The Stably Multiplicative Consistency of Fuzzy Preference Relation and Interval-Valued Hesitant Fuzzy Preference Relation

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-211131 ◽

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.

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

Algorithms ◽

10.3390/a11110182 ◽

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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Decision Making with Hesitant Fuzzy Preference Relation

Hesitant Fuzzy Decision Making Methodologies and Applications - Uncertainty and Operations Research ◽

10.1007/978-981-10-3265-3_6 ◽

2016 ◽

pp. 221-275

Author(s):

Huchang Liao ◽

Zeshui Xu

Keyword(s):

Decision Making ◽

Preference Relation ◽

Fuzzy Preference Relation ◽

Hesitant Fuzzy Preference Relation ◽

Fuzzy Preference

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Consistency Checking and Improving for Interval-Valued Hesitant Preference Relations

Symmetry ◽

10.3390/sym11040466 ◽

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.

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