Consistency Checking and Improving for Interval-Valued Hesitant Preference Relations

Group decision making (GDM), which aims to obtain a sensible decision result with several decision makers, is a common occurrence in daily life. Since the uncertainty of the objects is a thorny issue in the process of GDM, it is important to eliminate uncertainty in order to achieve an optimal decision result. Considerations of some types of preference relations based on various fuzzy sets have been presented and investigated in previous studies; in this paper, we define the interval-valued hesitant multiplicative preference relation (IVHMPR) and the multiplicative consistency of IVHMPR. Based on these, we provide a detailed discussion on the connections between the interval-valued hesitant fuzzy preference relation (IVHFPR) and the IVHMPR. Then, we give a method to check the for unacceptable consistency of IVHFPR and IVHMPR, and improve them to make the consistency acceptable. Finally, an illustrative example of selecting the optimal treatment for a lung cancer patient is given to demonstrate our work in detail.

Two Hesitant Multiplicative Decision-Making Algorithms and Their Application to Fog-Haze Factor Assessment Problem

Hesitant multiplicative preference relation (HMPR) is a useful tool to cope with the problems in which the experts utilize Saaty’s 1–9 scale to express their preference information over paired comparisons of alternatives. It is known that the lack of acceptable consistency easily leads to inconsistent conclusions, therefore consistency improvement processes and deriving the reliable priority weight vector for alternatives are two significant and challenging issues for hesitant multiplicative information decision-making problems. In this paper, some new concepts are first introduced, including HMPR, consistent HMPR and the consistency index of HMPR. Then, based on the logarithmic least squares model and linear optimization model, two novel automatic iterative algorithms are proposed to enhance the consistency of HMPR and generate the priority weights of HMPR, which are proved to be convergent. In the end, the proposed algorithms are applied to the factors affecting selection of fog-haze weather. The comparative analysis shows that the decision-making process in our algorithms would be more straight-forward and efficient.

MANAGING HESITANT INFORMATION IN GDM PROBLEMS UNDER FUZZY AND MULTIPLICATIVE PREFERENCE RELATIONS

In the process of group decision making (GDM), preference relations (e.g. fuzzy preference relation and multiplicative preference relation) are very popular tools to express decision makers' preferences, especially when a set of alternatives (or criteria) are compared. However, most of the existing preference relations don't consider the hesitancy information, which allows the decision makers to provide all the possible values when comparing two alternatives (or criteria), and is a common situation in daily life. In this paper, we first define the concept of hesitant fuzzy preference relation and study its properties, based on which we give an approach to GDM. Motivated by the multiplicative preference relation and the hesitant fuzzy set, we introduce the hesitant multiplicative set and develop a series of hesitant multiplicative aggregation operators. Hesitant multiplicative preference relation is also defined to provide decision makers a very useful tool to express their hesitant preferences over alternatives, and then is applied to GDM. Additionally, an example is given to illustrate our results.