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

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.

Consistency Checking and Improving for Interval-Valued Hesitant Preference Relations

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.

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

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.

PROBABILITY-HESITANT FUZZY SETS AND THE REPRESENTATION OF PREFERENCE RELATIONS

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.

Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

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.