Two regression methods for hesitant multiplicative preference relations with different consistencies

摘要

Multiplicative preference relation (MPR) is an efficient and widely used tool in describing the preferences of decision makers. The hesitant multiplicative preference relation (HMPR), as an extension of the MPR, is commonly used in collecting and representing all hesitant preferences and judgements of the decision makers. Considering that there usually appear some random or illogical preference degrees in the process of constructing the HMPRs, so it is necessary to derive a pithy preference relation (such as MPR) from the original HMPR through selecting the most proper and abandoning improper preference degrees, at the same time, the derived MPR is with the advantage of both terseness and the best consistency. Based on the multiplicative consistency measure of HMPRs, this paper proposes two regression methods to transform the HMPR into MPRs (called reduced MPRs). With the error analysis, the first proposed regression method provides some steps to not only extract the reduced MPRs from original HMPR but also calculate the consistencies of both the HMPR and the reduced MPRs. A case study reflects that the reduced MPR is with the highest consistency degree among those possible separated MPRs from HMPR. To apply this method to solve practical problems conveniently, a group decision-making procedure with hesitant multiplicative information is further given based on the first regression method. Time complexity comparison between our proposed method and an existing method indicates the effectiveness of our method. In addition, according to the weak consistency, we develop the second regression method and design an algorithm to obtain the reduced MPRs from the HMPR. Furthermore, we provide a method to check the weak consistency of the HMPR and repair the inconsistent one. Numerical examples verify that the second regression method proposed in this paper is an effective technique for checking the weak consistency and modifying the inconsistency HMPR to the one with weak cons