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.

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 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.

Some Algorithms for Group Decision Making with Intuitionistic Fuzzy Preference Information

2014 ◽  
Vol 22 (04) ◽  
pp. 505-529 ◽  
Author(s):  
Huchang Liao ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Preference Relation ◽  
Decision Makers ◽  
Fuzzy Preference Relation ◽  
Preference Information ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Preference Relation ◽  
Fuzzy Preference

Intuitionistic fuzzy preference relation has turned out to be a powerful structure in representing the decision makers' preference information especially when the decision makers are not able to express their preferences accurately due to the unquantifiable information, incomplete information, unobtainable information, partial ignorance, and so forth. The aim of this paper is to develop some techniques for group decision making with intuitionistic fuzzy preference information. Based on the multiplicative consistency of intuitionistic fuzzy preference relation, three algorithms are proposed for intuitionistic fuzzy group decision making. In the case that the decision makers act as separate individuals, the priority vector of each decision maker can be derived directly from the individual intuitionistic fuzzy preference relation, after which an overall priority vector is obtained by synthesizing those individual priorities together. As for the scenario that the decision makers act as one individual, two different algorithms based on the multiplicative consistency are proposed to deal with this case. The main idea of the former procedure is firstly constructing a social intuitionistic fuzzy preference relation, while that of the later is building a fractional programming model. Some practical examples are given to demonstrate the developed algorithms.

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.

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.

Sign in / Sign up

Export Citation Format

Share Document