Modified analytic hierarchy process to incorporate uncertainty and managerial aspects

The analytic hierarchy process (AHP) is a powerful multiple-criteria decision analysis technique for dealing with complex problems. Traditional AHP forces decision-makers to converge vague judgements to single numeric preferences in order to estimate the pairwise comparisons of all pairs of objectives and decision alternatives required in the AHP. The resultant rankings of alternatives cannot be tested for statistical significance and it lacks a systematic approach that addresses managerial/soft aspects. To overcome the above limitations, the present paper presents a modified analytic hierarchy process, which incorporates probabilistic distributions to include uncertainty in the judgements. The vector of priorities is calculated using Monte Carlo simulation. The final rankings are analysed for rank reversal using analysis of variance, and managerial aspects (stake holder analysis, soft system methods, etc.) are introduced systematically. The focus is on the actual methodology of the modified analytic hierarchy process, which is illustrated by a brief account of a case study

Group Evidential Reasoning Approach for MADA under Fuzziness and Uncertainties

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 aggregate the triangular fuzzy weights of attributes from a group of experts. -cut is then used to transform the combined triangular fuzzy weights to interval weights for the purpose of dealing with the fuzzy type of weight and utility in a consistent way. Several pairs of group evidential reasoning based nonlinear programming models are then designed to calculate the global fuzzy belief degrees and the overall expected interval utilities of each alternative with interval weights and interval utilities as constraints. A case study is conducted to show the validity and effectiveness of the proposed approach and sensitivity analysis is also conducted on interval weights generated by different -cuts