Abstract
We introduce a wide range of induced and linguistic generalized aggregation operators. First, we present the induced linguistic generalized ordered weighted averaging (ILGOWA) operator. It is a generalization of the OWA operator that uses linguistic variables, order inducing variables and generalized means in order to provide a more general formulation. One of its main results is that it includes a wide range of linguistic aggregation operators such as the induced linguistic OWA (ILOWA), the induced linguistic OWG (ILOWG) and the linguistic generalized OWA (LGOWA) operator. We further generalize the ILGOWA operator by using quasi-arithmetic means obtaining the induced linguistic quasi-arithmetic OWA (Quasi-ILOWA) operator and by using hybrid averages forming the induced linguistic generalized hybrid average (ILGHA) operator. We also present a further extension with Choquet integrals. We call it the induced linguistic generalized Choquet integral aggregation (ILGCIA). We end the paper with an application of the new approach in a linguistic group decision making problem.
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References
Beliakov G, Pradera A, Calvo T (2007) Aggregation functions: a guide for practitioners. Springer, Berlin
Bonissone PP (1982) A fuzzy sets based linguistic approach: theory and applications. In: Gupta MM, Sanchez E (eds) Approximate reasoning in decision analysis. North-Holland, Amsterdam, pp 329–339
Bryson N, Mobolurin A (1995) An action learning evaluation procedure for multiple criteria decision making problems. Eur J Oper Res 96: 379–386
Calvo T, Mayor G, Mesiar R (2002) Aggregation operators: new trends and applications. Physica-Verlag, New York
Carlsson C, Fuller R (2000) Benchmarking and linguistic importance weighted aggregations. Fuzzy Sets Syst 114: 35–42
Carlsson C, Fuller R, Majlender P (2003) A note on constrained OWA aggregation. Fuzzy Sets Syst 139: 543–546
Chang KH, Wen TC (2010) A novel efficient approach for DFMEA combining 2-tuple and the OWA operator. Expert Syst Appl 37: 2362–2370
Choquet G (1953) Theory of capacities. Ann Inst Fourier 5: 131–295
Emrouznejad A, Amin GR (2010) Improving minimax disparity model to determine the OWA operator weights. Inf Sci 180: 1477–1485
Fodor J, Marichal JL, Roubens M (1995) Characterization of the ordered weighted averaging operators. IEEE Trans Fuzzy Syst 3: 236–240
Herrera F, Martínez L (2000) A 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 8: 746–752
Herrera F, Herrera-Viedma E, Verdegay JL (1995) A sequential selection process in group decision making with a linguistic assessment approach. Inf Sci 85: 223–239
Herrera F, Herrera-Viedma E, Martínez L (2008) A fuzzy linguistic methodology to deal with unbalanced linguistic term sets. IEEE Trans Fuzzy Syst 16: 354–370
Karayiannis N (2000) Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators. IEEE Trans Neural Netw 11: 1093–1105
Merigó JM (2010) Fuzzy decision making using immediate probabilities. Comput Ind Eng 58: 651–657
Merigó JM, Casanovas M (2009) Induced aggregation operators in decision making with the Dempster-Shafer belief structure. Int J Intell Syst 24: 934–954
Merigó JM, Casanovas M (2010a) The fuzzy generalized OWA operator and its application in strategic decision making. Cybern Syst 41: 359–370
Merigó JM, Casanovas M (2010b) Fuzzy generalized hybrid aggregation operators and its application in decision making. Int J Fuzzy Syst 12: 15–24
Merigó JM, Casanovas M (2010c) Induced and heavy aggregation operators with distance measures. J Syst Eng Electron 21: 431–439
Merigó JM, Casanovas M (2010d) Decision making with distance measures and linguistic aggregation operators. Int J Fuzzy Syst 12: 190–198
Merigó JM, Gil-Lafuente AM (2008) The induced linguistic generalized OWA operator. In: Proceedings of the FLINS 2008 international conference, Madrid, pp 325–330
Merigó JM, Gil-Lafuente AM (2009) The induced generalized OWA operator. Inf Sci 179: 729–741
Merigó JM, Gil-Lafuente AM (2010) New decision making techniques and their application in the selection of financial products. Inf Sci 180: 2085–2094
Merigó JM, Casanovas M, Martínez L (2010) Linguistic aggregation operators for linguistic decision making based on the Dempster–Shafer theory of evidence. Int J Uncertain Fuzz Knowl Based Syst 18: 287–304
