A Brief Review of Fuzzy Aggregation
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Aug 24, 2018
Keywords:
fuzzy aggregation decision making
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Abstract
The concept and applications of fuzzy aggregation have been witnessed over the past decades, spanning from system control, decision-making as well as machine learning. Even now, the theoretical development of several models like OWA still continues, with further exploitation in many new problem domains. Given this insight, it is important to provide a review of landscape for fuzzy aggregation, with respect to both types and future challenges. The paper is to be useful for those who are interested in this subject in general, and others that are keen to employ a fuzzy aggregator in their research studies.
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[1]
T. Boongoen, “A Brief Review of Fuzzy Aggregation”, NKRAFA J SCI TECH, vol. 13, no. 1, pp. 59–66, Aug. 2018.
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References
[1] J.Aczel. On weighted of judgements. Aequationes Math, 27: 288-307, 1984.
[2] J.Aczel and C.Alsina. Classification of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Meth. Opl. Res, 48: 3-22, 1984.
[3] C.Alsina, E.Trillas and L.Valverde. On some logical connectives for fuzzy sets theory. J.Math. Anal. Appl, 93(1): 15-26, 1983.
[4] S.Auephanwiriyakul, J.Keller and P.Gader. Generalized Choquet fuzzy integral fusion. Information Fusion, 3: 69-85, 2002.
[5] G. Beliakov and J.Warren. Appropriate choice of aggregation operators in fuzzy decision support systems. IEEE Trans. Fuzzy Syst, 9(6): 773-784, 2001.
[6] G. Beliakov, A.Pradera and T.Calvo. Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg. New York: Berlin, 2007.
[7] G.Beliakov, T.Calvo and A.Pradera. Handling of neutral information by aggregation operators. Fuzzy Sets Syst, 158: 861-880, 2007.
[8] G.Beliakov, T.Calvo and A.Pradera. Absorbent tuples of aggregation operators. Fuzzy Sets Syst, 158: 1675-1691, 2007.
[9] P.Bonissone. Selecting uncertainty calculi and granularity: An experiment in trading off precision and complexity. Proceedings of the first Workshop on Uncertainty in Artificial Intelligence. Los Angeles: 57 - 66, 1985.
[10] T. Boongoen and Q. Shen. Clus-DOWA: A New Dependent OWA Operator. Proceedings of IEEE International Conference in Fuzzy Systems.
Hong Kong, China, 2008.
[11] G. Bordogna, M. Fedrizzi and G. Pasi. A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans. On Systems, Man and Cybernetics - part A, 27(1): 126-133, 1997.
[12] G.Buyukozkan, G. Mauris, O. Feyzioglu and L.Berrah. Providing eluci-dations of web site evaluation based on a multi-criteria aggregation with the Choquet integral. In Int. Fuzzy Systems Association World Congress (IFSA 2003): 131-134, Istanbul, Turkey, 2003.
[13] T.Calvo, B. De Baets and J.Fodor. The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems, 120: 385-394, 2001.
[14] T.Calvo, G.Mayor and R.Mesiar. (Eds.), Aggregation Operators. New York: Physica-Verlag, 2002.
[15] J.R.Chang, T.H. Ho, C.H.Cheng and A.P.Chen. Dynamic fuzzy OWA model for group multiple criteria decision making. Soft Computing,
10: 543-554, 2006.
[16] C.H.Cheng, J.R.Chang, T.H.Ho and A.P.Chen. Evaluating the Airline Service Quality by Fuzzy OWA Operators. Proceedings of the Modeling Decisions for Artificial Intelligence (MDAI): 77-88, Japan, 2005.
[17] G.Choquet. Theory of capacities. Annales de l’Institut Fourier, 5: 131-295, 1953.
[18] V.Cutello and J.Montero. Hierarchies of aggregation operators. International Journal of Intelligent Systems, 9: 1025-1045, 1994.
[19] B.De Baets and J.Fodor. Van Melle’s combining function in MYCIN is a representable uninorm: an alternative proof. Fuzzy Sets and Systems, 104: 133-136, 1999.
[20] D.Dubois and H.Prade. Triangular norms for fuzzy sets. Proceedings of the 2ndInternational Symposium of Fuzzy Sets, Linz, 39 - 68, 1981.
