Qualitative operators for reasoning maps: Evaluating multi-criteria options with networks of reasons

Cognitive/causal maps have been widely used as a powerful way of capturing decision-makers' views about a problem, representing it as a cause-effect discourse. Several ways of making causal inferences from this type of model have been proposed in the Operational Research and Artificial Intelligence literatures, but none, as far as we are aware, has attempted to use a causal map structure to perform a multi-criteria evaluation of decision alternatives. Recently, we have proposed a new multi-criteria method, denominated as a Reasoning Map, which permits the use of decision-makers' reasoning, structured as a network of means-and-ends (a particular type of causal map) to perform such an evaluation. In this manner, the model resembles the way that people talk and think about decisions in practice. The method also pays explicit attention to the cognitive limitations of decision-makers in providing preference information. Thus it employs qualitative assessment of preferences, utilises aggregation operators for qualitative data and provides also qualitative outputs. In this paper we discuss and evaluate possible ways of aggregating qualitative performance information in Reasoning Maps.

[1]  Prakash P. Shenoy,et al.  A Bayesian network approach to making inferences in causal maps , 2001, Eur. J. Oper. Res..

[2]  Ward Edwards,et al.  SIMPLICITY IN DECISION ANALYSIS: AN EXAMPLE AND A DISCUSSION , 1983 .

[3]  S. Greco,et al.  Decision Rule Approach , 2005 .

[4]  Valerie Belton,et al.  Reasoning maps for decision aid: an integrated approach for problem-structuring and multi-criteria evaluation , 2008, J. Oper. Res. Soc..

[5]  Bart Kosko,et al.  Fuzzy Cognitive Maps , 1986, Int. J. Man Mach. Stud..

[6]  O. Larichev Cognitive validity in design of decision‐aiding techniques , 1992 .

[7]  Jonathan Rosenhead,et al.  Problem structuring methods in action , 2004, Eur. J. Oper. Res..

[8]  Josep Domingo-Ferrer,et al.  Median‐based aggregation operators for prototype construction in ordinal scales , 2003, Int. J. Intell. Syst..

[9]  Theodor J. Stewart,et al.  Multiple criteria decision analysis - an integrated approach , 2001 .

[10]  Ronald R. Yager,et al.  Fusion of ordinal information using weighted median aggregation , 1998, Int. J. Approx. Reason..

[11]  Vicenç Torra,et al.  On aggregation operators for ordinal qualitative information , 2000, IEEE Trans. Fuzzy Syst..

[12]  Colin Eden,et al.  Analyzing cognitive maps to help structure issues or problems , 2004, Eur. J. Oper. Res..

[13]  D. Budescu,et al.  Consistency in interpretation of probabilistic phrases , 1985 .

[14]  Dennis M. Buede,et al.  Convergence in problem solving: a prelude to quantitative analysis , 1993, IEEE Trans. Syst. Man Cybern..

[15]  Valerie Belton,et al.  Supporting factoring transactions in Brazil using reasoning maps: a language-based DSS for evaluating accounts receivable , 2007, Decis. Support Syst..

[16]  David L. Olson,et al.  Verbal Decision Analysis , 2005 .

[17]  E F Wolstenholme,et al.  Qualitative vs quantitative modelling: the evolving balance , 1999, J. Oper. Res. Soc..

[18]  James C. Bezdek,et al.  Pool2: a generic system for cognitive map development and decision analysis , 1989, IEEE Trans. Syst. Man Cybern..

[19]  Thierry Marchant,et al.  Cognitive maps and fuzzy implications , 1999, Eur. J. Oper. Res..

[20]  Valerie Belton,et al.  Causal maps and the evaluation of decision options—a review , 2006, J. Oper. Res. Soc..

[21]  Jonathan Rosenhead,et al.  Rational Analysis for a Problematic World Revisited , 2001 .

[22]  J. Diffenbach Influence diagrams for complex strategic issues , 1982 .

[23]  Ronald R. Yager,et al.  An approach to ordinal decision making , 1995, Int. J. Approx. Reason..

[24]  A. Buss,et al.  Causes and reasons in attribution theory: A conceptual critique. , 1978 .

[25]  Frederick Hayes-Roth,et al.  Rule-based systems , 1985, CACM.

[26]  Marc Roubens,et al.  Advances in decision analysis , 1999 .

[27]  Shashi Shekhar,et al.  Cognitive Mapping , 2008, Encyclopedia of GIS.

[28]  Michael P. Wellman,et al.  Inference in cognitive maps , 1994 .

[29]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[30]  Prakash P. Shenoy,et al.  A causal mapping approach to constructing Bayesian networks , 2004, Decis. Support Syst..

[31]  Eelko Huizingh,et al.  A comparison of verbal and numerical judgments in the analytic hierarchy process , 1997 .

[32]  J. Bryson,et al.  Visible Thinking: Unlocking Causal Mapping for Practical Business Results , 2004 .

[33]  B. E. Partridge,et al.  The Nature of Managerial Work , 1974 .

[34]  Francisco Herrera,et al.  Linguistic decision analysis: steps for solving decision problems under linguistic information , 2000, Fuzzy Sets Syst..

[35]  D. E. Bell,et al.  Decision making: Descriptive, normative, and prescriptive interactions. , 1990 .

[36]  Valerie Belton,et al.  Qualitative operators for reasoning maps , 2009 .

[37]  Dennis M. Buede,et al.  Dynamic decision making: a comparison of approaches , 2000 .