Evidential reasoning using extended fuzzy Dempster-Shafer theory for handling various facets of information deficiency

International Journal of Intelligent Systems

Volumn 26, Issue 8, 2011, Pages 731-758

  Aminravan, Farzad ^a   Sadiq, Rehan ^a   Hoorfar, Mina ^a   Rodriguez, Manuel J ^b   Francisque, Alex ^a,b   Najjaran, Homayoun ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

^b UNIVERSITÉ LAVAL   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BELIEF DEGREES; DEMPSTER-SHAFER; DEMPSTER-SHAFER THEORY; EVIDENTIAL REASONING; EXPERIMENTAL DATA; EXPERT KNOWLEDGE; GENERALIZED FUZZY SET; INFERENCE METHODS; INTERVAL-VALUED; NON-LINEAR OPTIMIZATION PROBLEMS; NON-SPECIFICITY; QUALITY ASSESSMENT; SAMPLING POINTS; SIMULTANEOUS USE; UNIFIED APPROACH; WATER DISTRIBUTION NETWORKS; WATER QUALITY MONITORING;

FUZZY SETS; WATER DISTRIBUTION SYSTEMS; WATER QUALITY;

FORMAL LOGIC;

EID: 79959234500     PISSN: 08848173     EISSN: 1098111X     Source Type: Journal    
DOI: 10.1002/int.20491     Document Type: Article

References (73)