[21] D.Dubois and H.Prade. A review of fuzzy sets aggregation connectives. Information Sciences, 36: 85 - 121, 1985.
[22] D.Dubois and H.Prade. Weighted minimum and maximum operators in fuzzy set theory. Information Sciences, 39: 205-210, 1986.
[23] D. Dubois, H. Prade and C.Testemale. Weighted fuzzy pattern-matching. Fuzzy Sets and Systems, 28: 313-331, 1988.
[24] D.Dubois, J.L.Marichal, H.Prade, M.Roubens and R.Sabbadin. The use of the discrete Sugeno integral in decision making: a survey. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(5): 539-561, 2001.
[25] D.P. Filev and R.R.Yager. Fuzzy logic controllers with flexible structures. Proc. Second Int. Conf. on Fuzzy Sets and Neural Networks, Iizuka: 317- 320, 1992.
[26] D.Filev and R.R.Yager. On the issue of obtaining OWA operator weights. Fuzzy Sets and Systems, 94(2): 157-169, 1998.
[27] J.C. Fodor, R.R.Yager and A. Rybalov. Structure of Uninorms, International Journal of Uncertainty. Fuzziness and Knowledge- Based Systems, 5: 411-427, 1997.
[28] R.Fuller and P.Majlender. An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems, 124: 53-57, 2001.
[29] R.Fuller and P.Majlender. On obtaining minimal variablity OWA operator weights. Fuzzy Sets and Systems, 136: 203-215, 2003.
[30] P.Gader, W.H.Lee and X.P.Zhang. Renyi entropy with respect to choquet capacities. In Proc. IEEE Conf. Fuzzy Systems. Budapest, Hungary, 2004.
[31] M.Grabisch. On the use of fuzzyintegral as a fuzzy connective. Proceedings of the Second IEEE International Conference on Fuzzy Systems,
San Francisco: 213-218, 1993.
[32] M.Grabisch. Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems, 69: 279-298, 1995.
[33] M.Grabisch, H.T.Nguyen and E.A.Walker. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic, 1995.
[34] M.Grabisch. The application of fuzzy integrals in multicriteria decision making. European J. of Operational Research, 89: 445-456, 1996.
[35] M.Grabisch and F.Huet. Texture recognition by Choquet integral filters, in 6th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU): 1325-1330, Granada, Spain, 1996.
[36] M.Grabisch, S.A.Orlovski and R.R.Yager. Fuzzy aggregations of numerical preferences. In Slowinski R.(ed). Fuzzy Sets in Decision Analysis. Operations Research and Statistics. Kluwer Academic Publishers, 1998.
[37] M.Grabisch. Fuzzy integral for classification and feature extraction. In M.Grabisch, T.Murofushi and M.Sugeno (eds). Fuzzy Measures and Integrals-Theory and Applications: 415-434. Physica Verlag, 2000.
[38] M.Grabisch M, J.Duchene, F. Lino and P.Perny. Subjective evaluation of discomfort in sitting position. Fuzzy Optimization and Decision Making, 1(3): 287-312, 2002.
[39] F.Herrera, E.Herrera-Viedma and J.L.Verdegay. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78: 73-87, 1996.
[40] F.Herrera and L.Martinez. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Systems, Man and Cybernetics, 8: 746-752, 2000.
[41] F.Herrera and L.Martinez. A model based on linguistic 2-tuple for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision- making. IEEE Transactions on Systems, Man and Cybernetics, 31: 227-234, 2001.
[42] U.Hohle. Probabilistic uniformization of fuzzy topologies. Fuzzy Sets and Systems1, 1978.
[43] J.Kacprzyk and R.R.Yager(eds). The ordered weighted averaging operators: theory and applications. Norwell,MA: Kluwer Academic Publishers, 1997.
[44] J.M. Keller, P.D. Gader and A.K.Hocaoglu. Fuzzy integrals in image processing and recognition, in M.Grabisch. T.Murofushi and M.Sugeno(eds). Fuzzy Measures and Integrals - Theory and Applications: 435-466. Physica Verlag, 2000.
