Cong-Cong Li

Personalized individual semantics in computing with words for supporting linguistic group decision making. An application on consensus reaching

To propose a personalized individual semantics model (PIS).To propose personalized 2-tuple linguistic comparison and aggregation.To discuss the application of PIS to support linguistic consensus reaching. In group decision making (GDM) dealing with Computing with Words (CW) has been highlighted the importance of the statement, words mean different things for different people, because of its influence in the final decision. Different proposals that either grouping such different meanings (uncertainty) to provide one representation for all people or use multi-granular linguistic term sets with the semantics of each granularity, have been developed and applied in the specialized literature. Despite these models are quite useful they do not model individually yet the different meanings of each person when he/she elicits linguistic information. Hence, in this paper a personalized individual semantics (PIS) model is proposed to personalize individual semantics by means of an interval numerical scale and the 2-tuple linguistic model. Specifically, a consistency-driven optimization-based model to obtain and represent the PIS is introduced. A new CW framework based on the 2-tuple linguistic model is then defined, such a CW framework allows us to deal with PIS to facilitate CW keeping the idea that words mean different things to different people. In order to justify the feasibility and validity of the PIS model, it is applied to solve linguistic GDM problems with a consensus reaching process.

Connecting the linguistic hierarchy and the numerical scale for the 2-tuple linguistic model and its use to deal with hesitant unbalanced linguistic information

The 2-tuple linguistic representation model is widely used as a basis for computing with words (CW) in linguistic decision making problems. Two different models based on linguistic 2-tuples (i.e., the model of the use of a linguistic hierarchy and the numerical scale model) have been developed to address term sets that are not uniformly and symmetrically distributed, i.e., unbalanced linguistic term sets (ULTSs). In this study, we provide a connection between these two different models and prove the equivalence of the linguistic computational models to handle ULTSs. Further, we propose a novel CW methodology where the hesitant fuzzy linguistic term sets (HFLTSs) can be constructed based on ULTSs using a numerical scale. In the proposed CW methodology, we present several novel possibility degree formulas for comparing HFLTSs, and define novel operators based on the mixed 0-1 linear programming model to aggregate the hesitant unbalanced linguistic information.

An optimization-based approach to adjusting unbalanced linguistic preference relations to obtain a required consistency level

In certain real decision-making situations, decision makers often feel more comfortable providing their knowledge and preferences in linguistic terms. Unbalanced linguistic term sets may be used in decision problems with preference relations. However, the lack of consistency in decision-making with linguistic preference relations can lead to inconsistent conclusions. Based on the consistency measure of unbalanced linguistic preference relations, this paper proposes an optimization-based approach to improving the consistency level of unbalanced linguistic preference relations. This consistency-improving model preserves the utmost original knowledge and preferences in the process of improving consistency. Furthermore, it guarantees that the elements in the optimal adjusted unbalanced linguistic preference relation are all simple unbalanced linguistic terms. Finally, we propose a mixed 0-1 linear programming aimed to obtain the optimum solution to the proposed consistency improving model and to demonstrate its practicability.

Personalized individual semantics based on consistency in hesitant linguistic group decision making with comparative linguistic expressions

Abstract In decision making problems, decision makers may prefer to use more flexible linguistic expressions instead of using only one linguistic term to express their preferences. The recent proposals of hesitant fuzzy linguistic terms sets (HFLTSs) are developed to support the elicitation of comparative linguistic expressions in hesitant decision situations. In group decision making (GDM), the statement that words mean different things for different people has been highlighted and it is natural that a word should be defined by individual semantics described by different numerical values. Considering this statement in hesitant linguistic decision making, the aim of this paper is to personalize individual semantics in the hesitant GDM with comparative linguistic expressions to show the individual difference in understanding the meaning of words. In our study, the personalized individual semantics are carried out by the fuzzy envelopes of HFLTSs based on the personalized numerical scales of linguistic term set.

Consistency of hesitant fuzzy linguistic preference relations: An interval consistency index

Abstract The study of hesitant consistency is very important in decision-making with hesitant fuzzy linguistic preference relations (HFLPRs), and generally the normalization method is used as a tool to measure the consistency degree of a HFLPR. In this paper we propose a new hesitant consistency measure, called interval consistency index, to estimate the consistency range of a HFLPR. The underlying idea of the interval consistency index consists of measuring the worst consistency index and the best consistency index of a HFLPR. Furthermore, by comparative study, a connection is shown between the interval consistency index and the normalization method, demonstrating that the normalization method should be considered as an approximate average consistency index of a HFLPR.

The fusion process of interval opinions based on the dynamic bounded confidence

We propose the interval opinion dynamics with dynamic bounded confidence.We propose some sufficient conditions to form a consensus or fragmentations.We study the prosperities of the proposed model through simulation analysis. In this paper, we propose a novel opinion dynamics model that is based on bounded confidence and termed interval opinion dynamics with the dynamic bounded confidence. In this opinion dynamics model, the agents express their opinions in numerical intervals, and the bounded confidences vary in a specified interval as time varies (i.e., dynamic bounded confidence). Based on several theoretical analyses of the proposed opinion dynamics, we propose conditions that are sufficient to form a consensus or fragmentations among the agents. Moreover, we also design several simulation experiments to investigate the effects of the dynamic bounded confidence and interval widths on the proposed opinion dynamics and to illustrate the differences between the proposed model and the original opinion dynamics with bounded confidence.

Connecting the numerical scale model to the unbalanced linguistic term sets

Herrera and Martinez initiated a 2-tuple fuzzy linguistic representation model for computing with words (CWW). In addition to the Herrera and Martinez model, two different models based on linguistic 2-tuples (i.e., the model of Herrera et al. and the numerical scale model) have been developed to deal with term sets that are not uniformly and symmetrically distributed, i.e., unbalanced linguistic term sets (ULTSs). Both the model of Herrera et al. and the numerical scale model can deal with ULTSs, so a challenge is naturally proposed to analysts: how to compare these two different models. In this study, we provide a connection between the model of Herrera et al. and the numerical scale model. The results show that the model of Herrera et al. provides a new approach to set a numerical scale. Furthermore, we prove the equivalence of the linguistic computational models between the model of Herrera et al. and the numerical scale model, if the numerical scale is set based on the model of Herrera et al.

An optimization-based approach to estimate the range of consistency in hesitant fuzzy linguistic preference relations

The study of consistency is a very important problem in decision making using preference relations. This paper focuses on measuring the consistency of hesitant fuzzy linguistic preference relations (HFLPRs). In this paper we propose the optimization-based approach to estimate the range of consistency degree in a HFLPR. The underlying idea of the proposed approach consists in measuring the pessimistic consistency index (PCI) of HFLPRs, and also the optimistic consistency index (OCI) of HFLPRs. The PCI of HFLPRs is determined by its linguistic preference relation with the worst consistency degree, and the OCI of HFLPRs is determined by its linguistic preference relation with the best consistency degree. Furthermore, numerical examples are provided to show the use of the proposed consistency measure.