Resumen de Consensus models for large-scale group decision making with different types of preference relations
Xia Liu
Group decision making refers to the process in which two or more decision makers (DMs) or experts participate in the decision-making, and choose a common solution from the given alternatives [Kac86]. Nowadays, with the rapid development of social economy and information technology, the decision environment and groups have undergone significant changes. The scale of the groups involved in decision-making has gradually expanded, and the decision-making problems have become increasingly complex. Consequently, large-scale group decision making (LSGDM) problems have attracted widely attention recently [PMH14, QPM15, XWZ18].
In LSGDM issues, preference relation is one of the most usual preference structures to be used in expressing DMs’ assessment information, because it is a useful tool in modeling decision processes [HHVC01]. In LSGDM problems, different DMs generally have different culture, education backgrounds or personal interest preferences. Also, there are fuzziness and hesitancy natures in human judgment. When expressing their assessment information, DMs may have several possible numerical values and may perform hesitance to give the decisions. To deal with the DMs’ fuzziness and hesitancy in the decision-making processes, hesitant fuzzy preference relation (HFPR) was proposed in [ZXX17]. In HFPR, DM’s assessment information consists of hesitant fuzzy elements, which denote all possible preference values and can be utilized to effectively express DM’s hesitant and fuzzy information in LSGDM problems. Additionally, real LSGDM cases involve not only the calculation of mathematical models, but also the psychological behavior of DMs [DLL+17]. Self-confidence is a person’s psychological implication of self-statement, and can reflect one’s knowledge, experience or attitude in the LSGDM processes. Besides, DMs’ self-confidence is a factor affecting human decision making which has been proven in many researches [Hin90, JT67]. Recently, a new type of preference relations, i.e., self-confident fuzzy preference relations (SC-FPRs) was introduced by [LDC+17]. In an SC-FPR, the elements are composed of two components, the former represents the preference degree between pairs of alternatives, and the latter denotes the self-confidence level associated with the first component, as a psychological expression for personal self-estimation.
Generally, in real LSGDM problems, it is really hard to ensure the final decision(s) can be accepted by all the DMs since there are a large number of DMs participated. Hence, the consensus reaching processes (CRPs) were proposed to improve the efficiency of LSGDM problems [PMH14]. The CRPs aim to reduce the objections of the minority while pursuing the agreements of the majority and have become one of the main concerns in the LSGDM issues. Up to now, different consensus models have been proposed and made a considerable progress in LSGDM research [GXH18, WX18, DZZ+18]. However, the LSGDM that considers the DMs’ hesitancy and fuzziness still need to be further discussed. Moreover, LSGDM research that considers the multiple self-confidence of DMs remains a challenge.
To further enrich and improve the consensus research of LSGDM problems, This thesis focuses on the following three aspects of discussions.
Firstly, we mainly focus on the CRPs for hesitant fuzzy LSGDM problems. That is, DMs use HFPRs to express their assessment information, which can well represent the fuzziness and hesitancy of DM’s assessment information. To improve the efficiency of hesitant fuzzy LSGDM problems, we first propose a reliability index-based consensus reaching process (RI-CRP). By assessing the ordinal consistency of DM’s assessment information and measuring the deviation from collective opinion, the opinion reliability index of DM is given. To avoid unreliable information, we propose an unreliable DM management method to be used in the RI-CRP, based on the computation of DM’s opinion reliability index. An alternative ranking-based clustering (ARC) method with HFPRs is proposed to improve the efficiency of the RI-CRP. The similarity index between two DMs’ opinions is provided to ensure the ARC method can be effectively implemented. In the RI-CRP, a group consensus index (GCI) is given to measure the consensus level. To achieve a high level of consensus, the management processes for non cooperative clusters in the RI-CRP are proposed.
Secondly, considering the application of the new type of preference relations SC-FPRs in group decision making, we first give some operational laws for SC-FPRs. Subsequently, to improve the reliability of DMs’ assessment information, we make an additive consistency analysis on SCFPRs. An additive consistency index which considers the DMs’ self-confidence is presented to measure the consistency level of an SC-FPR. Moreover, an self-confidence driven consistency improvement algorithm is proposed to repair the inconsistency of SC-FPRs. Besides, we propose a novel self-confidence indices-based induced ordered weighted averaging (SCI-IOWA) operator for group decision making with SC-FPRs. A self-confidence score (SCS) function is designed to obtain the best alternative in group decision making with SC-FPRs. To further demonstrate the advantages of applying the SC-FPRs in group decision making problems, we deeply explored the consensus process in the social network environment based on SC-FPRs. A dynamic importance degree of DMs which combines the external trust and internal self-confidence is proposed to determine their weights. A novel GCI considering self-confidence is defined to assess the consensus level among DMs under the social network decision making situation. Meanwhile, a trust-based feedback mechanism is presented to improve the consensus efficiency.
Finally, based on the discussion of the operational laws and consistency analysis for SC-FPRs, we further deeply discuss the impact of DMs’ self-confidence on LSGDM, and analyze the CRPs in LSGDM with SC-FPRs. A new DMs clustering algorithm that considers DMs’ self-confidence is presented to improve the consensus efficiency. A GCI that considers DMs’ self-confidence is developed to measure the consensus level of the LSGDM with SC-FPRs. Meanwhile, a measure of overconfidence degree is introduced to estimate the contribution of the DM’s self-confidence to the collective consensus. Based on the overconfidence degree, the detailed overconfidence behavior detection and management is developed.
Overall, this thesis mainly focuses on the consensus models for LSGDM with different types of preference relations. The first one of this research is the consistency model for LSGDM based on HFPRs. And the second one is the CRPs for LSGDM with SC-FPRs.
The remainder of this thesis is organized as follows: Section 2 provides some related preliminaries used throughout this contribution. In Section 3, the basic ideas and the challenges that justify the development of this thesis are discussed. Section 4 proposes the objective of this thesis. Section 5 presents the methodology used in the thesis. A summary of the consensus models for LSGDM with different types of preference relations are presented in Section 6. Section 7 presents a discussion of the results obtained in the thesis. Finally, Section 8 draws the conclusion of this thesis and in Section 9 the future works are discussed.
