Hesitant Probabilistic Multiplicative Preference Relations in Group Decision Making

Applied Sciences

Wojciech Sałabun¹  Abbas Malik²  Zia Bashir³  Tabasam Rashid⁴  Jarosław Wątróbski⁵ 

[1] Department of Artificial Intelligence Method and Applied Mathematics in the Faculty of Computer Science and Information Technology, West Pomeranian University of Technology, 71-210 Szczecin, Poland;Department of Computer Science, School of Engineering, Computer and Mathematical Sciences, Auckland University of Technology, Auckland 1010, New Zealand;Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan;Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan;Faculty of Economics and Management, University of Szczecin, 71-101 Szczecin, Poland;

关键词: decision support system;    hesitant fuzzy sets;    multi-criteria group decision-making;    hesitant multiplicative set;    hesitant probabilistic multiplicative set;   

DOI  :  10.3390/app8030398

来源: DOAJ

【 摘 要 】

The preference of one alternative over another is a useful way to express the opinion of the decision-maker. In the process of group decision-making, preference relations are used in preference modeling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty and, in many scenarios of decision-making problems, the probabilities of different events affect the decision-making process directly. In order to deal with this issue, the hesitant probabilistic multiplicative preference relation (HPMPR) is defined in this paper. Furthermore, consistency of the HPMPR and consensus among decision makers are studied here. In this respect, many algorithms are developed to achieve consistency of HPMPRs, reasonable consensus between decision-makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision-making. Lastly, we present a case study with complete illustration of the proposed model and discuss the effects of probabilities on decision-making validating the importance of the introduction of probability in hesitant multiplicative preference relations.

【 授权许可】

Unknown