Interval-valued Hesitant Multiplicative Preference Relations and Their Application to Multi-criteria Decision Making

Abstract

Aims: The aim of this paper is to investigate interval-valued hesitant multiplicative preference relations and their application to multi-criteria decision making. Study Design: Based on pseudo-multiplication, we define some basic operations for the interval-valued hesitant multiplicative sets (IVHMSs) and develop several aggregation operators for aggregating the interval-valued hesitant multiplicative information. Some desired properties and special cases of the developed operators are also investigated. Furthermore, we present a new preference structure named as the interval-valued hesitant multiplicative preference relation (IVHMPR), each element of which is an IVHMS, denoting all the possible interval multiplicative preference values offered by the decision makers for a paired comparison of alternatives. Place and Duration of Study: Interval-valued hesitant fuzzy set (IVHFS), recently introduced by Chen et al., permits the membership degree of an element to a set to be represented as several possible interval values. However, it is noted that IVHFS uses 0.1–0.9 scale, which is inconsistent with some practical problems (e.g. the law of diminishing marginal utility in economics). Methodology: We use the unsymmetrical 1–9 scale instead of the symmetrical 0.1–0.9 scale to express the membership degree information in the IVHFS and introduce the concept of interval-valued hesitant multiplicative set (IVHMS). Results: An approach for multi-criteria decision making based on the interval-valued hesitant multiplicative preference relations (IVHMPRs) is developed and some numerical examples are provided to illustrate the developed approach. Conclusion: We compare the IVHMPR with the interval-valued hesitant preference relation (IVHPR) and the interval multiplicative preference relation (IMPR), and show the effectiveness and practicality of the IVHMPR.