## 1 Introduction
A number of preference relations have been developed in this manner and used in practical decision-making, such as multiplicative preference relations [19; 20; 22], fuzzy preference relations [23], multiplicative fuzzy preference relations [24], incomplete fuzzy preference relations [25; 26], linguistic preference relations [27; 28; 29], intuitionistic fuzzy preference relations [30; 31; 32; 33; 34], interval-valued hesitant preference relations [10], hesitant fuzzy preference relations [35; 36; 21; 37], and hesitant multiplicative preference relations [38; 39; 21]. The main goal of this paper is to develop an efficient group decision-making support system that will be capable of handling occurrence probabilities of multiplicative preference degrees. In this regard, a novel notion of hesitant probabilistic multiplicative preference relations is proposed that will model the vagueness and complexities of real life scenarios in a better way. In this line of research, [PERSON] and [PERSON] [40] proposed and studied probabilistic hesitant fuzzy preference relations and dealt with their consistency by defining the expected consistency; however, they do not address group decision-making. The group decision-making [24; 25; 41; 42; 43; 44] is more accurate than a single person's decision. Any group decision support system of preference relations must address the following critical issues. * Consistency of preference relations: Inconsistent preference relations lead to unrealistic decisions. Consistency is like transitivity in some sense [22; 27; 35; 38; 45; 46; 47]. Therefore, the preference relation must satisfy a certain level of consistency. * Consensus among decision-makers: In group decision-making, the diversity in nature, social backgrounds, education level, expertise, and experience of decision-makers may lead to differences in opinions, but it is important in many scenarios of group decision-making to develop a reasonable consensus between the decision-makers [22; 25; 35; 38; 47; 48; 49]. Thus, some measures are needed to remove the difference in opinion to some extent. To deal with both issues of consistency and consensus, in the HPMPR, multiplicative consistency and weak stochastic transitivity are used for multiplicative preference degree and their occurrence probabilities respectively, to define consistency. A novel deviation degree is introduced between two HPMPRs, based on a consistency measure of the HPMPR, and a consensus measure among decision-makers is defined. A series of novel algorithms are designed to find a consistent HPMPR, make the HPMPR acceptably consistent, and develop an acceptable consensus between decision-makers. The paper is structured in the following way. In Section 2, some preliminary concepts are discussed to clarify our proposed consistency and consensus measure. In Section 3, the HPMS and HPMPR are defined, and the consistency issue of the HPMPR is discussed. Section 4 is devoted to resolving the consensus issue, and an algorithm is presented for reaching an acceptable consensus among decision-makers. Section 5 is dedicated to presenting a complete group decision-making model dealing with both issues of consistency and consensus. In Section 6, a numerical analysis of the developed model is performed in a case study in order to demonstrate the relevance of our proposal. Section 7 ends the paper with some concluding remarks.