1. Klir GJ, Wierman MJ,. Uncertainty-based information. Heidelberg, Germany: Physica-Verlag; 1998. 186 p.
2. Dempster AP,. Upper and lower probabilities induced by a multivariate mapping. Ann Math Stat. 1967; 38: 325-339.
3. Shafer G,. A mathematical theory of evidence Princeton, NJ: Princeton University Press; 1976.
4. Parikh CR, Pont MJ, Barrie JN,. Application of Dempster-Shafer theory in condition monitoring applications: a case study. Pattern Recogn Lett. 2001; 22 (6-7):777-785.
5. Sadiq R, Rodriguez MJ,. Interpreting drinking water quality in the distribution system using Dempster-Shafer theory of evidence. Chemosphere. 2005; 59 (2): 177-188. (Pubitemid 40255659)
6. Sadiq R, Najjaran H, Kleiner Y,. Investigating evidential reasoning for the interpretation of microbial water quality in a distribution network. Stochastic Env Res Risk Assess. 2006; 21: 63-73. (Pubitemid 44490071)
7. Yang BS, Kim KJ,. Application of Dempster-Shafer theory in fault diagnosis of induction motors using vibration and current signals. Mech Syst Signal Process. 2006; 20 (2): 403-420. (Pubitemid 41606177)
8. Basir O, Yuan X,. Engine fault diagnosis based on multi-sensor information fusion using Dempster-Shafer evidence theory. Inform Fusion. 2007; 8 (4): 379-386. (Pubitemid 46818139)
9. Yager RR,. On the Dempster-Shafer framework and new combination rules. Inform Sci. 1987; 41 (2): 93-137.
10. Sentz K, Ferson S,. Combination of evidence in Dempster-Shafer theory. Sandia Report 0835; 2002.
11. Yang JB, Singh MG,. An evidential reasoning approach for multiple-attribute decision making with uncertainty. IEEE Trans Syst Man Cybern. 1994; 24 (1): 1-18.
12. Yen J,. A reasoning model based on an extended Dempster-Shafer theory. SPIE Milestone Ser. 1996; 124: 310-316.
13. Basir O, Karray F, Zhu H,. Connectionist-based Dempster-Shafer evidential reasoning for data fusion. IEEE Trans Neural Netw. 2005; 16 (6): 1513-1530. (Pubitemid 41709648)
14. Smets P,. The transferable belief model and other interpretations of Dempster-Shafer's model. Uncertain Artif Intell. 1991; 6: 375-383.
15. Smets P,. Application of the transferable belief model to diagnostic problems. Int J Intell Syst. 1998; 13 (2-3):127-157.
16. Smets P, Kennes R,. The transferable belief model. Artif Intell. 1994; 66 (2): 191-234.
17. Dubois D, Prade H,. A set-theoretic view of belief functions. Classic works of the Dempster-Shafer theory of belief functions. Int J Gen Syst. 2008; 12: 193-226.
18. Yang JB, Xu DL,. Nonlinear information aggregation via evidential reasoning in multiattribute decision analysis under uncertainty. IEEE Trans Syst Man Cybern A. 2002; 32 (3): 376-393.
19. Yang JB,., Xu DL,. On the evidential reasoning algorithm for multiple attribute decision analysis under uncertainty. IEEE Trans Syst Man Cybern A. 2002; 32 (3): 289-304.
20. Yang MS, Chen TC, Wu KL,. Generalized belief function, plausibility function, and Dempster's combinational rule to fuzzy sets. Int J Intell Syst. 2003; 18 (8): 925-937.
21. Liu J, Yang JB, Wang J, Sii HS,. Engineering system safety analysis and synthesis using the fuzzy rule-based evidential reasoning approach. Quality Reliab Eng Int. 2005; 21 (4): 387-411. (Pubitemid 40795493)
22. Wang YM, Yang JB, Xu DL,. Environmental impact assessment using the evidential reasoning approach. Eur J Oper Res. 2006; 174 (3): 1885-1913.
23. Yang JB, Liu J, Wang J, Sii HS, Wang HW,. Belief rule-base inference methodology using the evidential reasoning approachâRIMER. IEEE Trans Syst Man Cybern A 2006; 36 (2): 266-285. (Pubitemid 43280550)
24. Yang JB, Wang YM, Xu DL, Chin KS,. The evidential reasoning approach for MADA under both probabilistic and fuzzy uncertainties. Eur J Oper Res. 2006; 171 (1): 309-343. (Pubitemid 41690042)
25. Liu J, Yang JB, Wang J, Sii HS, Wang YM,. Fuzzy rule-based evidential reasoning approach for safety analysis. Int J Gen Syst. 2004; 33 (2): 183-204. (Pubitemid 40026237)
