Abstract
The determination of ordered weighted averaging (OWA) operator weights is a very important issue of applying the OWA operator for decision making. One of the first approaches, suggested by O’Hagan, determines a special class of OWA operators having maximal entropy of the OWA weights for a given level of orness; algorithmically it is based on the solution of a constrained optimization problem. In 2001, using the method of Lagrange multipliers, Fullér and Majlender solved this constrained optimization problem analytically and determined the optimal weighting vector. In 2003 Fullér and Majlender computed the exact minimal variability weighting vector for any level of orness using the Karush-Kuhn-Tucker second-order sufficiency conditions for optimality. The problem of maximizing an OWA aggregation of a group of variables that are interrelated and constrained by a collection of linear inequalities was first considered by Yager in 1996, where he showed how this problem can be modeled as a mixed integer linear programming problem. In 2003 Carlsson, Fullér and Majlender derived an algorithm for solving the constrained OWA aggregation problem under a simple linear constraint: the sum of the variables is less than or equal to one. In this paper we give a short survey of numerous later works which extend and develop these models.
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References
Aggarwal M (2015) On learning of weights through preferences. Inf Sci 321:90–102
Ahn BS (2008) Some quantier functions from weighting functions with constant value of orness. IEEE Trans Syst Man Cybern Part B 38:540–546
Ahn BS (2009) Some remarks on the LSOWA approach for obtaining OWA operator weights. Int J Intell Syst 24(12):1265–1279
Ahn BS (2010) Parameterized OWA operator weights: an extreme point approach. Int J Approx Reason 51:820–831
Ahn BS (2011) Compatible weighting method with rank order centroid: maximum entropy ordered weighted averaging approach. Eur J Oper Res 212:552–559
Amin GR, Emrouznejad A (2006) An extended minimax disparity to determine the OWA operator weights. Comput Ind Eng 50:312–316
Carlsson C, Fullér R, Majlender P (2003) A note on constrained OWA aggregations. Fuzzy Sets Syst 139:543–546
Carlsson C, Fedrizzi M, Fullér R (2004) Fuzzy logic in management. International series in operations research and management science, vol 66. Kluwer Academic Publishers, Boston
Chaji A (2017) Analytic approach on maximum Bayesian entropy ordered weighted averaging operators. Comput Ind Eng 105:260–264
Chang JR, Ho TH, Cheng CH, Chen AP (2006) Dynamic fuzzy OWA model for group multiple criteria decision. Soft Comput 10:543–554
Cheng CH, Wei LY, Liu JW, Chen TL (2013) OWA-based ANFIS model for TAIEX forecasting. Econ Model 30:442–448
Fullér R, Majlender P (2001) An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets Syst 124:53–57
Fullér R, Majlender P (2003) On obtaining minimal variability OWA operator weights. Fuzzy Sets Syst 136:203–215
Gao J, Li M, Liu H (2015) Generalized ordered weighted utility averaging-hyperbolic absolute risk aversion operators and their applications to group decision-making. Eur J Oper Res 243:258–270
Gong Y (2011) A combination approach for obtaining the minimize disparity OWA operator weights. Fuzzy Optim and Decis Mak 10:311–321
Gong Y, Dai L, Hu N (2016) An extended minimax absolute and relative disparity approach to obtain the OWA operator weights. J Intell Fuzzy Syst 31:1921–1927
Hong DH (2011) On proving the extended minimax disparity OWA problem. Fuzzy Sets Syst 168:35–46
Kaur Gurbinder, Dhar Joydip, Guha RK (2016) Minimal variability OWA operator combining ANFIS and fuzzy c-means for forecasting BSE index. Math Comput Simul 122:69–80
Kim Z, Singh VP (2014) Assessment of environmental flow requirements by entropy-based multi-criteria decision. Water Resour Manage 28:459–474
Kishor A, Singh A, Pal N (2014) Orness measure of OWA operators: a new approach. IEEE Trans Fuzzy Syst 22:1039–1045
Liu X, Chen L (2004) On the properties of parametric geometric OWA operator. Int J Approx Reason 35:163–178
Liu X (2005) On the properties of equidifferent RIM quantifier with generating function. Int J Gener Syst 34:579–594
Liu X (2007) The solution equivalence of minimax disparity and minimum variance problems for OWA operators. Int J Approx Reason 45:68–81
Liu X (2008) A general model of parameterized OWA aggregation with given orness level. Int J Approx Reason 48:598–627
Liu X, Han S (2008) Orness and parameterized RIM quantier aggregation with OWA operators: a summary. Int J Approx Reason 48:77–97
