A Semiring-based study of judgment matrices: Properties and models

Information Sciences

Volumn 181, Issue 11, 2011, Pages 2166-2176

  Hou, Fujun ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Consistency; Decision analysis; Judgment matrix; Semiring

Indexed keywords

CONSISTENCY; DECISION ANALYSIS; FIXED POINT EQUATION; FIXED POINTS; GROUP DECISION MAKING; IDEMPOTENCY; ILLUSTRATIVE EXAMPLES; JUDGMENT MATRIX; OPTIMIZATION MODELS; PREFERENCE INFORMATION; PRIORITY VECTOR; SEMI-RING; SEMIRINGS;

DECISION THEORY;

DECISION MAKING;

EID: 79953271048     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2011.01.020     Document Type: Article

References (51)

1. F.L. Baccelli, G. Cohen, G.J. Olsder, and J.P. Quadrat Synchronization and linearity: an algebra for discrete event systems Chichester 1993 Wiley
2. C.A. Bana e Costa, and J.C. Vansnick A critical analysis of the eigenvalue method used to derive priorities in AHP European Journal of Operational Research 187 2008 1422 1428
3. J. Barzilai, and B. Golany AHP rank reversal, normalization and aggregation rules INFOR 32 1994 57 64
4. J. Barzilai Deriving weights from pairwise comparison matrices Journal of the Operational Research Society 48 1997 1226 1232 (Pubitemid 127624631)
5. J. Barzilai, and F.A. Lootsma Power relations and group aggregation in the multiplicative AHP and SMART Journal of Multi-Criteria Decision Analysis 6 1997 155 165 (Pubitemid 127064546)
6. J. Barzilai Consistency measures for pairwise comparison matrices Journal of Multi-Criteria Decision Analysis 7 1998 123 132 (Pubitemid 128069422)
7. J. Barzilai On the decomposition of value functions Operations Research Letters 22 1998 159 170 (Pubitemid 128676374)
8. J. Barzilai, On MAUT, AHP, and PFM, in: Proceedings of the 5th International Symposium on the AHP, Kobe, 1999, pp. 57-60.
9. J. Barzilai, Notes on the Analytic Hierarchy Process, in: Proceedings of the NSF Design and Manufacturing Research Conference, Tampa, 2001, pp. 1-6.
10. V. Belton, and T. Gear On a shortcoming of Saaty's method of analytic hierarchies Omega 11 1983 228 230
11. V. Belton, and T. Gear The legitimacy of rank reversal - a comment Omega 11 1985 143 144
12. M. Bernasconi, C. Choirat, and R. Seri The analytic hierarchy process and the theory of measurement Management Science 56 2010 699 711
13. B. Cavallo, and L. D'Apuzzo A general unified framework for pairwise comparison matrices in multicriterial methods International Journal of Intelligent Systems 24 2009 377 398
14. T. Chang, and T. Wang Measuring the success possibility of implementing advanced manufacturing technology by utilizing the consistent fuzzy preference relations Expert Systems with Applications 36 2009 4313 4320
15. R.J. Chao, and Y.H. Chen Evaluation of the criteria and effectiveness of distance e-learning with consistent fuzzy preference relations Expert Systems with Applications 36 2009 10657 10662
16. F. Chiclana, F. Herrera, and E. Herrera-Viedma Integrating multiplicative preference relation in a multipurpose decision making model based on fuzzy preference relations Fuzzy Sets and Systems 122 2001 277 291 (Pubitemid 32590554)
17. G. Crawford, and C. Williams A note on the analysis of subjective judgment matrices Journal of Mathematical Psychology 29 1985 387 405
18. R.A. Cuninghame-Green Minimax algebra Lecture Notes in Economics and Mathematical Systems vol. 166 1979 Springer Berlin
19. L. Dale Monic and Monic-free ideals in a polynomial semiring PAMS 56 1976 45 50
20. J.S. Dyer Remarks on the analytic hierarchy process Management Science 36 1990 249 258
21. J.S. Dyer A clarification of remarks on the analytic hierarchy process Management Science 36 1990 274 275
22. L. Elsner, and P. van den Driessche Max-algebra and pairwise comparison matrices Linear Algebra and its Applications 385 2004 47 62
23. M. Fedrizzi On a consensus measure in a group MCDM problem J. Kacprzyk, M. Fedrizzi, Multiperson Decision Making Models using Fuzzy Sets and Possibility Theory 1990 Kluwer academic publ. 231 241
