Dealing with the problem of null weights and scores in Fuzzy Analytic Hierarchy Process

Fuzzy Analytic Hierarchy Process (Fuzzy AHP) has been widely adopted to support decision making problems. The Fuzzy AHP approach based on the synthetic extent analysis is the most applied approach to calculate the values of the criteria weights from fuzzy comparative matrices. The min operator is used to calculate the weights based on values of degree of possibility. If any of the degrees of possibilities is zero, the output of this operator will also be zero. Thus, the criterion weight or alternative score will be set to zero. If not prevented, this problem may lead to a distorted rank. Despite the fact that there are other propositions based on synthetic extent analysis method, none of the studies found in the literature investigate how the problem of null weights and scores can be avoided. This paper investigates different approaches of the Fuzzy AHP method to evaluate whether they can avoid the problem of null weights and scores without affecting the consistency of the results. Five different approaches based on synthetic extent analysis method were implemented and evaluated. Tests were performed considering 12 decision problems. The results indicated that the Fuzzy AHP approach proposed by Ahmed and Kilic is the most appropriate to overcome the problem of null weight of criteria and scores of alternatives without affecting the consistency of the results. Other benefits of using this approach are the simplicity of the computational implementation and better ability to differentiate the importance of the criteria when the weight values are very close.