A variable weight approach for evidential reasoning

Abstract

A variable weight approach was proposed to handle the probability deficiency problem in the evidential reasoning (ER) approach. The probability deficiency problem indicated that the inadequate information in the assessment result should be less than that in the input. However, it was proved that under certain circumstances, the ER approach could not solve the probability deficiency problem. The variable weight approach was based on two assumptions: 1) the greater weight should be given to the rule with more adequate information; 2) the greater weight should be given to the rules with less disparate information. Assessment results of two notional case studies show that 1) the probability deficiency problem is solved using the proposed variable weight approach, and 2) the information with less inadequacy and more disparity is provided for the decision makers to help reach a consensus.

Keywords

probability deficiency / evidential reasoning (ER) / inadequate information / variable weight / consensus

References

[1] FrankeV. Decision making under uncertainty: Using case studies for teaching strategy in complex environments [J]. Journal of Military and Strategic Studies, 2011, 13(2): 1-21

[2] ChenX-h, ZhouY-j, HuD-bin. A problem solving framework for group support system [J]. Journal of Central South University of Technology, 2002, 9(4): 7121-7131

[3] OberkampfW L, HeltonJ C, JoslynC. A. Challenge problems: Uncertainty in system response given uncertain parameters [J]. Reliability Engineering and System Safety, 2012, 85(1): 9-11

[4] HeltonJ C, OberkampfW L. Alternative representations of epistemic uncertainty [J]. Reliability Engineering & System Safety, 2004, 85(1/3): 1-10

[5] YangJ-bo. Rule and utility based evidential reasoning approach for multiple attribute decision analysis under uncertainty [J]. European Journal of Operational Research, 2001, 131(1): 31-61

[6] YangJ-b, LiuJ, WangJ, SiiH-s, WangH-wei. Belief rule-base inference methodology using the evidential reasoning approach-RIMER [J]. IEEE Transactions on Systems, Man, and Cybernetics, 2006, 36(2): 266-285

[7] YangY-m, YangJ-b, XuD-ling. Environmental impact assessment using the evidential reasoning approach [J]. European Journal of Operational Research, 2006, 174(3): 1885-1913

[8] FuC, YangS-lin. The combination of dependence-based interval-valued evidential reasoning approach with balanced scorecard for performance assessment [J]. Expert Systems with Applications, 2012, 39(3): 3717-3730

[9] ZhouZ-j, HuC-h, YangJ-b, XuD-l, ZhouD-hua. Online updating belief-rule-based systems for pipeline leak detection under expert intervention [J]. Expert Systems with Applications, 2009, 36(4): 7700-7709

[10] TangD-w, YangJ-b, ChinK-s, Wong ZoieS Y, LiuX-bao. A methodology to generate a belief rule base for customer perception risk analysis in new production development [J]. Expert Systems with Applications, 2011, 38(5): 5373-5383

[11] SiX-s, HuC-h, YangJ-b, ZhangQi. On the dynamic evidential reasoning algorithm for fault prediction [J]. Expert Systems with Applications, 2011, 38(5): 5061-5080

[12] FuC, YangS-lin. An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context [J]. European Journal of Operational Research, 2011, 212(1): 179-189

[13] JiangJ, LiX, ZhouZ-j, XuD-l, ChenY-wu. Weapon system capability assessment under uncertainty based on the evidential reasoning approach [J]. Expert Systems with Applications, 2011, 38(11): 13773-13784

[14] JiangJ, ChenY-w, TangD-w, ChenY-wang. TOPSIS with belief structure for group belief multiple criteria decision making [J]. International Journal of Automation and Computing, 2010, 7(3): 359-364

[15] YangJ-b, WongB Y H, XuD-l, LiuX-b, SteuerR E. Integrated bank performance assessment and management planning using hybrid minimax reference point-DEA approach [J]. European Journal of Operational Research, 2010, 207(3): 1506-1518

[16] XuD-l, YangS-lin. Integrated efficiency and trade-off analysis using DEA-oriented interactive minimax reference point approach [J]. Computers & Operational Research, 2011, 39(5): 1062-1073

[17] ApostolakisG. The concept of probability in safety assessment of technological systems [J]. Science, 1990, 250(4986): 1359-1364

[18] DuboisD, PradeHPossibility theory [M], 1998New YorkPlenum Press

[19] JiangJiangModeling, researching and learning approach to Evidential Network [D], 2011ChangshaNational University of Defense Technology

[20] DempsterA P. Upper and lower probabilities induced by multivalued mapping [J]. Annual Mathematics Statistics, 1967, 38(2): 325-339

[21] ShaferGA mathematical Theory of Evidence [M], 1976Princeton, New JeresyPrinceton University Press

[22] DenoeuxT. Reasoning with imprecise belief structures [J]. International Journal of Approximate Reasoning, 1999, 20(1): 79-111

[23] DenoeuxT. Conjunctive and disconjunctive combination of belief functions induced by non distinct bodies of evidence [J]. Artificial Intelligence, 2008, 172(2/3): 234-264

[24] JousselmeA L, GrenierD, BosseE. A new distance between two bodies of evidence [J]. Information Fusion, 2001, 2(2): 91-101

[25] LiuW-ru. Analyzing the degree of conflict among belief functions [J]. Artificial Intelligence, 2006, 170(11): 909-924

[26] JousselmeA L, MaupinP. Distance in evidence theory: Comprehensive survey and generalizations [J]. International Journal of Approximate Reasoning, 2012, 53(2): 118-145

[27] StasserG, TitusW. Pooling of unshared information in group decision making: Biased information sampling during discussion [J]. Journal of Personality and Social Psychology, 1985, 48(6): 1467-1478

[28] ArgoteL, McevilyB, ReagansR. Managing knowledge in organizations: An integrative framework and review of emerging themes [J]. Management Science, 2003, 49(4): 571-582

[29] KerrN L, TindateR S. Group performance and decision making [J]. Annual Review of Phycology, 2004, 55: 623-655