24. E.H. Forman, and S.I. Gass The analytic hierarchy process-an exposition Operations Research 49 2001 469 486
25. J.S. Golan Semirings and Their Applications 1999 Kluwer Dordrecht
26. D.A. Gregory, and N.J. Pullman Semiring rank: boolean rank and nonnegative rank factorizations Journal of Combinatorics, Information & System Sciences 8 1983 223 233
27. U. Hebisch, and H.J. Weinert Semirings and semifields Handbook of algebra Handbook of Algebra 1996 Elsevier New York
28. E. Herrera-Viedma, F. Herrera, F. Chiclana, and M. Luque Some issues on consistency of fuzzy preference relations European Journal of Operational Research 154 2004 98 109
29. K.H. Kim Boolean matrix theory and applications Pure and Applied Mathematics vol. 70 1982 Marcel Dekker New York
30. D. Knuth Finite semifields and projective planes Journal of Algebra 2 1965 182 217
31. . Korkmaz, H. Göken, and T. etinyoku An analytic hierarchy process and two-sided matching based decision support system for military personnel assignment Information Sciences 178 2008 2915 2927
32. P.J.M. van Laarhoven, and W. Pedrycz A fuzzy extension of Saaty's priority theory Fuzzy Sets and Systems 11 1983 199 227
33. S. Li, and M. Ying Soft constraint abstraction based on semiring homomorphism Theoretical Computer Science 403 2008 192 201
34. M.J. Liberatore, and R.L. Nydick The analytic hierarchy process in medical and health care decision making: A literature review European Journal of Operational Research 189 2008 194 207 (Pubitemid 351232135)
35. F.A. Lootsma Scale sensitivity in the Multiplicative AHP and SMART Journal of Multi-Criteria Decision Analysis 2 1993 87 110
36. J. Ma, Z.P. Fan, Y.P. Jiang, J.Y. Mao, and L. Ma A method for repairing the inconsistency of fuzzy preference relations Fuzzy Sets and Systems 157 2006 20 33 (Pubitemid 41525536)
37. E.S. Rosenbloom A probabilistic interpretation of the final rankings in AHP European Journal of Operational Research 96 1996 371 378
38. T.L. Saaty A scaling method for priorities in hierarchical structures Journal of Mathematical Psychology 15 1977 234 281
39. T.L. Saaty The Analytic Hierarchy Process 1980 McGraw-Hill New York
40. T.L. Saaty, and L.G. Vargas The legitimacy of rank reversal Omega 12 1984 513 516
41. T.L. Saaty Axiomatic foundation of the analytic hierarchy process Management Science 32 1986 841 855
42. T.L. Saaty Decision-making with the AHP: Why is the principal eigenvector necessary European Journal of Operational Research 145 2003 85 91
43. B. Schoner, and W.C. Wedley Ambiguous criteria weights in AHP - consequences and solutions Decision Sciences 20 1989 462 475
44. B. Schoner, W.C. Wedley, and E.U. Choo A unified approach to AHP with linking pins European Journal of Operational Research 64 1993 384 392 (Pubitemid 23619959)
45. T. Stewart A critical survey on the status of multiple criteria decision making theory and practice Omega 20 1992 569 586
46. T. Tanino Fuzzy preference orderings in group decision making Fuzzy Sets and Systems 12 1984 117 131 (Pubitemid 14569423)
47. O.S. Vaidya, and S. Kumar Analytic hierarchy process: An overview of applications European Journal of Operational Research 169 2006 1 29 (Pubitemid 41336610)
48. L.G. Vargas An overview of the analytic hierarchy process and its applications European Journal of Operational Research 48 1990 2 8
49. Y.M. Wang, K.S. Chin, and Y. Luo Aggregation of direct and indirect judgments in pairwise comparison matrices with a re-examination of the criticisms by Bana e Costa and Vansnick Information Sciences 179 2009 329 337
50. Z. Xu, and X. Cai Group consensus algorithms based on preference relations Information Sciences 181 2011 150 162
51. S. Zanakis, T. Mandakovic, S. Gupta, S. Sahay, and S. Hong A review of program evaluation and fund allocation within the service and government sectors Socio-Economic Planning Sciences 29 1995 59 79