Liu X (2009) On the methods of OWA operator determination with different dimensional instantiations. In: Proceedings of the 6th international conference on fuzzy systems and knowledge discovery, FSKD 2009, 14–16 Aug 2009, Tianjin, China, vol 7, pp 200–204. ISBN 978-076953735-1, Article number 5359982
Liu X (2011) A review of the OWA determination methods: classification and some extensions. In: Yager RR, Kacprzyk J, Beliakov G (eds) Recent developments in the ordered weighted averaging operators: theory and practice. Studies in fuzziness and soft computing, vol 265. Springer, pp 49–90. ISBN 978-3-642-17909-9
Liu X (2012) Models to determine parameterized ordered weighted averaging operators using optimization criteria. Inf Sci 190:27–55
Liu HC, Mao LX, Zhang ZY, Li P (2013) Induced aggregation operators in the VIKOR method and its application in material selection. Appl Math Model 37:6325–6338
Llamazares B (2007) Choosing OWA operator weights in the field of social choice. Inf Sci 177:4745–4756
Luukka P, Kurama O (2013) Similarity classifier with ordered weighted averaging operators. Expert Syst Appl 40:995–1002
Majlender P (2005) OWA operators with maximal Renyi entropy. Fuzzy Sets Syst 155:340–360
Mohammed EA, Naugler CT, Far BH (2016) Breast tumor classification using a new OWA operator. Expert Syst Appl 61:302–313
O’Hagan M (1988) Aggregating template or rule antecedents in real-time expert systems with fuzzy set logic. In: Proceedings of 22nd annual IEEE Asilomar conference signals, systems, computers, Pacific Grove, CA, pp 681-689
Reimann O, Schumacher C, Vetschera R (2017) How well does the OWA operator represent real preferences? Eur J Oper Res 258:993–1003
Sang X, Liu X (2014) An analytic approach to obtain the least square deviation OWA operator weights. Fuzzy Sets Syst 240:103–116
Troiano L, Yager RR (2005) A measure of dispersion for OWA operators. In: Liu Y, Chen G, Ying M (eds) Proceedings of the eleventh international fuzzy systems association world congress, 28–31 July 2005, Beijing, China. Tsinghua University Press and Springer, pp 82–87
Vergara VM, Xia S (2010) Minimization of uncertainty for ordered weighted average. Int J Intell Syst 25:581–595
Wang Y-M, Parkan C (2005) A minimax disparity approach for obtaining OWA operator weights. Inf Sci 75:20–29
Wang JW, Chang JR, Cheng CH (2006) Flexible fuzzy OWA querying method for hemodialysis database. Soft Comput 10:1031–1042
Wang YM, Luo Y, Liu XW (2007) Two new models for determining OWA operator weights. Comput Ind Eng 52:203–209
Wu J, Sun B-L, Liang C-Y, Yang S-L (2016) A linear programming model for determining ordered weighted averaging operator weights with maximal Yager’s entropy. Comput Ind Eng 57(3):742–747
Xu ZS (2006) Dependent OWA operators. Lect Notes Comput Sci 3885:172–178
Yager RR (1988) Ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern 18:183-190
Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59:125–148
Yager RR (1995) Measures of entropy and fuzziness related to aggregation operators. Inf Sci 82:147–166
Yager RR (1996) Constrained OWA aggregation. Fuzzy Sets Syst 81:89–101
Yager RR (1995) On the inclusion of variance in decision making under uncertainty. Int J Uncertain Fuzziness Knowl-Based Syst 4:401–419
Yager RR, Kacprzyk J (1997) The ordered weighted averaging operators: theory and applications. Kluwer, Norwell
Yager RR, Filev D (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern—Part B: Cybern 29:141–150
Yager RR (2007) Using stress functions to obtain OWA operators. IEEE Trans Fuzzy Syst 15:1122–1129
Yager RR (2010) Including a diversity criterion in decision making. Int J Intell Syst 25:958–969
Yari G, Chaji AR (2012) Maximum Bayesian entropy method for determining ordered weighted averaging operator weights. Comput Ind Eng 63:338–342
Zadrozny S, Kacprzyk J (2006) On tuning OWA operators in a flexible querying interface. Lect Notes Comput Sci 4027:97–108
Zhou L, Chen H, Liu J (2012) Generalized logarithmic proportional averaging operators and their applications to group decision making. Knowl-Based Syst 36:268–279
Zhou L, Chen H, Liu J (2012) Generalized weighted exponential proportional aggregation operators and their applications to group decision making. Appl Math Model 36:4365–4384
Zhou L, Tao Z, Chen H, Liu J (2015) Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making. Soft Comput 19:715–730
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Carlsson, C., Fullér, R. (2018). Maximal Entropy and Minimal Variability OWA Operator Weights: A Short Survey of Recent Developments. In: Collan, M., Kacprzyk, J. (eds) Soft Computing Applications for Group Decision-making and Consensus Modeling. Studies in Fuzziness and Soft Computing, vol 357. Springer, Cham. https://doi.org/10.1007/978-3-319-60207-3_12
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