A linguistic multicriteria analysis system combining fuzzy sets theory, ideal and anti-ideal points for location site selection Konstantinos Anagnostopoulos, Haris Doukas * , John Psarras National Technical University of Athens, School of Electrical and Computer Engineering, Decision Support Systems Lab (EPU-NTUA), 9, Iroon Polytechniou str., 15773 Athens, Greece Abstract Most multicriteria methods try to model human thinking and insert the results of this modelling into their procedures. Following this path, the proposed multicriteria approach first captures the imprecision and vagueness of data by using linguistic variables. At a second level, it utilises human processes of decision-making by creating decision rules and modelling them with functions used in fuzzy sets the- ory. This method also is compatible with the way fuzzy logic models and combines fuzzy propositions. The proposed method considers the ideal solution and the anti-ideal solution and assesses each alternative in terms of distance as well as similarity to the ideal solution and the anti-ideal solution. Distance and similarity measures for fuzzy numbers are used and their aggregation is guided by the decision rules in order to construct decision functions. Further, OWA operators with maximal entropy are used to aggregate across all criteria and determine the overall score of each alternative. It is shown that the proposed method presents flexibility in modelling the decision maker’s preferences and it is also appropriate and effective to handle multicriteria problems of considerable complexity. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Multicriteria analysis; Fuzzy numbers; Similarity measures; Distance measures 1. Introduction Real-life applications of multicriteria decision-making methods require the processing of imprecise, uncertain, qualitative or vague data. An efficient way to model uncer- tainty and imprecision is the use of fuzzy sets theory (Bell- man & Zadeh, 1970; Chen & Hwang, 1992). Fuzzy sets provide the flexibility required to represent and handle the uncertainty and imprecision resulting from a lack of knowledge or ill-defined information (Klir & Yuan, 1995; Slowinski, 1998; Yeh, Deng, & Chang, 2000; Zadeh, 1975). The research on fuzzy decision-making methods has produced many methods that use fuzzy data (Li, 1999; O ¨ lc ¸er & Odabas ßi, 2005; Triantaphyllou & Lin, 1996; Wang & Lin, 2003; Xu & Chen, 2007). Moreover, many applications have benefited from the development of fuzzy decision-making methods (Chen, 2001; Chen & Tzeng, 2004; Chiou, Tzeng, & Cheng, 2005; Ding & Liang, 2005; Geldermann, Spengler, & Rentz, 2000). Several fuzzy multicriteria methods evaluate the overall score of each alternative as a fuzzy number. Then, a fuzzy ranking method is necessary to compare the overall scores and order the alternatives. This comparison process can be quite complex and produce unreliable results, as it may: (1) involve considerable computations, (2) produce incon- sistency via respective fuzzy ranking methods, and (3) generate counter-intuitive ranking outcomes for similar fuzzy numbers (Yeh & Deng, 2004; Yeh et al., 2000). The use of the ideal solution to obtain a compromise solution to multicriteria problems was first suggested by Zeleny (1974). Hwang and Yoon (1981) introduced the multicriteria method TOPSIS which uses ideal and anti- ideal solutions to find the best alternative, considering that the chosen alternative should simultaneously have the shortest distance from the ideal solution and the lon- gest distance from the anti-ideal solution. The ideal 0957-4174/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2007.08.074 * Corresponding author. Tel.: +30 210 7722084x3555; fax: +30 210 7723550. E-mail address: h_doukas@epu.ntua.gr (H. Doukas). www.elsevier.com/locate/eswa Available online at www.sciencedirect.com Expert Systems with Applications 35 (2008) 2041–2048 Expert Systems with Applications