systems 20 (1) (2012) 109-119.
38. M. Espinilla, J. Liu, L. Martínez, An extended hierarchical linguistic model for decision-making problems, Computational Intelligence 27 (3) (2011) 489- 512.
39. N.C. Ho, W. Wechler, Hedge algebras: an algebraic approach to structures of sets of linguistic domains of linguistic truth variable, Fuzzy Sets and Systems 35 (3) (1990) 281-293.
40. N.C. Ho, W. Wechler, Extended hedge algebras and their application to fuzzy logic, Fuzzy Sets and Systems 52 (3) (1992) 259-281.
41. N.C. Ho, H.V. Nam, A theory of refinement structure of hedge algebras and its application to fuzzy logic, Logic, Algebra and Computer Science 46 (1999) 63- 91.
42. N.C. Ho, N.V. Long, Fuzziness measure on complete hedge algebras and quantifying semantics of terms in linear hedge algebras, Fuzzy Sets and Systems 158 (4) (2007) 452-471.
43. N.C. Ho, H.V. Nam, An algebraic approach to linguistic hedges in Zadeh's fuzzy logic, Fuzzy Sets and Systems 129 (2) (2002) 229-254.
44. J.G. Eisenhauer, Rank-ordering of risk preferences with conventional and discrete measures, The Quarterly Review of Economics and Finance 50 (3) (2010) 291-297.
45. D. Ruan, X. Zeng, Sensory Evaluation: Methodologies and Applications, Springer, Heidelberg, 2004.
46. H. Wang, Z. Lin, J. Liu, Preference based alternative ordering, in: The Proceedings of EUROFUSE Workshop 2007: New Trends in Preference Modeling and Applications, Barcelona, Spain, 2007, pp. 43-48.
47. F. Rossi, K.B. Venable, T. Walsh, Aggregating preferences cannot be fair, Intelligenza Artificiale 2 (2005) 30-38.
48. F. Chiclana, F. Herrera, E. Herrera-Viedma, Integrating three representation models in fuzzy multipurpose decision making based on fuzzy preference relations, Fuzzy Sets and Systems 97 (1) (1998) 33-48.
49. F. Chiclana, F. Herrera, E. Herrera-Viedma, Integrating multiplicative preference relations in a multipurpose decision-making model based on fuzzy preference relations, Fuzzy Sets and Systems 122 (2) (2001) 277-291.
50. F. Chiclana, E. Herrera-Viedma, F. Herrera, S. Alonso, Induced ordered weighted geometric operators and their use in the aggregation of multiplicative preference relations, International Journal of Intelligent Systems 19 (3) (2004) 233-255.
51. Ö. Evren, E.A. Ok, On the multi-utility representation of preference relations, Journal of Mathematical Economics 47 (4-5) (2011) 554-563.
52. S.M. Chen, S.J. Niou, Fuzzy multiple attributes group decision-making based on fuzzy preference relations, Expert Systems with Applications 38 (4) (2011) 3865-3872.
53. D. Black, Partial justification of the Borda count, Public Choice 28 (1) (1976) 1-15.
54. J.C. Heckelman, Probabilistic Borda rule voting, Social Choice and Welfare 21 (3) (2003) 455-468.
55. F. Chiclana, E. Herrera-Viedma, S. Alonso, F. Herrera, Cardinal consistency of reciprocal preference relations: a characterization of multiplicative transitivity, IEEE Transactions on Fuzzy Systems 17 (1) (2009) 14-23.
56. B. Van de Walle, B. De Baets, E. Kerre, Characterizable fuzzy preference structures, Annals of Operations Research 80 (1998) 105-136.
57. B. Van de Walle, B. De Baets, E. Kerre, A plea for the use of £ukasiewicz triplets in the definition of fuzzy preference structures (I) general argumentation, Fuzzy Sets and Systems 97 (3) (1998) 349-359.
58. T.L. Saaty, The Analytic Hierarchy Process, McGraw-Hill, New York, 1980.
59. T.L. Saaty, How to make a decision: the analytic hierarchy process, European Journal of Operational Research 48 (1) (1990) 9-26.
60. Z. Wu, J. Xu, A consistency and consensus based decision support model for group decision making with multiplicative preference relations, Decision Support Systems 52 (3) (2012) 757-767.
61. J.C. Fodor, M. Roubens, Valued preference structures, European Journal of Operational Research 79 (2) (1994) 277-286.
62. S.A. Orlovsky, Decision making with a fuzzy preference relation, Fuzzy Sets and Systems 1 (3) (1978) 155-167.
63. E. Herrera-Viedma, F. Chiclana, F. Herrera, S. Alonso, Group decision-making model with incomplete fuzzy preference relations based on additive consistency, IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics 37 (1) (2007) 176-189.
64. F. Herrera, E. Herrera-Viedma, J.L. Verdegay, Direct approach processes in group decision making using linguistic OWA operators, Fuzzy Sets and Systems 79 (2) (1996) 175-190.
65. E. Herrera-Viedma, L. Martínez, F. Mata, F. Chiclana, A consensus support system model for group decision-making problems with multigranular linguistic preference relations, IEEE Transactions on Fuzzy Systems 13 (5) (2005) 644-658.
