Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties

doi:10.1016/S0377-2217(99)00441-5

European Journal of Operational Research

Volume 131, Issue 1, 16 May 2001, Pages 31-61

https://doi.org/10.1016/S0377-2217(99)00441-5 Get rights and content

Abstract

In this paper generic decision models and both rule and utility based techniques for transforming assessment information are developed to enhance an evidential reasoning (ER) approach for dealing with multiple attribute decision analysis (MADA) problems of both a quantitative and qualitative nature under uncertainties. In the existing ER approach, a modelling framework is established for representing subjective assessments under uncertainty, in which a set of evaluation grades for a qualitative attribute is defined. The attribute may then be assessed to one or more of these grades with certain degrees of belief. Using such a distributed assessment framework, the features of a range of evidence can be catered for whilst the assessor is not forced to pre-aggregate various types of evidence into a single numerical value. Both complete and incomplete assessments can be accommodated in a unified manner within the framework.

For assessing different qualitative attributes, however, different sets of evaluation grades may need to be defined to facilitate data collection. Moreover, some attributes are quantitative and may be assessed using certain or random numbers. This increases complexity in attribute aggregation. In this paper, a generalised and extended decision matrix is constructed and rule and utility based techniques are developed for transforming various types of information within the matrix for aggregating attributes via ER. The transformation processes are characterised by a group of matrix equations. The techniques can be used in a hybrid way at different levels of an attribute hierarchy. It is proved in this paper that such transformations are equivalent with regard to underlying utility and rational in terms of preserving the features of original assessments. Complementary to distributed descriptions, utility intervals are introduced to describe and analyse incomplete and imprecise information. Two numerical examples are provided to demonstrate the implementation procedures of the new techniques and the potential and scope of the rule and utility based ER approach in supporting decision analysis under uncertainties.

Section snippets

Quantitative and qualitative MADA

A multiple attribute decision analysis (MADA) problem can be generally modelled using a decision matrix (Hwang and Yoon, 1981). Several approaches have been proposed to deal with MADA problems of both a quantitative and qualitative nature. Multiattribute utility (value) function approaches are among the simplest and most commonly used Keeney and Raiffa, 1976, Hwang and Yoon, 1981, Belton, 1986, Winston, 1994, Yang, 1996. If a MADA problem involves a large number of attributes and alternatives,

Rule based information transformation techniques

The purpose of defining a unique set of evaluation grades for a particular basic attribute is to facilitate raw data collection. The grades thus defined need to be interpreted and transformed for assessment of a general attribute. Such transformation can be conducted using the decision maker’s knowledge and experience described as rules. Both qualitative assessments and quantitative data can be transformed in this way.

Utility based information transformation technique

In Section 2, both qualitative assessments and quantitative data were transformed to a unified format using equivalence rules as defined in , , , . Assuming the equivalence of underlying utilities in those rules, we established equivalent transformation, though the explicit estimation of utilities was not required. This rule based technique is developed to provide a pragmatic means for extracting equivalence information from the decision maker for transforming information from one form to

Numerical example 1 – car performance assessment

The rule and utility based ER approach has been applied to solving decision problems in management and engineering. In the following sections, two examples are examined to demonstrate how the rule and the utility based transformation techniques can be implemented to support decision analysis under uncertainties in conjunction with the ER algorithm. The first car performance assessment is conducted using the rule based transformation technique, and the second motorcycle selection problem is

Example 2 – motorcycle assessment

To demonstrate the other features of the new ER approach, in this section we examine a motorcycle assessment problem by assuming incomplete and imprecise data of both a quantitative and qualitative nature. In the previous car ranking problem, qualitative attributes were assessed by simply selecting one of the nine defined evaluation grades (i.e. with 100% degree of belief). In this section, we use a belief structure to facilitate continuous and imprecise assessments for qualitative attributes.

Concluding remarks

The complexity in dealing with real-world decision problems results from the fact that both quantitative and qualitative attributes with uncertainties need to be handled together in a way that is rational, systematic, reliable, flexible, and transparent. The rule and utility-based ER approach developed in this paper provides a rigorous yet pragmatic way to support multiple attribute decision analysis (MADA) under uncertainties. This approach is not only capable of generating credible results

Acknowledgements

The author is grateful to the two anonymous referees for their constructive comments that helped to improve the quality of the paper to its current standard.

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Theory and MethodologyRule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties

Abstract

Section snippets

Quantitative and qualitative MADA

Rule based information transformation techniques

Utility based information transformation technique

Numerical example 1 – car performance assessment

Example 2 – motorcycle assessment

Concluding remarks

Acknowledgements

European Journal of Operational Research

European Journal of Operational Research

Journal of Mathematical Psychology

OMEGA International Journal of Management Science

Reliability Engineering and System Safety

European Journal of Operational Research

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Journal of Operational Research Society

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OMEGA International Journal of Management Science

The sports tourers

Motor Cycle International

Decision with Multiple Objectives: Preference and Value Tradeoffs

Theory and Methodology
Rule and utility based evidential reasoning approach for multiattribute decision analysis under uncertainties