[45] E.P.Klement. A theory of fuzzy measures: a survey, in M.Gupta and E.Sanchez(eds). Fuzzy Information and Decision Processes, North Holland: Amsterdam: 59-66, 1982.
[46] E.P.Klement, R.Mesiar and E.Pap. On the relationship of associative compensatory operators to triangular norms and conforms. International Journal Uncertainty. Fuzziness and Knowledge based Systems, 4(2): 129- 144, 1996.
[47] E.P.Klement, R.Mesiar and E.Pap. Triangular norms, Trends in Logic. Studia Logica Library, 8, Kluwer Academic Publishers, 2000.
[48] G.J.Klir. and T.A.Folger. Fuzzy Sets, Uncertainty and Information. Englewood Cliffs, N.J: Prentice-Hall, 1988.
[49] S.H.Kwon and M. Sugeno. A hierarchical subjective evaluation model using non-monotonic fuzzy measures and the Choquet integral. in M.Grabisc, T.Murofushi and M.Sugeno (eds). Fuzzy Measures and Integrals – Theory and Applications: 375-391. Physica Verlag, 2000.
[50] X.W.Liu and L.H.Chen. The equivalence of maximum entropy OWA operator and geometric OWA operator. International Conference on Machine Learning and Cybernetics: 2673-2676, 2003.
[51] B.Llamazares. Choosing OWA operator weights in the field of Social Choice. Information Sciences, 177(21): 4745-4756, 2007.
[52] M.K. Luhandjula. Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy Sets and Systems, 8: 245-252, 1982.
[53] J.L.Marichal.On Sugeno integral as an aggregation function. Fuzzy Sets and Systems, 114: 347-365, 2000.
[54] M.Mas, G.Mayor and J.Torrens. t-operators, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems, 7(1): 31-50, 1999.
[55] M.Mas, R.Mesiar, M.Monserrat and J.Torrens. Aggregation operators with annihilator. International Journal of General Systems, 34(1): 1-22, 2005.
[56] H.B.Mitchell and D.D.Estrakh. A modified OWA operator and its use in lossless DPCM image compression. International Journal of Uncertain Fuzziness. Knowledge Based Systems, 5 429-436, 1997.
[57] H.B.Mitchell and P.A.Schaefer. Multiple priorities in an induced ordered weighted averaging operator. International Journal ofIntelligent Systems, 15: 317-327, 2000.
[58] T.Murofushi and M.Sugeno. Non-additivity of fuzzy measures representing preferential dependence. In 2nd Int. Conf. on Fuzzy Systems and Neural Networks: 617-620 , Iizuka, Japan, 1992.
[59] T.Murofushi and M.Sugeno. Some quantities represented by the Choquet integral. Fuzzy Sets and Systems, 56: 229-235, 1993.
[60] M.O’Hagan. Aggregating template rule antecedents in real-time expert systems with fuzzy set logic. Proceedings of Annual IEEE Conference on Signals, Systems, and Computers: 681-689, 1988.
[61] J.Quiggin. A theory of anticipated utility. Journal of Economic Behavior and Organization, 3: 323-343, 1982.
[62] T.L.Saaty. The Analytic Hierarchy Process. New York: McGraw-Hill, 1980.
[63] B. Schweizer and A. Sklar A. Probabilistic metric spaces. Amsterdam: North-Holland,1983.
[64] U.Segal. Order indifference and rank dependent probabilities. Journal of Math. Economics, 22: 373-397, 1993.
[65] A.Soria-Frisch. Unsupervised construction of fuzzy measures through self-organizing feature maps and its application in color image segmentation. Int. J. Approx. Reason. 41: 23-42, 2006.
[66] M.Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.
[67] V.Torra. The weighted OWA operator. International Journal of Intelligent Systems, 12(2): 153-166, 1997.
[68] V.Torra. Learning weights for the quasi- weighted mean. IEEE Trans. Fuzzy Syst, 10(5): 653-666, 2002.
[69] V.Torra and Y.Narukawa. A View of Averaging Aggregation Operators. IEEE Transaction on Fuzzy Systems, 15(6): 1063-1967, 2007.
[70] V.Torra and Y.Narukawa. Modeling Decisions: Aggregation Operators and Information Fusion. , NewYork : Springer, 2007.
