Improving the consistency of incomplete hesitant multiplicative preference relation

OPSEARCH ◽  
2019 ◽  
Vol 56 (1) ◽  
pp. 324-343 ◽  
Author(s):  
Mamata Sahu ◽  
Anjana Gupta
Keyword(s):  
Preference Relation ◽  
Hesitant Multiplicative Preference Relation

scholarly journals Consistency Checking and Improving for Interval-Valued Hesitant Preference Relations

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 466
Author(s):  
Yuling Zhai ◽  
Zeshui Xu
Keyword(s):  
Group Decision ◽  
Preference Relation ◽  
Decision Makers ◽  
Optimal Decision ◽  
Consistency Checking ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Hesitant Multiplicative Preference Relation ◽  
Interval Valued

Group decision making (GDM), which aims to obtain a sensible decision result with several decision makers, is a common occurrence in daily life. Since the uncertainty of the objects is a thorny issue in the process of GDM, it is important to eliminate uncertainty in order to achieve an optimal decision result. Considerations of some types of preference relations based on various fuzzy sets have been presented and investigated in previous studies; in this paper, we define the interval-valued hesitant multiplicative preference relation (IVHMPR) and the multiplicative consistency of IVHMPR. Based on these, we provide a detailed discussion on the connections between the interval-valued hesitant fuzzy preference relation (IVHFPR) and the IVHMPR. Then, we give a method to check the for unacceptable consistency of IVHFPR and IVHMPR, and improve them to make the consistency acceptable. Finally, an illustrative example of selecting the optimal treatment for a lung cancer patient is given to demonstrate our work in detail.

scholarly journals Two Hesitant Multiplicative Decision-Making Algorithms and Their Application to Fog-Haze Factor Assessment Problem

Algorithms ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 154 ◽  
Author(s):  
Lidan Pei ◽  
Feifei Jin
Keyword(s):  
Decision Making ◽  
Preference Relation ◽  
Linear Optimization ◽  
Iterative Algorithms ◽  
Weight Vector ◽  
Factors Affecting ◽  
Linear Optimization Model ◽  
New Concepts ◽  
Priority Weights ◽  
Hesitant Multiplicative Preference Relation

Hesitant multiplicative preference relation (HMPR) is a useful tool to cope with the problems in which the experts utilize Saaty’s 1–9 scale to express their preference information over paired comparisons of alternatives. It is known that the lack of acceptable consistency easily leads to inconsistent conclusions, therefore consistency improvement processes and deriving the reliable priority weight vector for alternatives are two significant and challenging issues for hesitant multiplicative information decision-making problems. In this paper, some new concepts are first introduced, including HMPR, consistent HMPR and the consistency index of HMPR. Then, based on the logarithmic least squares model and linear optimization model, two novel automatic iterative algorithms are proposed to enhance the consistency of HMPR and generate the priority weights of HMPR, which are proved to be convergent. In the end, the proposed algorithms are applied to the factors affecting selection of fog-haze weather. The comparative analysis shows that the decision-making process in our algorithms would be more straight-forward and efficient.

MANAGING HESITANT INFORMATION IN GDM PROBLEMS UNDER FUZZY AND MULTIPLICATIVE PREFERENCE RELATIONS

2013 ◽  
Vol 21 (06) ◽  
pp. 865-897 ◽  
Author(s):  
MEIMEI XIA ◽  
ZESHUI XU
Keyword(s):  
Preference Relation ◽  
Decision Makers ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Hesitant Multiplicative Preference Relation ◽  
Multiplicative Preference Relations ◽  
Common Situation ◽  
Fuzzy Preference

In the process of group decision making (GDM), preference relations (e.g. fuzzy preference relation and multiplicative preference relation) are very popular tools to express decision makers' preferences, especially when a set of alternatives (or criteria) are compared. However, most of the existing preference relations don't consider the hesitancy information, which allows the decision makers to provide all the possible values when comparing two alternatives (or criteria), and is a common situation in daily life. In this paper, we first define the concept of hesitant fuzzy preference relation and study its properties, based on which we give an approach to GDM. Motivated by the multiplicative preference relation and the hesitant fuzzy set, we introduce the hesitant multiplicative set and develop a series of hesitant multiplicative aggregation operators. Hesitant multiplicative preference relation is also defined to provide decision makers a very useful tool to express their hesitant preferences over alternatives, and then is applied to GDM. Additionally, an example is given to illustrate our results.

Model and Method for Contributor’s Quality Assessment in Community Image Tagging Systems

2018 ◽  
pp. 45-51
Author(s):  
A. V. Ponomarev
Keyword(s):  
Large Scale ◽  
Wide Spectrum ◽  
Preference Relation ◽  
Pairwise Comparison ◽  
Ground Truth ◽  
Comparison Method ◽  
Characteristic Matrix ◽  
Image Tagging ◽  
Proposed Model

Introduction: Large-scale human-computer systems involving people of various skills and motivation into the information processing process are currently used in a wide spectrum of applications. An acute problem in such systems is assessing the expected quality of each contributor; for example, in order to penalize incompetent or inaccurate ones and to promote diligent ones.Purpose: To develop a method of assessing the expected contributor’s quality in community tagging systems. This method should only use generally unreliable and incomplete information provided by contributors (with ground truth tags unknown).Results:A mathematical model is proposed for community image tagging (including the model of a contributor), along with a method of assessing the expected contributor’s quality. The method is based on comparing tag sets provided by different contributors for the same images, being a modification of pairwise comparison method with preference relation replaced by a special domination characteristic. Expected contributors’ quality is evaluated as a positive eigenvector of a pairwise domination characteristic matrix. Community tagging simulation has confirmed that the proposed method allows you to adequately estimate the expected quality of community tagging system contributors (provided that the contributors' behavior fits the proposed model).Practical relevance: The obtained results can be used in the development of systems based on coordinated efforts of community (primarily, community tagging systems). 

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.

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