scholarly journals MANAGING CONSENSUS BY MULTI-STAGE OPTIMIZATION MODELS WITH LINGUISTIC PREFERENCE ORDERINGS AND DOUBLE HIERARCHY LINGUISTIC PREFERENCES

2020 ◽  
Vol 26 (3) ◽  
pp. 642-674 ◽  
Author(s):  
Xunjie Gou ◽  
Zeshui Xu ◽  
Wei Zhou
Keyword(s):  
Decision Making ◽  
Preference Relation ◽  
Preference Ordering ◽  
Multi Stage ◽  
Continuous Scale ◽  
Decision Making Problem ◽  
Linguistic Preference Relation ◽  
Precise Relationship ◽  
Consensus Optimization ◽  
Novel Concept

Preference ordering structures are useful and popular tools to represent experts’ preferences in the decision making process. In the existing preference orderings, they lack the research on the precise relationship between any two adjacent alternatives in the preference orderings, and the decision making methods are unreasonable. To overcome these issues, this paper establishes a novel concept of linguistic preference ordering (LPO) in which the ordering of alternatives and the relationships between two adjacent alternatives should be fused well, and develops two transformation models to transform each LPO into the corresponding double hierarchy linguistic preference relation with complete consistency. Additionally, to fully respect the experts’ expression habits and provide more refined solutions to experts, this paper establishes a multi-stage consensus optimization model by considering the suggested preferences represented in both the continuous scale and the discrete scale, and develops a multi-stage interactive consensus reaching algorithm to deal with multi-expert decision making problem with LPOs. Furthermore, some numerical examples are presented to illustrate the developed methods and models. Finally, some comparative analyses between the proposed methods and models and some existing methods have been made to show the advantages of the proposed methods and models.

Expected consistency-based model and multiplicative DEA cross-efficiency for group decision-making with incomplete distribution linguistic preference relations

2021 ◽  
pp. 1-21
Author(s):  
Jinpei Liu ◽  
Longlong Shao ◽  
Ligang Zhou ◽  
Feifei Jin
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Optimization Model ◽  
Group Decision ◽  
Preference Relation ◽  
Preference Relations ◽  
Priority Vector ◽  
Linguistic Preference Relation ◽  
Multiplicative Preference Relations ◽  
High Consistency

Faced with complex decision problems, Distribution linguistic preference relation (DLPR) is an effective way for decision-makers (DMs) to express preference information. However, due to the complexity of the decision-making environment, DMs may not be able to provide complete linguistic distribution for all linguistic terms in DLPRs, which results in incomplete DLPRs. Therefore, in order to solve group decision-making (GDM) with incomplete DLPRs, this paper proposes expected consistency-based model and multiplicative DEA cross-efficiency. For a given incomplete DLPRs, we first propose an optimization model to obtain complete DLPR. This optimization model can evaluate the missing linguistic distribution and ensure that the obtained DLPR has a high consistency level. And then, we develop a transformation function that can transform DLPRs into multiplicative preference relations (MPRs). Furthermore, we design an improved multiplicative DEA model to obtain the priority vector of MPR for ranking all alternatives. Finally, a numerical example is provided to show the rationality and applicability of the proposed GDM method.

scholarly journals A Multicriteria Decision-Making Approach Based on Fuzzy AHP with Intuitionistic 2-Tuple Linguistic Sets

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Shahzad Faizi ◽  
Tabasam Rashid ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Ahp ◽  
Preference Relation ◽  
Multicriteria Decision Making ◽  
Transformation Mechanism ◽  
Analytic Hierarchy ◽  
Multicriteria Decision ◽  
Linguistic Representation ◽  
Representation Model ◽  
Linguistic Preference Relation