[71] L.Troiano and R.R. Yager. Recursive and iterative OWA operators, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems, 13(6): 579-599, 2005.
[72] A.Tsadiras and K. Margaritis. The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons. Fuzzy Sets and Systems, 93: 263-274, 1999.
[73] I.B.Turksen. Interval-value fuzzy sets and compensatory AND. Fuzzy Sets and Systems, 51(3): 295-307, 1992.
[74] A.Verkeyn, D.Botteldooren, B.De Baets and
G. De Tr ́e. Sugeno integrals for the modelling of noise annoyance aggregation. In T.Bilgic, B.De Baets and O.Kaynak(eds). Fuzzy Sets and Systems – IFSA, 2003: 277-284. Springer Verlag, 2003.
[75] Z.Wang , K.S.Leung, M.L.Wong, J.Fang and K.Xu. Nonlinear nonnegative multiregressions based on Choquet integrals, Int. J. of Approximate Reasoning, 25:71-87, 2000.
[76] X.Z.Wang and J.F.Chen. Multiple neural networks fusion model based on choquet fuzzy integral. In Proc.3d Int. Conf. Machine Learning and Cybernetics, Shanghai, 2004.
[77] Y.M. Wang and C.Parkan. A minimax disparity approach for obtaining OWA operator weights. Information Sciences, 175: 20-29, 2005.
[78] J.W.Wang, J.R.Chang and C.H.Cheng. Flexible fuzzy OWA querying method for hemodialysis database. Soft Computing, 10(11): 1031-1042, 2006.
[79] Z.Xu. An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20(8): 843-865, 2005.
[80] Z.Xu. Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2): 231-238, 2006.
[81] Z.Xu., Dependent OWA operators, in Proceedings of Int. Conf. on Modeling Decisions for Artificial Intelligence MDAI: 172-178, 2006.
[82] R.R.Yager. On the aggregation of processing units in neural networks. In Proc. 1st IEEE Int. Conf. on Neural Networks, San Diego: 927-933, 1987.
[83] R.R.Yager. A note on weighted queries in information retrieval systems. J. Amer. Soc. Information Sciences, 28: 23-24, 1987.
[84] R.R.Yager. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transaction on Systems, Man and Cybernetics, 18: 183-190, 1988.
[85] R.R.Yager. Connectives and quantifiers in fuzzy sets. Fuzzy Sets and Systems, 40: 39-75, 1991.
[86] R.R.Yager. OWA Neurons: A new class of fuzzy neurons. in Proc. Int. Joint on Neural Networks, Baltimore: 226-231, 1992.
[87] R.R.Yager. Fuzzy quotient operator. In Proc. Fourth Int. Conf. on In- formation Processing and Management of Uncertainty. Palma de Majorca: 317-322, 1992.
[88] R.R.Yager. L.S.Goldstein and E.Mendels. FUZMAR: an approach to aggregating market research data based on fuzzy reasoning. Fuzzy Sets and Systems, 68(1): 1-11, 1994.
[89] R.R.Yager. Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems, 11: 49-73, 1996.
[90] R.R.Yager and A.Rybalov. Uninorm Aggregation Operators. Fuzzy Sets and Systems, 80: 111-120, 1996.
[91] R.R.Yager and A.Rybalov. Full reinforcement operators in aggregation techniques. IEEE Transactions on Systems. Man and Cybernetics,
28: 757- 769, 1998.
[92] R.R.Yager. Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems, 122: 167-175, 2001.
[93] R.R.Yager. Centered OWA operators. Soft Computing, 11(7): 631-639, 2007.
[94] Y.Zhang and Z.P.Fan. An approach to multiple attribute group decision making with linguistic information based on ETOWA operators. Proceedings of International Conference of Computers and Industrial Engineering, Taiwan, China, 2006.
[95] H.J.Zimmermann and P.Zysno. Latent connectives in human decision making. Fuzzy Sets and Systems, 4: 37-51, 1980.
[96] T.Boongoen, N. Iam-On and B.Undara. Improving Face Detection with Bi-Level Classification Model. NKRAFA Journal of Science and Technology, 12: 52-63, 2016.