26. Zadeh LA,. The concept of a linguistic variable and its application to approximate reasoning, parts 1, 2, and 3. Inform Sci. 1975; 8 (2): 199-249.
27. Zadeh LA,. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 1978; 1 (1): 3-28.
28. Dubois D, Prade H,. The use of fuzzy numbers in decision analysis. In:, Gupta MM, Sanchez E, editors. Fuzzy information and decision processes New York: North Holland; 1982. pp 309-321. (Pubitemid 14645784)
29. Dubois D, Prade H,. Evidence measures based on fuzzy information. Automatica. 1985; 21 (5): 547-562. (Pubitemid 15587153)
30. Dubois D, Prade H,. Decision evaluation methods under uncertainty and imprecision. In:, Kacprzyk J, Fedrizzi M, editors. Combining fuzzy imprecision with probabilistic uncertainty in decision making. Lecture Notes in Econ Math Syst 1989;310: 48-65.
31. Yager RR,. Generalized probabilities of fuzzy events from fuzzy belief structures. Inform Sci. 1982; 28 (1): 45-62.
32. Yen J,. Generalzing the Dempster-Shafer theory to fuzzy sets. IEEE Trans Systems Man Cybern. 1990; 20 (3): 559-569.
33. Zhu H, Basir O,. An adaptive fuzzy evidential nearest neighbor formulation for classifying remote sensing images. IEEE Trans Geosci Remote Sensing. 2005; 43 (8): 1874-1889. (Pubitemid 41329035)
34. Zadeh LA,. Toward a generalized theory of uncertainty (GTU)âan outline. Inform Sci. 2005; 172 (1-2):1-40.
35. Zhu H., Basir O,. A novel fuzzy evidential reasoning paradigm for data fusion with applications in image processing. Soft ComputâA Fusion Found Method Appl. 2006; 10 (12): 1169-1180. (Pubitemid 44123029)
36. Binaghi E, Madella P,. Fuzzy Dempster-Shafer reasoning for rule-based classifiers. Int J Intell Syst. 1999; 14 (6): 559-583.
37. Zhou M, Liu XB, Yang JB,. Evidential reasoning-based nonlinear programming model for MCDA under fuzzy weights and utilities. Int J Intell Syst. 2010; 25 (1): 31-58.
38. Denoeux T,. Reasoning with imprecise belief structures. Int J Approxim Reason. 1999; 20 (1): 79-111. (Pubitemid 129533466)
39. Denoeux T,. Modeling vague beliefs using fuzzy-valued belief structures. Fuzzy Sets Syst. 2000; 116 (2): 167-199.
40. Lee E, Zhu,. An interval Dempster-Shafer approach. Comput Math Appl 1992; 24 (7): 89-95.
41. Nguyen HT, Kreinovich V, Zuo Q,. Interval-valued degrees of belief: applications of interval computations to expert systems and intelligent control. Int J Uncertain, Fuzziness Knowl Based Syst. 1997; 5: 317-358. (Pubitemid 127530908)
42. Wang YM, Yang JB, Xu DL, Chin KS,. The evidential reasoning approach for multiple attribute decision analysis using interval belief degrees. Eur J Oper Res. 2006; 175 (1): 35-66.
43. Wang YM, Yang JB, Xu DL, Chin KS,. On the combination and normalization of interval-valued belief structures. Inform Sci. 2007; 177 (5): 1230-1247.
44. Xu DL, Yang JB, Wang YM,. The evidential reasoning approach for multi-attribute decision analysis under interval uncertainty. Eur J Oper Res. 2006; 174 (3): 1914-1943.
45. Guo M, Yang JB, Chin KS, Wang H,. The evidential reasoning approach for multi-attribute decision analysis under both fuzzy and interval uncertainty. In: Interval/probabilistic uncertainty and non-classical logics. Applied Soft Computing 2008;46: 129-140.
46. Guo M, Yang JB, Chin KS, Wang HW, Liu XB,. Evidential reasoning approach for multiattribute decision analysis under both fuzzy and interval uncertainty. IEEE Trans Fuzzy Syst. 2009; 17 (3): 683-697.
47. Yager RR, Filev DP,. Including probabilistic uncertainty in fuzzy logic controller modeling using Dempster-Shafer theory. IEEE Trans Syst Man Cybern. 1995; 25 (8): 1221-1230.
48. Miao YZ, Ma XP, Zhang HX, Zhang JW, Zhao ZX,. An improved extension of the DS evidence theory to fuzzy sets. In: Proc Int Multi-Conf on Computing in the Global Information Technology; 2008. pp 148-153.
49. Tsiporkova-Hristoskova E, De Baets B, Kerre E,. A fuzzy inclusion based approach to upper inverse images under fuzzy multivalued mappings. Fuzzy Sets Syst. 1997; 85 (1): 93-108. (Pubitemid 127699100)
