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A consistency-based procedure to estimate missing pairwise preference values. (English) Zbl 1148.68470

Summary: We present a procedure to estimate missing preference values when dealing with pairwise comparison and heterogeneous information. This procedure attempts to estimate the missing information in an expert’s incomplete preference relation using only the preference values provided by that particular expert. Our procedure to estimate missing values can be applied to incomplete fuzzy, multiplicative, interval-valued, and linguistic preference relations. Clearly, it would be desirable to maintain experts’ consistency levels. We make use of the additive consistency property to measure the level of consistency and to guide the procedure in the estimation of the missing values. Finally, conditions that guarantee the success of our procedure in the estimation of all the missing values of an incomplete preference relation are given.

MSC:

68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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[1] Multi-criteria decision making methods: a comparative study. Dordrecht: Kluwer Academic Publishers; 2000. · Zbl 0980.90032
[2] . Fuzzy preference modelling and multicriteria decision support. Dordrecht: Kluwer Academic Publishers; 1994. · Zbl 0827.90002 · doi:10.1007/978-94-017-1648-2
[3] Chiclana, Fuzzy Sets Syst 97 pp 33– (1998)
[4] González-Pachón, Int J Approx Reason 33 pp 133– (2003)
[5] Kacprzyk, Fuzzy Sets Syst 18 pp 105– (1986) · Zbl 0613.90057
[6] Orlovski, Fuzzy Sets Syst 1 pp 155– (1978)
[7] Kahraman, Inform Sci 157 pp 135– (2003)
[8] Świtalski, Fuzzy Sets Syst 137 pp 85– (2003)
[9] Herrera, Eur J Oper Res 129 pp 372– (2001)
[10] Macharis, Eur J Oper Res 153 pp 307– (2004)
[11] The analytic hierarchy process. New York: McGraw-Hill; 1980.
[12] . Models, methods, concepts and applications of the analytic hierarchy process. Boston, MA: Kluwer; 2000.
[13] Stam, Eur J Oper Res 145 pp 92– (2003)
[14] Bilgiç, Eur J Oper Res 105 pp 162– (1998)
[15] Herrera, Eur J Oper Res 166 pp 115– (2005)
[16] Szmidt, Int J Intell Syst 18 pp 837– (2003)
[17] Xu, Fuzzy Optim Decis Making 3 pp 217– (2004)
[18] Herrera, Eur J Oper Res 120 pp 144– (2000)
[19] Xu, Inform Sci 166 pp 19– (2004)
[20] Xu, Int J Approx Reason 36 pp 261– (2004)
[21] Kim, Eur J Oper Res 118 pp 139– (1999)
[22] Herrera-Viedma, Eur J Oper Res 154 pp 98– (2004)
[23] , , . A learning procedure to estimate missing values in fuzzy preference relations based on additive consistency. In: Proc 1st Int Conf on Modeling Decisions for Artificial Intelligence (MDAI 2004), Barcelona (Spain). Lecture Notes in Artificial Intelligence vol. 3131. Berlin: Springer-Verlag; 2004. pp. 227–238. · Zbl 1109.68534
[24] Miller, Psychol Rev 63 pp 81– (1956)
[25] Zadeh, Inform Sci 8 pp 199– (1975)
[26] Herrera, IEEE Trans Fuzzy Syst 8 pp 746– (2000)
[27] Herrera, Int J Uncertain, Fuzziness and Knowl-Based Syst 92 pp 33– (2001)
[28] Tanino, Fuzzy Sets Syst 12 pp 117– (1984) · Zbl 0567.90002
[29] Chiclana, Fuzzy Sets Syst 122 pp 277– (2001)
[30] Herrera-Viedma, IEEE Trans Syst, Man Cybern, Part B 37 pp 176– (2007)
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