[2] J.Aczel and C.Alsina. Classification of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Meth. Opl. Res, 48: 3-22, 1984.
[3] C.Alsina, E.Trillas and L.Valverde. On some logical connectives for fuzzy sets theory. J.Math. Anal. Appl, 93(1): 15-26, 1983.
[4] S.Auephanwiriyakul, J.Keller and P.Gader. Generalized Choquet fuzzy integral fusion. Information Fusion, 3: 69-85, 2002.
[5] G. Beliakov and J.Warren. Appropriate choice of aggregation operators in fuzzy decision support systems. IEEE Trans. Fuzzy Syst, 9(6): 773-784, 2001.
[6] G. Beliakov, A.Pradera and T.Calvo. Aggregation Functions: A Guide for Practitioners. Springer, Heidelberg. New York: Berlin, 2007.
[7] G.Beliakov, T.Calvo and A.Pradera. Handling of neutral information by aggregation operators. Fuzzy Sets Syst, 158: 861-880, 2007.
[8] G.Beliakov, T.Calvo and A.Pradera. Absorbent tuples of aggregation operators. Fuzzy Sets Syst, 158: 1675-1691, 2007.
[9] P.Bonissone. Selecting uncertainty calculi and granularity: An experiment in trading off precision and complexity. Proceedings of the first Workshop on Uncertainty in Artificial Intelligence. Los Angeles: 57 - 66, 1985.
[10] T. Boongoen and Q. Shen. Clus-DOWA: A New Dependent OWA Operator. Proceedings of IEEE International Conference in Fuzzy Systems.
Hong Kong, China, 2008.
[11] G. Bordogna, M. Fedrizzi and G. Pasi. A linguistic modeling of consensus in group decision making based on OWA operators. IEEE Trans. On Systems, Man and Cybernetics - part A, 27(1): 126-133, 1997.
[12] G.Buyukozkan, G. Mauris, O. Feyzioglu and L.Berrah. Providing eluci-dations of web site evaluation based on a multi-criteria aggregation with the Choquet integral. In Int. Fuzzy Systems Association World Congress (IFSA 2003): 131-134, Istanbul, Turkey, 2003.
[13] T.Calvo, B. De Baets and J.Fodor. The functional equations of Frank and Alsina for uninorms and nullnorms. Fuzzy Sets and Systems, 120: 385-394, 2001.
[14] T.Calvo, G.Mayor and R.Mesiar. (Eds.), Aggregation Operators. New York: Physica-Verlag, 2002.
[15] J.R.Chang, T.H. Ho, C.H.Cheng and A.P.Chen. Dynamic fuzzy OWA model for group multiple criteria decision making. Soft Computing,
10: 543-554, 2006.
[16] C.H.Cheng, J.R.Chang, T.H.Ho and A.P.Chen. Evaluating the Airline Service Quality by Fuzzy OWA Operators. Proceedings of the Modeling Decisions for Artificial Intelligence (MDAI): 77-88, Japan, 2005.
[17] G.Choquet. Theory of capacities. Annales de l’Institut Fourier, 5: 131-295, 1953.
[18] V.Cutello and J.Montero. Hierarchies of aggregation operators. International Journal of Intelligent Systems, 9: 1025-1045, 1994.
[19] B.De Baets and J.Fodor. Van Melle’s combining function in MYCIN is a representable uninorm: an alternative proof. Fuzzy Sets and Systems, 104: 133-136, 1999.
[20] D.Dubois and H.Prade. Triangular norms for fuzzy sets. Proceedings of the 2ndInternational Symposium of Fuzzy Sets, Linz, 39 - 68, 1981.
[21] D.Dubois and H.Prade. A review of fuzzy sets aggregation connectives. Information Sciences, 36: 85 - 121, 1985.
[22] D.Dubois and H.Prade. Weighted minimum and maximum operators in fuzzy set theory. Information Sciences, 39: 205-210, 1986.
[23] D. Dubois, H. Prade and C.Testemale. Weighted fuzzy pattern-matching. Fuzzy Sets and Systems, 28: 313-331, 1988.
[24] D.Dubois, J.L.Marichal, H.Prade, M.Roubens and R.Sabbadin. The use of the discrete Sugeno integral in decision making: a survey. Int. J. of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(5): 539-561, 2001.
