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 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.

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.

scholarly journals A New Model for Deriving the Priority Weights from Hesitant Triangular Fuzzy Preference Relations

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yuan Liu ◽  
Gongtian Shen ◽  
Zhangyan Zhao ◽  
Zhanwen Wu
Keyword(s):  
Fuzzy Set ◽  
Failure Modes ◽  
Preference Relation ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Preference Relation ◽  
New Model ◽  
Hesitant Fuzzy Preference Relation ◽  
Priority Weights ◽  
Hesitant Triangular Fuzzy Set ◽  
Fuzzy Preference

Fuzzy preference relation is a common tool to express the uncertain preference information of decision maker in the process of decision making. However, the traditional fuzzy preference relation will fail under hesitant fuzzy environment as the membership has a single value. In addition, it is very difficult to obtain the precise membership values. Therefore, a new model of fuzzy preference relation is proposed in this paper. Firstly, the concept of hesitant triangular fuzzy preference relation is defined and its properties are investigated based on the concepts of hesitant fuzzy set, hesitant triangular fuzzy set, fuzzy preference relation, and hesitant fuzzy preference relation. Then, the steps of applying this novel model are offered for the case of determining the weights of failure modes. Finally, an example is used to illustrate the proposed model.

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 Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 185 ◽  
Author(s):  
Atiq-ur Rehman ◽  
Mustanser Hussain ◽  
Adeel Farooq ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Preference Relation ◽  
Selection Procedure ◽  
Feedback Mechanism ◽  
Decision Makers ◽  
Consensus Process ◽  
Preference Relations ◽  
Priority Weights ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

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