10.2190/ES.33.2.a V4T3812K3N82872K 1 Environmental Project Evaluation Using Intuitionistic Fuzzy Information 87 99 20120409 20120409 20120409 20120409 V4T3812K3N82872K.pdf http://baywood.metapress.com/link.asp?target=contribution&id=V4T3812K3N82872K 2 P. N. Smith University of Queensland, Australia An intuitionistic fuzzy set (IFS) is a generalization of a fuzzy set characterized by a truth membership function and a false membership function. The former is a lower bound on the grade of membership of the evidence in favor of a particular element belonging to the set and the latter is a lower bound on the negation of that element belonging to the set, derived from evidence against that element belonging to the set. A similar concept is a vague set, though vague sets have been shown to be identical to IFSs. In the context of project evaluation, an IFS may be used to represent the degree to which a project satisfies a criterion or factor and the degree to which it does not. Aggregation of such IFSs has been considered in recent years to identify a best project in terms of several factors. A particular desirable way to aggregate IFSs is in terms of an ordered weighted average (OWA) which can be expressed in different forms, such as arithmetic and geometric. In an OWA, weights are applied to the position of an element in the aggregation. In addition, hybrid OWA operators may be developed to not only weight the position of elements in the aggregation but the element itself. A simple example based on a hypothetical but realistic example by Horsak and Damico [4] is given which involves the location of a hazardous waste disposal facility (PCB-contaminated transformer fluids) at one of three sites based on 10 factors. P. N. Smith, Andness-Directed Weighted Averaging Operators: Possibilities for Environmental Project Evaluation, <i>Journal of Environmental Systems, 30</i>, pp. 333-348, 2003-2004. P. N. Smith, Numeric Ordered Weighted Averaging Operators: Possibilities for Environmental Project Evaluation, <i>Journal of Environmental Systems, 28</i>, pp. 175-191, 2000-2001. P. N. Smith, Linguistic Ordered Weighted Averaging Operators: Possibilities for Environmental Project Evaluation, <i>Journal of Environmental Systems, 28</i>, pp. 257-269, 2000-2001. R. Horsak and S. Damico, Selection and Evaluation of Hazardous Waste Disposal Sites Using Fuzzy Set Analysis, <i>Journal of the Air Pollution Control Association, 35</i>, pp. 1081-1085, 1985. G. Anandalingam and M. Westfall, Selection of Hazardous Waste Disposal Alternatives Using Multiattribute Utility Theory and Fuzzy Set Theory, <i>Journal of Environmental Systems, 18</i>, pp. 69-85, 1988. L. A. Zadeh, Fuzzy Sets, <i>Information and Control, 8</i>, pp. 338-353, 1965. K. Atanassov, Intuitionistic Fuzzy Sets, <i>Fuzzy Sets and Systems, 20</i>, pp. 87-96, 1986. K. Atanssov, <i>Intuitionistic Fuzzy Sets: Theory and Applications</i>, Physica-Verlag, Heidelberg, Germany, 1999. C. Cornelis, G. Deschrijverand, and E. E. Kerre, Implication in Intuitionistic Fuzzy and Interval-Valued Fuzzy Set Theory: Construction, Classification, Application, <i>International Journal of Approximate Reasoning, 35</i>, pp. 55-95, 2004. L. A. Zadeh, The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I, <i>Information Sciences, 8</i>, pp. 199-249, 1975. W. L. Gau and D. J. Buehrer, Vague Sets, <i>IEEE Transactions on Systems Man and Cybernetics, 18</i>, pp. 610-614, 1993. H. Bustince and P. Burillo, Vague Sets are Intuitionistic Fuzzy Sets, <i>Fuzzy Sets and Systems, 79</i>, pp. 403-405, 1996. M. Hersh, <i>Mathematical Modelling for Sustainable Development</i>, Springer, Berlin, 2006. S. M. Chen and J. M. Tan, Handling Multicriteria Fuzzy Decisionmaking Problems based on Vague Set Theory, <i>Fuzzy Sets and Systems, 67</i>, pp. 163-172, 1994. D. H. Hong and C. H. Choi, Multicriteria Fuzzy Decision-Making Problems Based on Vague Set Theory, <i>Fuzzy Sets and Systems, 114</i>, pp. 103-113, 2000. J. Ye, Improved Method of Multicriteria Fuzzy Decision-Making Based on Vague Sets, <i>Computer-Aided Design, 39</i>, pp. 164-169, 2007. L. Lin, X-H. Yuan, and Z-Q. Xia, Multicriteria Fuzzy Decision-Making Methods Based on Intuitionistic Fuzzy Sets, <i>Journal of Computer and System Sciences, 73</i>, pp. 84-88, 2007. Z. S. Xu, Intuitionistic Fuzzy Aggregation Operators, <i>IEEE Transactions on Fuzzy Systems, 15</i>, pp. 1179-1187, 2007. Z. Xu and R. R. Yager, Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets, <i>International Journal of General Systems, 35</i>, pp. 417-433, 2006. J. Wang, S-Y. Liu, and J. Zhang, An Extension of TOPSIS for Fuzzy MCDM Based on Vague Set Theory, <i>Journal of Systems Science and Systems Engineering, 14</i>, pp. 1861-9576 (online version), 2005.