Proceedings of the Eighth International Conference on Machine Learning and Cybernetics, Baoding, 12-15 July 2009 978-1-4244-3703-0/09/$25.00 ©2009 IEEE 1309 A GOAL PROGRAMMING METHOD FOR GENERATING PRIORITY WEIGHTS BASED ON INTERVAL-VALUED INTUITIONISTIC PREFERENCE RELATIONS ZHOU-JING WANG 1 , WEI-ZE WANG 1 , KEVIN W. LI 2 1 Department of Automation, Xiamen University, Xiamen, Fujian 361005, China 2 Odette School of Business, University of Windsor, Windsor, Ontario N9B 3P4, Canada E-MAIL: wangzj@xmu.edu.cn Abstract: Interval-valued intuitionistic preference relations are a powerful means to expressing a decision maker’s uncertainty and hesitation about its preference over criteria in the process of multi-criteria decision making. In this paper, we define the notion of consistent interval-valued intuitionistic preference relations. Goal programming models are established for generating priority interval weights based on interval-valued intuitionistic preference relations. Two illustrative numerical examples are furnished to demonstrate how to apply the approach. Keywords: Interval-valued intuitionistic preference relation; Priority interval weight; Consistency; Goal programming 1. Introduction As an important extension of fuzzy logic, intuitionistic fuzzy sets (IFSs) [1] allow a decision-maker (DM) to express both the degree of belonging of an element to a particular set (membership function) and the degree of non-belonging to the set (nonmembership function). In an IFS, the membership and nonmembership functions are real-valued. To further enhance the capability of handling uncertainty in the membership and nonmembership functions, Atanassov and Gargov [2] have extended the notion of IFSs to interval-valued intuitionistic fuzzy sets (IVIFSs) by allowing the membership and nonmembership functions to assume interval values. Current research has been focusing on the basic theory of IVIFSs such as basic relations and operations of IVIFSs [3], the correlation and correlation coefficients of IVIFSs [4-7], the topology of IVIFSs [8], relationships between IFSs, L-fuzzy sets, interval-valued fuzzy sets and IVIFSs [9-11], and the entropy and subsethood of IVIFSs [12]. Recent efforts have been directed to apply IVIFSs to multiattribute decision analysis. For instance, Xu [13] proposes some aggregation operators for multiattribute decision analysis with interval- valued intuitionistic fuzzy information. Xu and Yager [14] further investigate dynamic intuitionistic fuzzy aggregation operators and devise two procedures for dynamic intuitionistic fuzzy multiattribute decision making with intuitionistic fuzzy numbers (IFNs) or interval-valued intuitionistic fuzzy numbers (IVIFNs). Wang et al. [15] develop a framework for handling multiattribute decision making with IVIFS assessments and incomplete attribute weights. In the process of multicriteria decision making, a DM is expected to provide its preference over criteria, which may be conveniently characterized by fuzzy preference relations [16-18] when the DM has only vague knowledge about its preference of one criterion over another. In this case, it is more appropriate to express the DM’s preference in an interval number rather than an exact numerical value. Xu and Chen [19] define some new concepts such as additive and multiplicative consistent interval fuzzy preference relations, and develop some linear programming models to derive interval weights based on various interval fuzzy preference relations. Szmidt and Kacprzyk [20] investigate how to reach consensus with intuitionistic fuzzy preference relations in group decision making. Xu [21] introduces consistent, incomplete, and acceptable preference relations and develops another approach to group decision making under the intuitionistic fuzzy environment. In this article, it is assumed that the DM provides its preference over multiple criteria in terms of interval-valued intuitionistic fuzzy numbers (IVIFNs). We shall develop a method for generating priority weights based on these interval-valued intuitionistic fuzzy preference relations. The remainder of this paper is organized as follows: Section 2 reviews some basic concepts related to IFSs and IVIFSs. Section 3 introduces the concept of consistent interval-valued intuitionistic fuzzy preference relations. In Authorized licensed use limited to: Nanjing Southeast University. Downloaded on June 29,2010 at 02:28:55 UTC from IEEE Xplore. Restrictions apply.