50. Yager RR,. Dempster-Shafer belief structures with interval valued focal weights. Int J Intell Syst. 2001; 16 (4): 497-512. (Pubitemid 32416029)
51. Démotier S, Schön W, Denoeux T,. Risk assessment based on weak information using belief functions: a case study in water treatment, IEEE Trans Syst Man Cybern C 2006; 36 (3): 382-396.
52. Hua Z, Gong B, Xu X,. A DS-AHP approach for multi-attribute decision making problem with incomplete information. Expert Syst Appl. 2008; 34 (3): 2221-2227. (Pubitemid 350298240)
53. Wang YM, Yang JB, Xu DL,. A preference aggregation method through the estimation of utility intervals. Comput Oper Res. 2005; 32 (8): 2027-2049.
54. Cornelis C, Atanassov KT, Kerre EE,. Intuitionistic fuzzy sets and interval-valued fuzzy sets: a critical comparison. In: Proc EUSFLAT; 2003. pp 10-12.
55. Gorzaczany MB,. A method of inference in approximate reasoning based on interval-valued fuzzy sets. Fuzzy Sets Syst. 1987; 21 (1): 1-17.
56. Turksen I,. Interval-valued fuzzy sets based on normal forms. Fuzzy Sets Syst. 1986; 20: 191-210.
57. Dubois D, Prade H,. Interval-valued fuzzy sets, possibility theory and imprecise probability. In: Proc Int Conf on Fuzzy Logic and Technology 2005. pp 314-319.
58. Atanassov G,. Interval valued intuitionistic fuzzy sets. Fuzzy Sets Syst. 1989; 31 (3): 343-349.
59. Bustince H,. Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets. Int J Approx Reason. 2000; 23 (3): 137-209.
60. Cornelis C, Deschrijver G, Kerre EE,. Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. Int J Approx Reason 2004; 35 (1): 55-95.
61. Zimmermann HJ, Zysno P,. Latent connectives in human decision making. Fuzzy Sets Syst. 1980; 4 (1): 37-51.
62. Zimmermann HJ,. Fuzzy set theory and its applications. Dordrecht, The Netherlands: Springer; 2001. 514 p.
63. Yager RR,. On the determination of strength of belief for decision support under uncertaintyâpart II: fusing strengths of belief. Fuzzy Sets Syst. 2004; 142: 129-142.
64. Tesfamariam S, Sadiq R, Najjaran H,. Decision making under uncertaintyâan example for seismic risk management. Risk Anal. 2009; 30 (1): 87-94.
65. Swamee PK, Tyagi A,. Describing water quality with aggregate index. J Env Eng. 2000; 126: 451-455.
66. Sadiq R, Haji SA, Cool G, Rodriguez MJ,. Using penalty functions to evaluate aggregation models for environmental indices. J Env Manag. 2010; 91 (3): 706-716.
67. USEPA. Technologies and techniques for early warning systems to monitor and evaluate drinking water quality: a state-of-the-art review. U.S. Environmental Protection Agency. 600/R-05/156; 2005.
68. USEPA. Distribution system water quality monitoring: sensor technology evaluation methodology and results. U.S. Environmental Protection Agency. 600/R-09/076; 2009.
69. Hall J, Zaffiro AD, Marx RB, Kefauver PC, Krishnan ER, Haught RC, Herrmann, JG,. On-line water quality parameters as indicators of distribution system contamination. J Am Water Works Assoc. 2007; 99 (1): 66-77.
70. Jeffrey YY, Goodrich JA, Clark RM, Li SY,. Modeling and testing of reactive contaminant transport in drinking water pipes: chlorine response and implications for online contaminant detection. Water Res. 2008; 42 (6-7):1397-1412.
71. Fransicque A, Rodriquez MJ, Sadiq R, Miranda LF, Proulx F,. Prioritizing monitoring locations in a water distribution network: a fuzzy risk approach. J Water Supply: Res TechnolâAQUA 2009; 58 (7): 488-509.
72. Payment P, Waite M, Dufour A,. Introducing parameters for the assessment of drinking water quality. In:, Dufour A, Snozzi M, Koster W, Bartram J, Ronchi E, Fewtre L, editors. Assessing microbial safety of drinking water: Improving approaches and methods. WHO and OECD. New York: IWA Publishing; 2003.
73. USEPA. Drinking water; national primary water rules and regulations; filtration, disinfection, turbidity, Giardia lamblia, viruses, Legionella and heterotrophic bacteria final rule. 40 CRF parts 141 and 142, U.S. Environmental Protection Agency. Fed. Reg. 54(124), 27486-27541; 2004. Available at Access Date: 12/12/ 2010.