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Representation of The Pairwise Comparisons in AHP Using Hesitant Cloud Linguistic Term Sets

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Huang H.-C. , Yang X.

Fundamenta Informaticae

2016

tom Vol. 144, nr 3/4

349--362

The analytic hierarchy process (AHP) is the most popular extension to the pairwise comparisons method which is based on the observation that it is much easier to rank several objects when restricted to two objects at one time. As the pairwise comparisons are subjective, the use of linguistic expressions rather than numerical values is straightforward and friendlier due to the uncertainties that are inherent in human judgments. In this paper, to handle the uncertainty and hesitancy in practical decisionmaking situations, we represent pairwise comparisons in AHP using hesitant cloud linguistic term sets (HCLTSs) which are proposed based on hesitant fuzzy linguistic term sets (HFLTSs) and normal cloud models. Then, the synthetic cloud model aggregation algorithm is proposed to transform the HCLTS pairwise comparison matrix into the positive reciprocal synthetic cloud matrix. A prioritization method using the geometric mean technique is adopted, and the ranking method based on comparing of the parameters of normal cloud models is proposed. Thus, we extend the traditional AHP method in hesitant and uncertain environment, and we call it HCLTS-AHP method. The comparative linguistic expressions of preferences become more flexible and richer and are more similar to human beings’ cognitive models. Furthermore, the synthetic cloud model is consistent with objectivity and the calculations are easy to implement. An illustrated example is applied to the ranking of four alternatives to show the usefulness of the proposed HCLTS-AHP method.