Resumen de Double hierarchy linguistic preference information: consistency, consensus and large-scale group decision making
Xunjie Gou
Group decision making (GDM) refers to inviting a group of experts to evaluate, prioritize or select the optimal one among some available alternatives in actual decision making process. During GDM, linguistic information is more in line with the real thoughts of experts. Motivated by Computing with Words (CW), in recent years, lots of linguistic models were developed to represent complex linguistic information. Additionally, most of linguistic models can be used to express some simple linguistic information by one hierarchy linguistic label. However, because of people’s cognition process and the decision making information are more and more complex, sometimes these linguistic models cannot describe some complex linguistic terms or linguistic term sets (LTSs) comprehensively and accurately. Therefore, a concept of double hierarchy linguistic term set (DHLTS) is proposed by adding a second hierarchy LTS to each linguistic term in the first hierarchy LTS, which can be used to handle complex linguistic terms well by dividing them into two simple linguistic hierarchies where the first hierarchy LTS is the main linguistic hierarchy and the second hierarchy LTS is the linguistic feature or detailed supplementary of each linguistic term in the first hierarchy LTS. In addition, the extension of DHLTS in hesitant fuzzy environment named double hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is developed to express uncertain complex linguistic information.
In this thesis, we focus on the discussions about three main aspects.
Firstly, we mainly analyze the basic concepts of DHLTS and DHHFLTS, propose some equivalent transformation functions, and then develop some operations and properties of DHHFLTSs. In addition, considering that the distance and similarity measures are fundamentally important in amounts of research fields, we define the axioms of distance and similarity measures between two DHHFLTSs, and then introduce a series of distance and similarity measures between two DHHFLTSs.
Secondly, considering that more and more experts prefer to give their preferences by making pairwise comparisons between any two alternatives, meanwhile this kind of preference reflects the relationships between different alternatives intuitively. Therefore, preference relation becomes one of the popular and effective tools. Based on the DHHFLTS and preference form, we give a concept of double hierarchy hesitant fuzzy linguistic preference relation (DHHFLPR). Then, to avoid the occurrence of some self-contradictory situations, it is very important to carry out the consistency checking and improving process for each DHHFLPR in GDM process. Therefore, we discuss some additive consistency measures for DHHFLPRs. For the purpose of judging whether a DHHFLPR is of acceptable consistency or not, we define a consistency index of DHHFLPR and develop a novel method to improve the existing methods for calculating the consistency thresholds. Then we present two convergent consistency repairing algorithms based on automatic improving method and feedback improving method respectively to improve the consistency index of a given DHHFLPR with unacceptable consistency.
Finally, with the progress of science and technology and the development of network environment, the communications between people are increasingly convenient. Large-scale group decision making (LSGDM) has become the focuses of decision-making problems. Generally, a GDM problem can be called LSGDM problem when the number of experts is more than 20 [LC06]. This thesis mainly studies LSGDM from two aspects. 1) We discuss the clustering method and the consensus reaching process in LSGDM with double hierarchy hesitant fuzzy linguistic preference information. We also propose the similarity degree-based clustering method, the double hierarchy information entropy-based weights-determining method and the consensus measures. 2) In LSGDM, sometimes some experts do not modify their preferences or even do it on the contrary way to the remaining experts, and some different opinions or minority preferences are often cited as obstacles to decision making [PMH14, XDC15]. Therefore, this thesis gives a concept of double hierarchy linguistic preference relation (DHLPR) and develops a consensus model to manage minority opinions and non-cooperative behaviors in LSGDM with DHLPRs. Additionally, to establish the consensus model, some basic tools such as the distance-based cluster method, the weight-determining method, and the comprehensive adjustment coefficient-determining method are developed.
In addition to the discussions of the core knowledge of DHLTS, DHHFLTS, DHLPR and DHHFLPR, this thesis discusses some different decision making models under different decision making contexts. We mainly discuss three different decision making contexts, i.e., multiple criteria decision making (MCDM), GDM, and LSCDM.
All in all, 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 models. The second part is a compilation of the main publications that are associated with this thesis. The rest of this thesis are 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 introduces the objectives of this thesis. Section 5 presents the methodologies used in this thesis. a summary of the proposals included in this thesis is presented in Section 6. Section 7 presents a discussion of the results obtained in this thesis. Section 8 discusses the conclusion of this thesis. Finally, some future works are discussed in Section 9.