[25] D.P. Filev and R.R.Yager. Fuzzy logic controllers with flexible structures. Proc. Second Int. Conf. on Fuzzy Sets and Neural Networks, Iizuka: 317- 320, 1992.
[26] D.Filev and R.R.Yager. On the issue of obtaining OWA operator weights. Fuzzy Sets and Systems, 94(2): 157-169, 1998.
[27] J.C. Fodor, R.R.Yager and A. Rybalov. Structure of Uninorms, International Journal of Uncertainty. Fuzziness and Knowledge- Based Systems, 5: 411-427, 1997.
[28] R.Fuller and P.Majlender. An analytic approach for obtaining maximal entropy OWA operator weights. Fuzzy Sets and Systems, 124: 53-57, 2001.
[29] R.Fuller and P.Majlender. On obtaining minimal variablity OWA operator weights. Fuzzy Sets and Systems, 136: 203-215, 2003.
[30] P.Gader, W.H.Lee and X.P.Zhang. Renyi entropy with respect to choquet capacities. In Proc. IEEE Conf. Fuzzy Systems. Budapest, Hungary, 2004.
[31] M.Grabisch. On the use of fuzzyintegral as a fuzzy connective. Proceedings of the Second IEEE International Conference on Fuzzy Systems,
San Francisco: 213-218, 1993.
[32] M.Grabisch. Fuzzy integral in multicriteria decision making. Fuzzy Sets and Systems, 69: 279-298, 1995.
[33] M.Grabisch, H.T.Nguyen and E.A.Walker. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference. Kluwer Academic, 1995.
[34] M.Grabisch. The application of fuzzy integrals in multicriteria decision making. European J. of Operational Research, 89: 445-456, 1996.
[35] M.Grabisch and F.Huet. Texture recognition by Choquet integral filters, in 6th Int. Conf. on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU): 1325-1330, Granada, Spain, 1996.
[36] M.Grabisch, S.A.Orlovski and R.R.Yager. Fuzzy aggregations of numerical preferences. In Slowinski R.(ed). Fuzzy Sets in Decision Analysis. Operations Research and Statistics. Kluwer Academic Publishers, 1998.
[37] M.Grabisch. Fuzzy integral for classification and feature extraction. In M.Grabisch, T.Murofushi and M.Sugeno (eds). Fuzzy Measures and Integrals-Theory and Applications: 415-434. Physica Verlag, 2000.
[38] M.Grabisch M, J.Duchene, F. Lino and P.Perny. Subjective evaluation of discomfort in sitting position. Fuzzy Optimization and Decision Making, 1(3): 287-312, 2002.
[39] F.Herrera, E.Herrera-Viedma and J.L.Verdegay. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets and Systems, 78: 73-87, 1996.
[40] F.Herrera and L.Martinez. A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Transactions on Systems, Man and Cybernetics, 8: 746-752, 2000.
[41] F.Herrera and L.Martinez. A model based on linguistic 2-tuple for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision- making. IEEE Transactions on Systems, Man and Cybernetics, 31: 227-234, 2001.
[42] U.Hohle. Probabilistic uniformization of fuzzy topologies. Fuzzy Sets and Systems1, 1978.
[43] J.Kacprzyk and R.R.Yager(eds). The ordered weighted averaging operators: theory and applications. Norwell,MA: Kluwer Academic Publishers, 1997.
[44] J.M. Keller, P.D. Gader and A.K.Hocaoglu. Fuzzy integrals in image processing and recognition, in M.Grabisch. T.Murofushi and M.Sugeno(eds). Fuzzy Measures and Integrals - Theory and Applications: 435-466. Physica Verlag, 2000.
[45] E.P.Klement. A theory of fuzzy measures: a survey, in M.Gupta and E.Sanchez(eds). Fuzzy Information and Decision Processes, North Holland: Amsterdam: 59-66, 1982.
[46] E.P.Klement, R.Mesiar and E.Pap. On the relationship of associative compensatory operators to triangular norms and conforms. International Journal Uncertainty. Fuzziness and Knowledge based Systems, 4(2): 129- 144, 1996.
