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Xu Z.,PLA University of Science and Technology
IEEE Transactions on Fuzzy Systems | Year: 2013

An intuitionistic multiplicative preference relation was recently introduced by Xia et al. to characterize the preference information that is given by a decision maker over a set of objects. All the elements of the intuitionistic multiplicative preference relation are the 2-tuples, which can simultaneously depict the degree that one object is prior to another, and the degree that the object is not prior to another. Each part of the 2-tuples takes its value from the closed interval [1/9, 9], and thus can describe the decision maker's preferences over objects more comprehensively than the traditional multiplicative preference relation. How to derive the priority weights of the objects from an intuitionistic multiplicative preference relation is an important research topic for decision making with intuitionistic multiplicative preference information. In this paper, we shall focus on solving this issue. We first define the concepts of expected intuitionistic multiplicative preference relation, left and right error matrices, etc. Then based on the geometric aggregation operator and the error propagation formula, we derive the priority weight intervals from an intuitionistic multiplicative preference relation. After that, some approaches to decision making based on intuitionistic multiplicative preference relations are developed, and furthermore, two practical examples are given to illustrate our approaches. © 1993-2012 IEEE. Source


Xu Z.,Shanghai JiaoTong University | Xu Z.,PLA University of Science and Technology
Information Sciences | Year: 2010

The Choquet integral is a very useful way of measuring the expected utility of an uncertain event [G. Choquet, Theory of capacities, Annales de l'institut Fourier 5 (1953) 131-295]. In this paper, we use the Choquet integral to propose some intuitionistic fuzzy aggregation operators. The operators not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements or their ordered positions. It is worth pointing out that most of the existing intuitionistic fuzzy aggregation operators are special cases of our operators. Moreover, we propose the interval-valued intuitionistic fuzzy correlated averaging operator and the interval-valued intuitionistic fuzzy correlated geometric operator to aggregate interval-valued intuitionistic fuzzy information, and apply them to a practical decision-making problem involving the prioritization of information technology improvement projects. © 2009 Elsevier Inc. All rights reserved. Source


Zhu B.,Nanjing Southeast University | Xu Z.,PLA University of Science and Technology
IEEE Transactions on Fuzzy Systems | Year: 2014

Hesitant fuzzy linguistic term sets (HFLTSs) are used to deal with situations in which the decision makers (DMs) think of several possible linguistic values or richer expressions than a single term for an indicator, alternative, variable, etc. Compared with fuzzy linguistic approaches, they are more convenient and flexible to reflect the DMs' preferences in decision making. For further applications of HFLTSs to decision making, we develop a concept of hesitant fuzzy linguistic preference relations (HFLPRs) as a tool to collect and present the DMs' preferences. Due to the importance of the consistency measures using preference relations in decision making, we develop some consistency measures for HFLPRs to ensure that the DMs are being neither random nor illogical. A consistency index is defined to establish the consistency thresholds of HFLPRs to measure whether an HFLPR is of acceptable consistency. For HFLPRs with unacceptable consistency, we develop two optimization methods to improve the consistency until they are acceptable. Several illustrative examples are given to validate the consistency measures and the optimization methods. © 2013 IEEE. Source


Xu Z.,PLA University of Science and Technology
Knowledge-Based Systems | Year: 2012

Intuitionistic fuzzy preference relation is a suitable tool used to describe uncertain or vague preference information provided by a decision maker in fuzzy decision making situations. A key step in decision making with an intuitionistic preference relation is to derive the priority vector of the intuitionistic preference relation. In this paper, we develop an error-analysis-based method for the priority of an intuitionistic preference relation, and then a possibility degree formula is used to derive the ranking of the considered alternatives. Moreover, a numerical analysis on the developed method is conducted through an illustrative example. © 2012 Elsevier B.V. All rights reserved. Source


Xu Z.,PLA University of Science and Technology
Computers and Industrial Engineering | Year: 2013

In group decision making under uncertainty, interval preference orderings as a type of simple uncertain preference structure, can be easily and conveniently used to express the experts' evaluations over the considered alternatives. In this paper, we investigate group decision making problems with interval preference orderings on alternatives. We start by fusing all individual interval preference orderings given by the experts into the collective interval preference orderings through the uncertain additive weighted averaging operator. Then we establish a nonlinear programming model by minimizing the divergences between the individual uncertain preferences and the group's opinions, from which we derive an exact formula to determine the experts' relative importance weights. After that, we calculate the distances of the collective interval preference orderings to the positive and negative ideal solutions, respectively, based on which we use a TOPSIS based approach to rank and select the alternatives. All these results are also reduced to solve group decision making problems where the experts' evaluations over the alternatives are expressed in exact preference orderings. A numerical analysis of our model and approach is finally carried out using two illustrative examples. © 2013 Published by Elsevier Ltd. Source

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