66. C. Tan, D.D. Wu, B. Ma, Group decision making with linguistic preference relations with application to supplier selection, Expert Systems with Applications 38 (12) (2011) 14382-14389.
67. Z. Xu, Incomplete linguistic preference relations and their fusion, Information Fusion 7 (3) (2006) 331-337.
68. J.C. Fodor, M. Roubens, Fuzzy Preference Modelling and Multicriteria Decision Support, Kluwer, Dordrecht, 1994.
69. J.C. Fodor, B. de Baets, Fuzzy preference modelling: fundamentals and recent advances, in: H. Bustince, F. Herrera, J. Montero (Eds.), Fuzzy Sets and Their Extensions: Representation, Aggregation and Models, Springer, Heidelberg, 2008, pp. 207-217.
70. P. Perny, B. Roy, The use of fuzzy outranking relations in preference modelling, Fuzzy Sets and Systems 49 (1) (1992) 33-53.
71. P. Perny, M. Roubens, Fuzzy preference modelling, in: R. Swiski (Ed.), Fuzzy Sets in Decision Analysis, Operations Research and Statistics, Kluwer, Dordrecht, 1998, pp. 3-30.
72. E. Hüllermeier, K. Brinker, Learning valued preference structures for solving classification problems, Fuzzy Sets and Systems 159 (18) (2008) 2337-2352.
73. C. Mousset, Families of relations modelling preferences under incomplete information, European Journal of Operational Research 192 (2) (2009) 538- 548.
74. T.L. Saaty, L.G. Vargas, Uncertainty and rank order in the analytic hierarchy process, European Journal of Operational Research 32 (1) (1987) 107-117.
75. S. Genç, F.E. Boran, D. Akay, Z. Xu, Interval multiplicative transitivity for consistency, missing values and priority weights of interval fuzzy preference relations, Information Sciences 180 (24) (2010) 4877-4891.
76. Z. Xu, Consistency of interval fuzzy preference relations in group decision making, Applied Soft Computing 11 (5) (2011) 3898-3909.
77. F. Liu, W.G. Zhang, J.H. Fu, A new method of obtaining the priority weights from an interval fuzzy preference relation, Information Sciences 185 (1) (2012) 32-42.
78. T.C. Wang, Y.H. Chen, A new method on decision-making using fuzzy linguistic assessment variables and fuzzy preference relations, in: The Proceedings of the 9th World Multi-Conference on Systems, Cybernetics and Informatics, Orlando, USA, 2005, pp. 360-363.
79. T.C. Wang, Y.H. Chen, Applying fuzzy linguistic preference relations to the improvement of consistency of fuzzy AHP, Information Sciences 178 (19) (2008) 3755-3765.
80. S.C. Hsu, T.C. Wang, Solving multi-criteria decision making with incomplete linguistic preference relations, Expert Systems with Applications 38 (9) (2011) 10882-10888.
81. R.R. Yager, On ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Transactions on Systems, Man and Cybernetics 18 (1) (1988) 183-190.
82. V. Torra, The weighted OWA operator, International Journal of Intelligence Systems 12 (2) (1997) 153-166.
83. Z. Xu, Q. Da, The ordered weighted geometric averaging operators, International Journal of Intelligence Systems 17 (7) (2002) 709-716.
84. Z. Xu, Induced uncertain linguistic OWA operators applied to group decision making, Information Fusion 7 (2) (2006) 231-238.
85. R.R. Yager, Z. Xu, The continuous ordered weighted geometric operator and its application to decision making, Fuzzy Sets and Systems 157 (10) (2006) 1393-1402.
86. X.B. Li, D. Ruan, J. Liu, Y. Xu, A linguistic-valued weighted aggregation operator to multiple attribute group decision making with quantitative and qualitative information, International Journal of Computational Intelligence Systems 1 (3) (2008) 274-284.
87. J. Lin, Y. Jiang, Some hybrid weighted averaging operators and their application to decision making, Information Fusion (2011), http:// dx.doi.org/10.1016/j.inffus.2011.06.001.
88. R.R. Yager, Families of OWA operators, Fuzzy Sets and Systems 59 (2) (1993) 125-143.
89. V. Torra, Y. Narukawa, A view of averaging aggregation operators, IEEE Transactions on Fuzzy Systems 15 (6) (2007) 1063-1067.
90. P.C. Fishburn, Utility Theory for Decision Making, Krieger, Melbourne, FL, 1979.
91. P.C. Fishburn, The Theory of Social Choice, Princeton University Press, Princeton, NJ, 1973.
92. N. Wilson, A logic of soft constraints based on partially ordered preferences, Journal of Heuristics 12 (4-5) (2006) 241-262.
93. S. Bistarelli, U. Montanari, F. Rossi, Semiring-based constraint satisfaction and optimization, Journal of the ACM 44 (2) (1997) 201-236.
94. S. Bistarelli, U. Montanari, F. Rossi, Semiring-based constraint logic programming: syntax and semantics, ACM Transactions on Programming Languages and System 23 (1) (2001) 1-29.
