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

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 of 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.