In the modern literature related to linguistic decision-making, the 2-tuple linguistic representation model and its useful applications in various fields have been extensively studied and used during the last decade. Recently, some useful multicriteria decision-making (MCDM) methods have been introduced based on fuzzy analytic hierarchy process (AHP) for 2-tuple linguistic representation model. By keeping in mind the importance of this linguistic model, in this paper, we introduce a fuzzy AHP methodology for intuitionistic 2-tuple linguistic sets (I2TLSs) which is a useful extension of the 2-tuple linguistic representation model. This study is comprised of four stages. In the first stage, we define some operational laws for I2TL elements (I2TLEs) and prove some related important properties. In the second stage, intuitionistic 2-tuple linguistic preference relation (I2TLPR) and multiplicative I2TLPR are defined using I2TLSs. In the 3rd stage, a transformation mechanism is introduced which can transform an I2TLPR to a corresponding intuitionistic preference relation (IPR) and vice versa. In the fourth stage, an approach is proposed for checking the consistency of an I2TLPR and presented a method to repair the inconsistent one by using the proposed transformation mechanism. Finally, a numerical example is given and comparative analysis is carried out with the TOPSIS method to verify the validity of the proposed method.

An approach to hesitant fuzzy multi-stage multi-criterion decision making

Kybernetes ◽  
2014 ◽  
Vol 43 (9/10) ◽  
pp. 1447-1468 ◽  
Author(s):  
Huchang Liao ◽  
Zeshui Xu ◽  
Jiuping Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Variable ◽  
Entropy Method ◽  
Aggregation Operators ◽  
Average Deviation ◽  
Content Type ◽  
Preference Information ◽  
Multi Stage ◽  
Fuzzy Aggregation ◽  
Decision Making Problem

Purpose – The purpose of this paper is to develop some weight determining methods for hesitant fuzzy multi-criterion decision making (MCDM) in which the preference information on attributes is collected over different periods. Design/methodology/approach – Based on the proposed weight determining methods and dynamic hesitant fuzzy aggregation operators, an approach is developed to solve the hesitant fuzzy multi-stage multi-attribute decision-making problem where all the preference information of attributes over different periods is represented in hesitant fuzzy values. Findings – In order to determine the weights associated with dynamic hesitant fuzzy operators, the authors propose the improved maximum entropy method and the minimum average deviation method. Research limitations/implications – This paper does not consider the multi-stage multi-criteria group decision-making problem. Practical implications – An example concerning the evaluation of rangelands is given to illustrate the validation and efficiency of the proposed approach. It should be stated that the proposed approach can also be implemented into other multi-stage MCDM problems. Originality/value – The concept of hesitant fuzzy variable (HFV) is defined. Some operational laws and properties of the HFVs are given. Moreover, to fuse the multi-stage hesitant fuzzy information, the aggregation operators of hesitant fuzzy sets are extended to that of the HFVs.

AN APPROACH TO GROUP DECISION MAKING BASED ON INCOMPLETE LINGUISTIC PREFERENCE RELATIONS

2005 ◽  
Vol 04 (01) ◽  
pp. 153-160 ◽  
Author(s):  
ZESHUI XU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Linguistic Variables ◽  
Preference Relations ◽  
Weighted Arithmetic ◽  
Operational Laws ◽  
Linguistic Preference Relation

In this paper, we introduce some operational laws of linguistic variables and define some linguistic preference relations such as incomplete linguistic preference relation and improved linguistic preference relation, etc. We then utilize the extended arithmetic averaging (EAA) operator and the extended weighted arithmetic averaging (EWAA) operator to develop an approach to group decision making based on incomplete linguistic preference relations. Finally, we give an illustrative example to verify the developed approach.

EOWA AND EOWG OPERATORS FOR AGGREGATING LINGUISTIC LABELS BASED ON LINGUISTIC PREFERENCE RELATIONS

2004 ◽  
Vol 12 (06) ◽  
pp. 791-810 ◽  
Author(s):  
Z. S. XU
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Geometric Mean ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Ordered Weighted Averaging ◽  
Linguistic Preference Relation ◽  
Linguistic Labels

In this paper, we define two types of linguistic preference relations (multiplicative linguistic preference relation and additive linguistic preference relation), and study some of their desirable properties. We introduce the extended geometric mean (EGM) operator, extended arithmetical averaging (EAA) operator, extended ordered weighted averaging (EOWA) operator and extended ordered weighted geometric (EOWG) operator. An approach based on the EGM and EOWG operators and multiplicative linguistic preference relations and an approach based on the EAA and EOWA operators and additive linguistic preference relations are proposed to ranking the alternatives in the group decision-making problems. Finally, we give a numerical example to illustrate the developed approaches.

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