Linguistic Decision Making: Numerical Scale Model and Consistency-Driven Methodology

1 Introduction 1.1 Computing with words in decision making 1.2 Linguistic symbolic computational models 1.2.1 The 2-tuple linguistic model 1.2.2 The proportional 2-tuple linguistic model 1.2.3 Linguistic hierarchy 1.2.4 Hesitant linguistic term set 1.3 A core problem in linguistic decision making References 2 Numerical scale model 2.1 Numerical scale 2.1.1 The definition of numerical scale 2.1.2 Interval numerical scale 2.2 Linguistic computational model 2.2.1 Linguistic computational framework 2.2.2 Linguistic aggregation 2.2.3 Illustrative example 2.3 Setting the interval numerical scale based on IT2 FSs 2.3.1 Generalizing the Wang and Hao model 2.3.2 Comparative study References 3 A unified framework 3.1 Connecting numerical scale model to linguistic hierarchy 3.1.1 Definition of unbalanced linguistic term sets 3.1.2 The revised retranslation process in linguistic hierarchy 3.1.3 Equivalence between numerical scale model and linguistic hierarchy 3.2 Hesitant unbalanced linguistic information 3.2.1 Possibility degree formulas 3.2.2 Unbalanced hesitant linguistic aggregation References 4 Consistency of interval-like reciprocal preference relations 4.1 Consistency of interval-valued reciprocal preference relations 4.1.1 Interval-valued reciprocal preference relations 4.1.2 Average-case consistency measure 4.1.3 Average-case consistency improving method 4.2 Consistency of hesitant linguistic preference relations 4.2.1 Hesitant linguistic preference relations 4.2.2 Interval consistency measure 4.2.3 Interval consistency measure VS Normalization method 4.2.4 Connection among ICI, NCI, and ACI References 5 Consistency-driven methodology 5.1 Personalized individual semantics in linguistic term sets 5.1.1 Consistency-driven methodology to set personalized interval numerical scales 5.1.2 A CWW framework with PISs 5.2 Personalized individual semantics in hesitant linguistic contexts 5.2.1 Personalizing hesitant individual semantics 5.2.2 Numerical examples and analysis 5.2.3 Discussion: Advantages and limitations References 6 Applications in various decision problems 6.1 The analytic hierarchy process 6.1.1 Basic knowledge 6.1.2 The framework of the AHP with PISs 6.1.3 Consistency-driven methodology to deal with PISs 6.1.4 Personalized AHP interval numerical scales 6.2 Consensus model in linguistic GDM problem 6.2.1 A GDM framework with PISs 6.2.2 Consensus reaching process 6.3 MAGDM with linguistic preference information on alternatives 6.3.1 MAGDM with numerical preference information 6.3.2 A PIS based MAGDM framework 6.3.3 Obtaining the individual numerical scales with PISs 6.3.4 Numerical and simulation analysis References