95. C. Domshlak, S. Prestwich, F. Rossi, K.B. Venable, T. Walsh, Hard and soft constraints for reasoning about qualitative conditional preferences, Journal of Heuristics 12 (4-5) (2006) 263-285.
96. C. Domshlak, R. Brafman, CP-nets - reasoning and consistency testing, in: The Proceedings of the Eighth International Conference on Principles of Knowledge Representation and Reasoning, Toulouse, France, 2002, pp. 121-132.
97. X.Y. Zhu, Z.H. Zhang, A CP-Nets-based model and verification for consumercentric information service composition, in: The Proceedings of 2011 International Conference on Internet Technology and Applications (iTAP), Wuhan, China, 2011, pp. 1-4.
98. J. Lang, Logical preference representation and combinatorial vote, Annals of Mathematics and Artificial Intelligence 42 (1-3) (2004) 37-71.
99. C. Boutilier, F. Bacchus, R.I. Brafman, UCP-Networks: A directed graphical representation of conditional utilities. in: The Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence, Seattle, USA, 2001, pp. 56-64.
100. P. Châtel, I. Truck, J. Malenfant, LCP-Nets: a linguistic approach for nonfunctional preferences in a semantic SOA environment, Journal of Universal Computer Science 16 (1) (2010) 198-217.
101. P. Châtel, I. Truck, J. Malenfant, A linguistic approach for non-functional preferences in a semantic SOA environment, in: The Proceedings of the 8th International FLINS Conference, Madrid, Spain, 2008, pp. 889-894.
102. M. Dummett, Voting Procedures, Oxford University Press, New York, 1984.
103. D.G. Saari, Geometry of Voting, Springer, Berlin-Heidelberg-New York, 1994.
104. S.J. Brams, P.C. Fishburn, Approval Voting, Springer, Heidelberg, 2007.
105. M. Balinski, R. Laraki, Majority Judgment: Measuring, Ranking, and Electing, The MIT Press, Cambridge, MA, 2011.
106. W.W. Cohen, R.E. Schapire, Y. Singer, Learning to order things, Journal of Artificial Intelligence Research 10 (1999) 243-270.
107. J.C. Augusto, H. Wang, J. Liu, Situation assessment in disaster management, International Journal of Computational Intelligence Systems 1 (3) (2008) 237-247.
108. K. Arrow, Social Choice and Individual Values, John Wiley and Sons, Chicester, 1951.
109. D. Dubois, J.L. Koning, Social choice axioms for fuzzy set aggregation, Fuzzy Sets and Systems 43 (3) (1991) 257-274.
110. M.S. Pini, F. Rossi, K.B. Venable, T. Walsh, Incompleteness and incomparability in preference aggregation, in: The Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), Hyderabad, India, 2007, pp. 1464-1469.
111. Y. Xu, J. Liu, L. Martínez, D. Ruan, Some views on information fusion and logic based approaches in decision making under uncertainty, Journal of Universal Computer Science 16 (1) (2010) 3-21.
112. S.K. Das, A logical reasoning with preference, Decision Support Systems 15 (1) (1995) 19-25.
113. S. Benferhat, D. Dubois, H. Prade, From semantic to syntactic approaches to information combination in possibilistic logic, in: B. Bouchon-Meunier (Ed.), Aggregation and Fusion of Imperfect Information, Physica-Verlag, Heidelberg, 1998, pp. 141-161.
114. Y. Xu, D. Ruan, K. Qin, J. Liu, Lattice-valued Logic: An Alternative Approach to Treat Fuzziness and Incomparability, Springer-Verlag, Heidelberg, 2003.
115. Y. Xu, S. Chen, J. Ma, Linguistic truth-valued lattice implication algebra and its properties, in: The Proceedings of IMACS Multiconference on "Computational Engineering in Systems Applications", Beijing, China, 2006, pp. 1413-1418.
116. J. Lai, Y. Xu, Linguistic truth-valued lattice-valued propositional logic system lP(X) based on linguistic truth-valued lattice implication algebra, Information Sciences 180 (10) (2010) 1990-2002.
117. Y. Xu, S. Chen, J. Liu, D. Ruan, Weak completeness of resolution in a linguistic truth-valued propositional logic, in: The Proceedings of the 9th IFSA World Congress: Theory and Applications of Fuzzy Logic and Soft Computing, Cancun, Mexico, 2007, pp. 358-366.
118. S. Chen, Y. Xu, J. Ma, A linguistic truth-valued uncertainty reasoning model based on lattice-valued logic, Lecture Notes in Artificial Intelligence 3613 (2005) 276-284.
119. Y. Xu, J. Liu, D. Ruan, T.T. Lee, On the consistency of rule bases based on lattice-valued first-order logic LF(X), International Journal of Intelligent Systems 21 (4) (2006) 399-424.
120. Z. Lu, J.C. Augusto, J. Liu, H. Wang, A linguistic truth-valued temporal reasoning system (LTR) and its application to the design of an intelligent environment, International Journal of Computational Intelligence Systems 5 (1) (2012) 173-196.