A Convex Combination Approach for the Weights of Interval Fuzzy Preference Relation

In the analytical hierarchy process (AHP), it needs the decision maker to establish a pairwise comparison matrix requires n(n–1)/2 judgments for a level with n criteria (or alternatives). In some instances, the decision maker may have to deal with the problems in which only partial information and uncertain preference relation is available. Consequently, the decision maker may provide interval fuzzy preference relation with incomplete information. In this paper, we focus our attention on the investigation of incomplete interval fuzzy preference relation. We first extend a characterization to the interval fuzzy preference relation which is based on the additive transitivity property. Using the characterization, we propose a method to construct interval additive consistent fuzzy preference relations from a set of n–1 preference data. The study reveals that the proposed method can not only alleviate the comparisons, but also ensure interval preference relations with the additive consistent property. We also develop a novel procedure to deal with the analytic hierarchy problem for group decision making with incomplete interval fuzzy preference relations. Finally, a numerical example is illustrated and a supplier selection case in supply chain management is investigated using the proposed method.

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Revisiting multiplicative consistency of interval fuzzy preference relation

Computers & Industrial Engineering ◽

10.1016/j.cie.2019.04.030 ◽

2019 ◽

Vol 132 ◽

pp. 325-332 ◽

Cited By ~ 4

Author(s):

Huimin Zhang

Keyword(s):

Preference Relation ◽

Fuzzy Preference Relation ◽

Multiplicative Consistency ◽

Interval Fuzzy Preference Relation ◽

Fuzzy Preference

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

Journal of Algorithms & Computational Technology ◽

10.1177/1748301816665022 ◽

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.

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

Mathematical Problems in Engineering ◽

10.1155/2015/180892 ◽

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.

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