Mesiar R (1995) Choquet-like integrals. J Math Anal Appl 194: 477–488
Mesiar R, Pap E (2008) Aggregation of infinite sequences. Inf Sci 178: 3557–3564
Sugeno M (1974) Theory of fuzzy integrals and its applications. PhD Thesis, Tokyo Institute of Technology
Tan C, Chen X (2010a) Induced Choquet ordered averaging operator and its application in group decision making. Int J Intell Syst 25: 59–82
Tan C, Chen X (2010b) Intuitionistic fuzzy Choquet integral operator for multi-criteria decision making. Expert Syst Appl 37: 149–157
Wang JH, Hao J (2006) A new version of 2-tuple fuzzy linguistic representation model for computing with words. IEEE Trans Fuzzy Syst 14: 435–445
Wei GW (2009) Uncertain linguistic hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment. Int J Uncertain Fuzz Knowl Based Syst 17: 251–267
Wei GW, Zhao X, Lin R (2010) Some induced aggregating operators with fuzzy number intuitionistic fuzzy information and their applications to group decision making. Int J Comput Intell Syst 3: 84–95
Xu ZS (2004) EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int J Uncertain Fuzz Knowledge-Based Syst 12: 791–810
Xu ZS (2006a) Induced uncertain linguistic OWA operators applied to group decision making. Inform Fusion 7: 231–238
Xu ZS (2006b) On generalized induced linguistic aggregation operators. Int J General Syst 35: 17–28
Xu ZS (2006c) A note on linguistic hybrid arithmetic averaging operator in group decision making with linguistic information. Group Decis Negotiat 15: 581–591
Xu ZS (2008) Linguistic aggregation operators: an overview. In: Bustince H, Herrera F, Montero J (eds) Fuzzy sets and their extensions: representation, aggregation and models. Springer, Berlin, pp 163–181
Xu ZS (2009) An interactive approach to multiple attribute group decision making with multigranular uncertain linguistic information. Group Decis Negotiat 18: 119–145
Xu ZS (2010a) Choquet integrals of weighted intuitionistic fuzzy information. Inf Sci 180: 726–736
Xu ZS (2010b) A deviation-based approach to intuitionistic fuzzy multiple attribute group decision making. Group Decis Negotiat 19: 57–76
Xu ZS, Da QL (2003) An overview of operators for aggregating information. Int J Intell Syst 18: 953–969
Xu YJ, Da QL, Liu XW (2010) Some properties of linguistic preference relation and its ranking in group decision making. J Syst Eng Electron 21: 244–249
Yager RR (1988) On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans Syst Man Cybern B 18: 183–190
Yager RR (1993) Families of OWA operators. Fuzzy Sets Syst 59: 125–148
Yager RR (2003) Induced aggregation operators. Fuzzy Sets Syst 137: 59–69
Yager RR (2004a) Choquet aggregation using order inducing variables. Int J Uncertain Fuzz Knowl Based Syst 12: 69–88
Yager RR (2004b) Generalized OWA aggregation operators. Fuzzy Optim Decis Mak 3: 93–107
Yager RR (2010) Norms induced from OWA operators. IEEE Trans Fuzzy Syst 18: 57–66
Yager RR, Filev DP (1999) Induced ordered weighted averaging operators. IEEE Trans Syst Man Cybern B 29: 141–150
Yager RR, Kacprzyk J (1997) The ordered weighted averaging operators: theory and applications. Kluwer, Norwell
Zadeh LA (1975) The concept of a linguistic variable and its application to approximate reasoning. Part 1. Inf Sci 8:199–249; Part 2. Inf Sci 8:301–357; Part 3. Inf Sci 9:43–80
Zhao H, Xu ZS, Ni M, Liu S (2010) Generalized aggregation operators for intuitionistic fuzzy sets. Int J Intell Syst 25: 1–30
Zhou LG, Chen HY (2010a) Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. Int J Intell Syst 25: 683–707
Zhou LG, Chen HY (2010b) Continuous generalized OWA operator and its application to decision making. Fuzzy Sets Syst (in press). doi:10.1016/j.fss.2010.05.009
Zhou SM, John RI, Chiclana F, Garibaldi JM (2010) On aggregating uncertain information by type-2 OWA operators for soft decision making. Int J Intell Syst 25: 540–558
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Merigó, J.M., Gil-Lafuente, A.M., Zhou, LG. et al. Induced and Linguistic Generalized Aggregation Operators and Their Application in Linguistic Group Decision Making. Group Decis Negot 21, 531–549 (2012). https://doi.org/10.1007/s10726-010-9225-3
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DOI: https://doi.org/10.1007/s10726-010-9225-3