Selection of appropriate location based on signed distance based ranking approach with interval type-2 trapezoidal fuzzy preference relations

Abstract

In real life situation, it is often difficult to judge the relative importance of different parameters being considered for evaluating some alternatives. In the context of fuzzy sets, it is a situation where it is difficult to define precise membership grades for attribute values. Here we require more generalized type of fuzzy sets which have a greater representational power than ordinary fuzzy sets. For this purpose we use “interval type-2 trapezoidal fuzzy preference relations (IT2TrFPRs)” in this article as a generalization of fuzzy preference relations and consider the environment discussed above, where there is no information on priority weights. A collective decision matrix will be constructed on the basis of hybrid averages using weighted averaging and signed distance based OWA operation. Then a least deviation model will be employed in order to determine the priority weight vectors. Finally, the alternatives will be ranked on the basis of weighted normalized signed distance of each alternative from the ideal solution. Moreover, a real life example of location selection is illustrated to elaborate the effectiveness of the proposed scheme.

Keywords

• Interval valued fuzzy set (IVFS)
• Generalized fuzzy number (GFN)
• Interval type-2 trapezoidal fuzzy number (IT2TrFN)
• Interval type-2 trapezoidal fuzzy preference relation (IT2TrFPR)
• Hybrid averaging (HA) operation
• Group decision making (GDM)