[47] E.P.Klement, R.Mesiar and E.Pap. Triangular norms, Trends in Logic. Studia Logica Library, 8, Kluwer Academic Publishers, 2000.
[48] G.J.Klir. and T.A.Folger. Fuzzy Sets, Uncertainty and Information. Englewood Cliffs, N.J: Prentice-Hall, 1988.
[49] S.H.Kwon and M. Sugeno. A hierarchical subjective evaluation model using non-monotonic fuzzy measures and the Choquet integral. in M.Grabisc, T.Murofushi and M.Sugeno (eds). Fuzzy Measures and Integrals – Theory and Applications: 375-391. Physica Verlag, 2000.
[50] X.W.Liu and L.H.Chen. The equivalence of maximum entropy OWA operator and geometric OWA operator. International Conference on Machine Learning and Cybernetics: 2673-2676, 2003.
[51] B.Llamazares. Choosing OWA operator weights in the field of Social Choice. Information Sciences, 177(21): 4745-4756, 2007.
[52] M.K. Luhandjula. Compensatory operators in fuzzy linear programming with multiple objectives. Fuzzy Sets and Systems, 8: 245-252, 1982.
[53] J.L.Marichal.On Sugeno integral as an aggregation function. Fuzzy Sets and Systems, 114: 347-365, 2000.
[54] M.Mas, G.Mayor and J.Torrens. t-operators, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems, 7(1): 31-50, 1999.
[55] M.Mas, R.Mesiar, M.Monserrat and J.Torrens. Aggregation operators with annihilator. International Journal of General Systems, 34(1): 1-22, 2005.
[56] H.B.Mitchell and D.D.Estrakh. A modified OWA operator and its use in lossless DPCM image compression. International Journal of Uncertain Fuzziness. Knowledge Based Systems, 5 429-436, 1997.
[57] H.B.Mitchell and P.A.Schaefer. Multiple priorities in an induced ordered weighted averaging operator. International Journal ofIntelligent Systems, 15: 317-327, 2000.
[58] T.Murofushi and M.Sugeno. Non-additivity of fuzzy measures representing preferential dependence. In 2nd Int. Conf. on Fuzzy Systems and Neural Networks: 617-620 , Iizuka, Japan, 1992.
[59] T.Murofushi and M.Sugeno. Some quantities represented by the Choquet integral. Fuzzy Sets and Systems, 56: 229-235, 1993.
[60] M.O’Hagan. Aggregating template rule antecedents in real-time expert systems with fuzzy set logic. Proceedings of Annual IEEE Conference on Signals, Systems, and Computers: 681-689, 1988.
[61] J.Quiggin. A theory of anticipated utility. Journal of Economic Behavior and Organization, 3: 323-343, 1982.
[62] T.L.Saaty. The Analytic Hierarchy Process. New York: McGraw-Hill, 1980.
[63] B. Schweizer and A. Sklar A. Probabilistic metric spaces. Amsterdam: North-Holland,1983.
[64] U.Segal. Order indifference and rank dependent probabilities. Journal of Math. Economics, 22: 373-397, 1993.
[65] A.Soria-Frisch. Unsupervised construction of fuzzy measures through self-organizing feature maps and its application in color image segmentation. Int. J. Approx. Reason. 41: 23-42, 2006.
[66] M.Sugeno. Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of Technology, 1974.
[67] V.Torra. The weighted OWA operator. International Journal of Intelligent Systems, 12(2): 153-166, 1997.
[68] V.Torra. Learning weights for the quasi- weighted mean. IEEE Trans. Fuzzy Syst, 10(5): 653-666, 2002.
[69] V.Torra and Y.Narukawa. A View of Averaging Aggregation Operators. IEEE Transaction on Fuzzy Systems, 15(6): 1063-1967, 2007.
[70] V.Torra and Y.Narukawa. Modeling Decisions: Aggregation Operators and Information Fusion. , NewYork : Springer, 2007.
[71] L.Troiano and R.R. Yager. Recursive and iterative OWA operators, International Journal of Uncertainty. Fuzziness and Knowledge-Based Systems, 13(6): 579-599, 2005.
