Abstract
Abstract Multiple attribute decision analysis (MADA) problems often include both qualitative and quantitative attributes which may be either precise or inaccurate. The evidential reasoning (ER) approach is one of reliable and rational methods for dealing with MADA problems and can generate aggregated assessments from a variety of attributes. In many real world decision situations, accurate assessments are difficult to provide such as in group decision situations. Extensive research in dealing with imprecise or uncertain belief structures has been conducted on the basis of the ER approach, such as interval belief degrees, interval weights and interval uncertainty. In this paper, the weights of attributes and utilities of evaluation grades are considered to be fuzzy numbers for the ER approach. Fuzzy analytic hierarchy process (FAHP) is used for generating triangular fuzzy weights for attributes from a triangular fuzzy judgment matrix provided by an expert. The weighted arithmetic mean method is proposed to...
Highlights
Multiple attribute decision analysis (MADA) with various types of attributes is common in practice.1 For instance, in a project evaluation problem, both quantitative attributes measured by numerical values and qualitative attributes judged by linguistic variables need to be taken into account
Numerical values associated with these grades are used to transform the subjective judgment of an alternative on a qualitative attribute to a numerical value, or the numerical value assessed to a quantitative attribute is transformed to degrees on several evaluation grades
We investigate a decision situation where a group of experts are involved in providing uncertain weights, in particular triangular fuzzy weights
Summary
Multiple attribute decision analysis (MADA) with various types of attributes is common in practice. For instance, in a project evaluation problem, both quantitative attributes measured by numerical values and qualitative attributes judged by linguistic variables need to be taken into account. The evidential reasoning (ER) approach was introduced in 1990s2,3 based on the Dempster-Shafer (D-S) theory and is well-suited to dealing with complex MADA problems It uses a distributed assessment based on several defined evaluation grades to present incomplete or fuzzy subjective judgments and it is convenient to combine different types of attributes. The global fuzzy belief degrees are generated based on the interval weights calculated by the α-cut method and the ER algorithm through four groups of ER based nonlinear programming models. Fuzzy utilities are used in the ER approach and assumed to be constraints in the nonlinear programming models for the computation of the general assessment value for the presentation of risk preferences from different DMs or the attitude changes of DMs towards risk.
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