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 Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-24 ◽  
Author(s):  
Zia Bashir ◽  
Tabasam Rashid ◽  
Mobashir Iqbal
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Decision Makers ◽  
Decision Support Model ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Fuzzy Preference

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

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.

scholarly journals PROBABILITY-HESITANT FUZZY SETS AND THE REPRESENTATION OF PREFERENCE RELATIONS

2018 ◽  
Vol 24 (3) ◽  
pp. 1029-1040 ◽  
Author(s):  
Bin ZHU ◽  
Zeshui XU
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Preference Relation ◽  
Decision Makers ◽  
Stochastic Method ◽  
Hesitant Fuzzy Sets ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Hesitant Fuzzy Preference Relation ◽  
Consensus Index

Probability interpretations play an important role in understanding decision makers’ (DMs) behaviour in decision making. In this paper, we extend hesitant fuzzy sets to probability-hesitant fuzzy sets (P-HFSs) to enhance their modeling ability by taking DMs’ probabilistic preferences into consideration. Based on P-HFSs, we propose the concept of probability-hesitant fuzzy preference relation (P-HFPR) to collect the preferences. We then develop a consensus index to measure the consensus degrees of P-HFPR, and a stochastic method to improve the consensus degrees. All these results are essential for further research on P-HFSs.

scholarly journals Additively Consistent Interval-Valued Intuitionistic Fuzzy Preference Relations and Their Application to Group Decision Making

Information ◽  
2018 ◽  
Vol 9 (10) ◽  
pp. 260 ◽  
Author(s):  
Hua Zhuang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Weighted Averaging ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Priority Weights ◽  
Interval Valued ◽  
Fuzzy Preference

This paper aims to propose an innovative approach to group decision making (GDM) with interval-valued intuitionistic fuzzy (IVIF) preference relations (IVIFPRs). First, an IVIFPR is proposed based on the additive consistency of an interval-valued fuzzy preference relation (IVFPR). Then, two mathematical or adjusted programming models are established to extract two special consistent IVFPRs. In order to derive the priority weight of an IVIFPR, after taking the two special IVFPRs into consideration, a linear optimization model is constructed by minimizing the deviations between individual judgments and between the width degrees of the interval priority weights. For GDM with IVIFPRs, the decision makers’ weights are generated by combining the adjusted subjective weights with the objective weights. Subsequently, using an IVIF-weighted averaging operator, the collective IVIFPR is obtained and utilized to derive the IVIF priority weights. Finally, a practical example of a supplier selection is analyzed to demonstrate the application of the proposed method.

Decision-Making Models Based on Satisfaction Degree with Incomplete Hesitant Fuzzy Preference Relation

2021 ◽  
Author(s):  
Jian Li ◽  
Li-li Niu ◽  
Qiongxia Chen ◽  
Zhong-xing Wang
Keyword(s):  
Decision Making ◽  
Programming Model ◽  
Preference Relation ◽  
Weight Vector ◽  
Decision Makers ◽  
Fuzzy Preference Relation ◽  
Satisfaction Degree ◽  
Hesitant Fuzzy Preference Relation ◽  
Decision Making Models ◽  
Fuzzy Preference

Abstract To address the situation where the incomplete hesitant fuzzy preference relation (IHFPR) is necessary, this paper develops decision-making models based on decision makers’ satisfaction degree with IHFPR. First, the consistency measures from the perspectives of additive and multiplicative consistent IHFPR are defined based on the relationships between the IHPFRs and their corresponding priority weight vector, respectively. Second, two decision-making models are developed in view of the proposed additive and multiplicative consistency measures. The main characteristic of the constructed model sarethey taking into account the decision makers’ satisfaction degree. The objective functions of the models are developed by maximizing the parameter of satisfaction degree. Third, a square programming model is developed to obtain the decision makers’ weights byutilizing the optimal priority weight vectors information, the solution of the model is obtained by solving the partial derivatives ofLagrange function.Finally, a procedure for multi-criteria decision-making (MCDM) problems with IHFPRs is given, and an illustrative example in conjunction with comparative analysis is used to demonstrate the proposed models are feasible and efficiency for practical MCDM problems.

