A Hybrid DHFEA/AHP Method for Ranking Units with Hesitant Fuzzy Data

Abstract

One of the attractive subjects in decision analysis is the investigating of the uncertain data which is inevitable in many real-world applications. A variety of tools can be used by researchers to study the problems in the presence of uncertain data. For example, fuzzy sets theory has been introduced to investigate the uncertain data which formulates the uncertainty by using the membership functions. However, in many real world applications, it is difficult to determine the exact amount of the membership value and so the skepticism can be raised during the decision-making process. The new perspective manages the uncertainty caused by the skepticism and in this case, the most important issues are to collect the hesitant fuzzy information and to select the optimal alternative. This study develops the deviation-oriented hesitant fuzzy envelopment analysis (DHFEA) based on the slack based measure (SBM) in terms of deviation values; and on basis of different production possibility set (PPS) can be formulated. For this purpose, a two-stage method is proposed for ranking the Decision Making Units (DMUs) by using the DHFEA and the Analytic Hierarchy Process (AHP). Given that in many cases the importance of input or output indices plays an important role in decision-making, therefore, the first stage of the proposed method evaluates and compares the DMUs and the second stage constructs the pair-wise comparisons matrix by using the obtained results of DHFEA model and then proposes a complete ranking of DMUs by applying AHP method. The potential application of the proposed method is illustrated with a numerical example with the hesitant fuzzy data and the obtained results are compared with the results of the existing ranking methods.