Abstract
AbstractWe provide a methodology to perform an extensive and systematized analysis of problems where experts voice their opinions on the attributes of projects through a hesitant fuzzy decision matrix. This provides the decision-maker with ample information on which he or she can rely in order to make the final decision, in the form of segments instead of numbers. These segments derive from weighted average of new parametric expressions for two tenable indices of satisfaction, the distance to an ideal or the similarity to an anti-ideal, and permit to give a profuse unified picture of the relative performance of the projects. When the parameter grows, these indices tend to replicate the evaluation by respective simplistic expressions that only depend on the least, resp., the largest, evaluation and the number of evaluations in each cell.
Highlights
The classical group decision making problem concerns the context where a group of experts have to make a decision on a set of alternatives, attending to either one or multiple criteria
We suggest respective novel parametric indicators for such proxies that incorporate the relative importance of the attributes through ex-ante allocations of weights. Their asymptotic behavior, i.e., the role of the parameter, is disclosed: when the parameter goes to infinity these indicators tend to provide an evaluation by respective simplistic expressions that only depend on the least, resp., the largest, evaluation and the number of evaluations on each attribute
We have provided a novel methodology that permits to perform an extensive and systematized analysis of problems with a precise specification: experts voice their opinions on the attributes of projects through a hesitant fuzzy decision matrix, that is, an m × n matrix whose cells contain hesitant fuzzy elements (HFEs)
Summary
The classical group decision making problem concerns the context where a group of experts have to make a decision on a set of alternatives, attending to either one or multiple criteria. It has long been recognized that fuzzy sets (FS) and fuzzy logic provide useful tools for the management of human subjectivity in decisionmaking contexts[12,21,18,37]. In some practical problems, imprecise human knowledge (and especially group knowledge) cannot be suitably represented by fuzzy sets and some generalizations are needed. This was established as early as in Zadeh[50]. The motivation for using this concept in decision making is clearly explained e.g., in Xu46. This reference justifies that hesitant fuzzy elements and sets have produced an extensive theoretical and applied literature 30,32,40,43,56. The authors summarize many useful and valuable decision making methods to solve hes-
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