ON COMPATIBILITY OF UNCERTAIN MULTIPLICATIVE LINGUISTIC PREFERENCE RELATIONS AND ITS APPLICATION TO GROUP DECISION MAKING

2013 ◽  
Vol 21 (01) ◽  
pp. 9-28 ◽  
Author(s):  
LIGANG ZHOU ◽  
HUAYOU CHEN
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Scientific Basis ◽  
Decision Makers ◽  
Preference Relations ◽  
Compatibility Index ◽  
Optimal Weights ◽  
Linguistic Preference Relation

The aim of this work is to develop a new compatibility for the uncertain multiplicative linguistic preference relations and determine the optimal weights of decision makers (DMs), which are very suitable to deal with group decision making (GDM) problems involving uncertain multiplicative linguistic preference relations. First, the concepts of compatibility degree and compatibility index for the two uncertain multiplicative linguistic preference relations are proposed. Then we prove the property that the synthetic uncertain linguistic preference relation is of acceptable compatibility under the condition that uncertain multiplicative linguistic preference relations given by DMs are all of acceptable compatibility with a specific linguistic preference relation, which is the scientific basis of using the uncertain multiplicative linguistic preference relations in the GDM. Next, in order to determine the weights of decision makers, we construct an optimal model based on the criterion of minimizing the compatibility index. Finally, we develop an application of the optimal weights approach compared with the equal weights approach where we analyze a GDM regarding the selection of investment.

scholarly journals An Optimization-Based Approach to Social Network Group Decision Making with an Application to Earthquake Shelter-Site Selection

2019 ◽  
Vol 16 (15) ◽  
pp. 2740 ◽  
Author(s):  
Zhang ◽  
Wang ◽  
Tang ◽  
Dong
Keyword(s):  
Decision Making ◽  
Social Network ◽  
Group Decision Making ◽  
Social Trust ◽  
Group Decision ◽  
Preference Relation ◽  
Decision Makers ◽  
Preference Relations ◽  
Shelter Site ◽  
The Social

The social network has emerged as an essential component in group decision making (GDM) problems. Thus, this paper investigates the social network GDM (SNGDM) problem and assumes that decision makers offer their preferences utilizing additive preference relations (also called fuzzy preference relations). An optimization-based approach is devised to generate the weights of decision makers by combining two reliable resources: in-degree centrality indexes and consistency indexes. Based on the obtained weights of decision makers, the individual additive preference relations are aggregated into a collective additive preference relation. Further, the alternatives are ranked from best to worst according to the obtained collective additive preference relation. Moreover, earthquakes have occurred frequently around the world in recent years, causing great loss of life and property. Earthquake shelters offer safety, security, climate protection, and resistance to disease and ill health and are thus vital for disaster-affected people. Selection of a suitable site for locating shelters from potential alternatives is of critical importance, which can be seen as a GDM problem. When selecting a suitable earthquake shelter-site, the social trust relationships among disaster management experts should not be ignored. To this end, the proposed SNGDM model is applied to evaluate and select earthquake shelter-sites to show its effectiveness. In summary, this paper constructs a novel GDM framework by taking the social trust relationship into account, which can provide a scientific basis for public emergency management in the major disasters field.

MULTIPLICATIVE CONSISTENCY OF HESITANT FUZZY PREFERENCE RELATION AND ITS APPLICATION IN GROUP DECISION MAKING

2014 ◽  
Vol 13 (01) ◽  
pp. 47-76 ◽  
Author(s):  
HUCHANG LIAO ◽  
ZESHUI XU ◽  
MEIMEI XIA
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Aggregation Operators ◽  
Fuzzy Preference Relation ◽  
Multiplicative Consistency ◽  
Hesitant Fuzzy Preference Relation ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the multiplicative consistency of the hesitant fuzzy preference relation. First of all, we explore some properties of the hesitant fuzzy preference relation and develop some new aggregation operators. Then we introduce the concepts of multiplicative consistency, perfect multiplicative consistency and acceptable multiplicative consistency for a hesitant fuzzy preference relation, based on which, two algorithms are given to improve the inconsistency level of a hesitant fuzzy preference relation. Furthermore, the consensus of group decision making is studied based on the hesitant fuzzy preference relations. Finally, several illustrative examples are given to demonstrate the practicality of our algorithms.

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