[72] A.Tsadiras and K. Margaritis. The MYCIN certainty factor handling function as uninorm operator and its use as a threshold function in artificial neurons. Fuzzy Sets and Systems, 93: 263-274, 1999.
[73] I.B.Turksen. Interval-value fuzzy sets and compensatory AND. Fuzzy Sets and Systems, 51(3): 295-307, 1992.
[74] A.Verkeyn, D.Botteldooren, B.De Baets and
G. De Tr ́e. Sugeno integrals for the modelling of noise annoyance aggregation. In T.Bilgic, B.De Baets and O.Kaynak(eds). Fuzzy Sets and Systems – IFSA, 2003: 277-284. Springer Verlag, 2003.
[75] Z.Wang , K.S.Leung, M.L.Wong, J.Fang and K.Xu. Nonlinear nonnegative multiregressions based on Choquet integrals, Int. J. of Approximate Reasoning, 25:71-87, 2000.
[76] X.Z.Wang and J.F.Chen. Multiple neural networks fusion model based on choquet fuzzy integral. In Proc.3d Int. Conf. Machine Learning and Cybernetics, Shanghai, 2004.
[77] Y.M. Wang and C.Parkan. A minimax disparity approach for obtaining OWA operator weights. Information Sciences, 175: 20-29, 2005.
[78] J.W.Wang, J.R.Chang and C.H.Cheng. Flexible fuzzy OWA querying method for hemodialysis database. Soft Computing, 10(11): 1031-1042, 2006.
[79] Z.Xu. An overview of methods for determining OWA weights. International Journal of Intelligent Systems, 20(8): 843-865, 2005.
[80] Z.Xu. Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2): 231-238, 2006.
[81] Z.Xu., Dependent OWA operators, in Proceedings of Int. Conf. on Modeling Decisions for Artificial Intelligence MDAI: 172-178, 2006.
[82] R.R.Yager. On the aggregation of processing units in neural networks. In Proc. 1st IEEE Int. Conf. on Neural Networks, San Diego: 927-933, 1987.
[83] R.R.Yager. A note on weighted queries in information retrieval systems. J. Amer. Soc. Information Sciences, 28: 23-24, 1987.
[84] R.R.Yager. On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transaction on Systems, Man and Cybernetics, 18: 183-190, 1988.
[85] R.R.Yager. Connectives and quantifiers in fuzzy sets. Fuzzy Sets and Systems, 40: 39-75, 1991.
[86] R.R.Yager. OWA Neurons: A new class of fuzzy neurons. in Proc. Int. Joint on Neural Networks, Baltimore: 226-231, 1992.
[87] R.R.Yager. Fuzzy quotient operator. In Proc. Fourth Int. Conf. on In- formation Processing and Management of Uncertainty. Palma de Majorca: 317-322, 1992.
[88] R.R.Yager. L.S.Goldstein and E.Mendels. FUZMAR: an approach to aggregating market research data based on fuzzy reasoning. Fuzzy Sets and Systems, 68(1): 1-11, 1994.
[89] R.R.Yager. Quantifier guided aggregation using OWA operators. International Journal of Intelligent Systems, 11: 49-73, 1996.
[90] R.R.Yager and A.Rybalov. Uninorm Aggregation Operators. Fuzzy Sets and Systems, 80: 111-120, 1996.
[91] R.R.Yager and A.Rybalov. Full reinforcement operators in aggregation techniques. IEEE Transactions on Systems. Man and Cybernetics,
28: 757- 769, 1998.
[92] R.R.Yager. Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems, 122: 167-175, 2001.
[93] R.R.Yager. Centered OWA operators. Soft Computing, 11(7): 631-639, 2007.
[94] Y.Zhang and Z.P.Fan. An approach to multiple attribute group decision making with linguistic information based on ETOWA operators. Proceedings of International Conference of Computers and Industrial Engineering, Taiwan, China, 2006.
[95] H.J.Zimmermann and P.Zysno. Latent connectives in human decision making. Fuzzy Sets and Systems, 4: 37-51, 1980.
[96] T.Boongoen, N. Iam-On and B.Undara. Improving Face Detection with Bi-Level Classification Model. NKRAFA Journal of Science and Technology, 12: 52-63, 2016.