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.

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.

scholarly journals Compatibility measurement-based group decision making with interval fuzzy preference relations

2016 ◽  
Vol 11 (1) ◽  
pp. 31-39
Author(s):  
Xue-Yang Zhang ◽  
Zhou J Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Fuzzy Preference Relation ◽  
Interval Numbers ◽  
Preference Relations ◽  
Interval Fuzzy Preference Relation ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In this paper, we put forward a ratio-based compatibility degree between any two ]0,1[-valued interval numbers to measure how proximate they approach to each other. A compatibility measurement is presented to evaluate the compatibility degree between a pair of ]0,1[-valued interval fuzzy preference relations (IFPRs). By employing the geometric mean, a measurement formula is proposed to calculate how close one interval fuzzy preference relation is to all the other interval fuzzy preference relations in a group. We devise an induced interval fuzzy ordered weighted geometric (IIFOWG) operator to aggregate ]0,1[-valued interval numbers, and apply the induced interval fuzzy ordered weighted geometric operator to fuse interval fuzzy preference relations into a collective one. Based on the compatibility measurement between two interval fuzzy preference relations, a notion of acceptable consensus of interval fuzzy preference relations is introduced to check the consensus level between an individual interval fuzzy preference relation and a collective interval fuzzy preference relation, and a novel procedure is developed to handle group decision-making problems with interval fuzzy preference relations. A numerical example with respect to the evaluation of e-commerce websites is provided to illustrate the proposed procedure.

scholarly journals Geometric Least Square Models for Deriving[0,1]-Valued Interval Weights from Interval Fuzzy Preference Relations Based on Multiplicative Transitivity

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Xuan Yang ◽  
Zhou-Jing Wang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Least Square ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Interval Fuzzy Preference Relation ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

This paper presents a geometric least square framework for deriving[0,1]-valued interval weights from interval fuzzy preference relations. By analyzing the relationship among[0,1]-valued interval weights, multiplicatively consistent interval judgments, and planes, a geometric least square model is developed to derive a normalized[0,1]-valued interval weight vector from an interval fuzzy preference relation. Based on the difference ratio between two interval fuzzy preference relations, a geometric average difference ratio between one interval fuzzy preference relation and the others is defined and employed to determine the relative importance weights for individual interval fuzzy preference relations. A geometric least square based approach is further put forward for solving group decision making problems. An individual decision numerical example and a group decision making problem with the selection of enterprise resource planning software products are furnished to illustrate the effectiveness and applicability of the proposed models.

A Large Group Decision-Making Method Based on Fuzzy Preference Relation

2017 ◽  
Vol 16 (03) ◽  
pp. 881-897 ◽  
Author(s):  
Shenghai Zhou ◽  
Xuanhua Xu ◽  
Yanju Zhou ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Decision Maker ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Fuzzy Preference Relation ◽  
Preference Relations ◽  
Large Group ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

Aiming at the large group decision-making problem in which every decision maker compares pairwise alternatives with fuzzy preference relations, this paper proposes a fuzzy preference relation decision-making method of large group based on conflicts. Firstly, priority should be given to the preference difference under complex large group environment, so we define the conflict degree of two fuzzy preference relations, which contributes to cluster analysis on preferences of the decision maker and thus forms several different clusters. Based on this, we simulate and analyze the threshold of conflict degree. Then we develop the entropy weight method to get the relevant weight of each cluster, and use the weight to aggregate the cluster preferences in order to attain the large group preference based on fuzzy preference relation. Next, an iteration algorithm is introduced to find a solution which could acquire the group alternatives fuzzy preference relation of a certain conflict level and obtain the ranking result of alternatives. Finally, a case analysis is given to illustrate the effectiveness of the method proposed.

A novel group decision making method for interval-valued pythagorean fuzzy preference relations

2021 ◽  
pp. 1-23
Author(s):  
Ziyu Yang ◽  
Liyuan Zhang ◽  
Tao Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Programming Model ◽  
Preference Relation ◽  
Uncertain Information ◽  
Multiplicative Consistency ◽  
Priority Weights ◽  
Interval Valued ◽  
Fuzzy Preference

Interval-valued Pythagorean fuzzy preference relation (IVPFPR) plays an important role in representing the complex and uncertain information. The application of IVPFPRs gives better solutions in group decision making (GDM). In this paper, we investigate a new method to solve GDM problems with IVPFPRs. Firstly, novel multiplicative consistency and consensus measures are proposed. Subsequently, the procedure for improving consistency and consensus levels are put forward to ensure that every individual IVPFPR is of acceptable multiplicative consistency and consensus simultaneously. In the context of minimizing the deviations between the individual and collective IVPFPRs, the objective experts’ weights are decided according to the optimization model and the aggregated IVPFPR is derived. Afterwards, a programming model is built to derive the normalized Pythagorean fuzzy priority weights, then the priority weights of alternatives are identified as well. An algorithm for GDM method with IVPFPRs is completed. Finally, an example is cited and comparative analyses with previous approaches are conducted to illustrate the applicability and effectiveness of the proposed method.

scholarly journals An Algorithm for Interval-Valued Intuitionistic Fuzzy Preference Relations in Group Decision Making Based on Acceptability Measurement and Priority Weight Determination

Algorithms ◽  
2018 ◽  
Vol 11 (11) ◽  
pp. 182
Author(s):  
Hua Zhuang ◽  
Yanzhao Tang ◽  
Meijuan Li
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Weighted Averaging ◽  
Consistency Index ◽  
Multiplicative Consistency ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Fuzzy Preference

Group decision making with intuitionistic fuzzy preference information contains two key issues: acceptability measurement and priority weight determination. In this paper, we investigate the above two issues with respect to multiplicative interval-valued intuitionistic fuzzy preference relation (IVIFPR). Firstly, a consistency index is defined to measure the multiplicative consistency degree of IVIFPR and an optimization model is established to improve the consistency degree of IVIFPR to an acceptable one. Next, in terms of priority weight determination, an error-analysis-based extension method is proposed to obtain priority weight vector from the acceptable IVIFPR. For GDM problems, decision makers’ weights are derived by the proposed multiplicative consistency index. Subsequently, the collective IVIFPR is obtained by using an interval-valued intuitionistic fuzzy (IVIF) weighted averaging operator. Finally, a step-by step algorithm for GDM with IVIFPRs is given, and an example of enterprise innovation partner selection is analyzed, and comparative analyses with existing approaches are performed to demonstrate that the proposed algorithm is both effective and practical in dealing with GDM problems.

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