Relationship-based clustering algorithm and consensus reaching process for large scale decision making problems using sparse representation and social network analysis

Résumé

With the applications of e-democracy, social networks, and public participation, the scale of decision makers (DMs) is sharply enlarging for decision making problems. It makes the final decision more dicult to be reached and the large-scale decision making (LSDM) problems have increasingly attracted the widespread attention of researchers. The LSDM event usually is a complex decision making event with multi-attribute provided for several alternatives and involving in more than 20 DMs [XDC15]. The DMs in an LSDM event can be experts with professional knowledge, or experts representing for the interests of multiple stakeholders, or the public. All the LSDM-related researches are about the following two aspects: to improve the efficiency of the decision making process, which means to reach the consensus within fewer rounds; and to improve the acceptance degree of DMs for the final selection, which means letting more DMs accept the final selection or letting fewer DMs oppose to the final selection. To achieve an acceptable selection with all DMs in limited iterations is the most considerable problem in the research field of the LSDM scenario. In order to improve the efficiency of the decision making processes, the consensus reaching process (CRP) [DZZ+18] is implemented in more and more LSDM models. The clustering algorithm is one of the most utilized skills in CRPs for the LSDM problems to divide DMs into several small groups according to their characteristics [PMH14], which can help to improve the efficiency of the decision making process for LSDM problems. Although many CRPs and clustering methods are proposed for LSDM problems in the last decades, there are still three gaps existed in LSDM scenarios. • The existing LSDM methods are almost based on the hypothesis that: all the alternatives are qualified without any defect. In fact, it is hard to ensure that all the original alternatives are all well qualified before making decisions, especially for multi-attribute LSDM scenarios. If a defective alternative is selected as the final choice, it will cause a decision failure. • The existing-LSDM-applicable clustering methods are almost supervised, which need some observation of the initial data or need to set several parameters, which will reduce the objectiveness of the clustering results. Moreover, the relationship information is less used in the clustering process. • Most of the CRPs or LSDM models utilize the positive relationships of DMs and consensus degree to support the decision making process. The conflict relationships of DMs and their conflict performance are ignored in the existing LSDM models. Before doing any decision process, the defective alternatives should be identified, improved or removed to guarantees the validity and scientificity of the decision procedures. Moreover, with the development of social media, the relationships among DMs in an LSDM event become more and more common, unpredictable and complex. In general, the relationships among DMs can be divided into three types: positive, neutral and negative relationships. Similarly, DMs’ performances in an LSDM event can be classified into three kinds: positive, neutral, and non-cooperative. Social Network Analysis (SNA) [WF94] is widely implemented in the relationship-based LSDM models [WZLC19]. Sharing different relationships, DMs can influence others differently, which can lead them to perform different behaviors and present different contributions in CRPs of LSDM scenarios. It can be further used in the clustering algorithms to classify DMs according to their relationship performance and used to design CRPs for LSDM problems. Based on these analyses above, to tackle the mentioned gaps, this thesis focuses on proposing a defective alternative detecting model, relationship-based-unsupervised clustering algorithms, and more effiective CRPs for LSDM problems. The following research topics are discussed in this thesis: 1. How to detect defective alternatives in multi-attribute LSDM scenarios? The definition of “defective alternative” is proposed in this thesis. To distinguish the alternatives, a concept is denoted as a defectiveness degree to quantify the degree of defectiveness. According to the defectiveness degree of alternatives, the alternatives can be divided into three sets: qualified, slightly defective, and excessively defective alternative sets. A corresponding defective alternative detection (DAD) process is proposed, which can be implemented before the decision making process of LSDM problems. 2. How to cluster DMs utilizing their positive/trust relationships and considering different relationship strength for LSDM problems? The interest preference and relationship performance can be reflected in the DMs’ assessment information. For a DM in an LSDM event, he/she will trust a few DMs and present conflict relationships to a small amount of DMs. For most other DMs, he/she will have neutral relationships. That is, in an LSDM event, DMs’ positive/trust and conflict relationships present sparsity, which can be identified with the sparse representation (SR) model [WYG+08]. By utilizing the characters of DMs’ relationships, the identified relationship information can be further used to cluster DMs according to their relationship performance. 3. Is there any classification of DMs conflict behaviors? How to govern the conflict relationships for LSDM problems? The conflict relationships among DMs are directed. If we consider two DMs that share a conflict relationship, there must be an actor and a receiver. The concepts of opinion conflict and behavior conflict are given in this thesis. If a DM receives many conflict relationships, that is, some other DMs may have opinion conflict relationships towards him/her. If a DM has many conflict relationships with other DMs in LSDM events, they may present behavior conflict relationships towards some other DMs. Then a clustering process can be carried out to distinguish DMs with their performance of conflict relationships and a corresponding conflict degree-based CRP is proposed to govern the conflict performance of DMs for LSDM problems. Intuitionistic fuzzy sets (IFSs)[Ata12] is considered as the representation of assessment information in the studies of the proposed clustering methods and LSDM models. This thesis consists of two main parts: the first one illustrates the existing problems, the basic concepts, and models, and the results obtained from the proposed clustering algorithms and LSDM models. The second part is a compilation of the main publications that are associated with this thesis. The rest of the thesis is organized as follows: Section 2 provides some related preliminaries used throughout this contribution. The basic ideas and the challenges that justify the development of this thesis are discussed in Section 3. Section 4 introduces the objectives of this thesis. Section 5 presents the methodologies used in this thesis. Section 6 summaries the proposals included in this thesis. Section 7 presents a discussion of the results obtained from this thesis. Some conclusions and remarks are drawn in Section 8, and Section 9 draws some future works.