Trapezoid fuzzy linguistic prioritized weighted average operators and their application to multiple attribute group decision-making
Tóm tắt
The prioritized weighted average (PWA) operator was originally introduced by Yager. The prominent characteristic of the PWA operator is that it takes into account prioritization among attributes and decision makers. Motivated by the idea of PWA operator, we develop some prioritized weighted aggregation operators for aggregating trapezoid fuzzy linguistic information. The properties of the new aggregation operators are studied in detail. Furthermore, based on the proposed operators, some approaches to deal with multiple attribute group decision-making problems under trapezoid fuzzy linguistic environments are developed. Finally, a practical example is provided to illustrate the multiple attribute group decision-making process.
Tài liệu tham khảo
Beliakov G, Pradera A, Calvo T: Aggregation functions: a guide for practitioners. Springer, Berlin; 2007.
Calvo T, Mayor G, Mesiar R: Aggregation operators: new trends and applications. Physica-Verlag, Berlin; 2002.
Xu ZS: Da, QL: An overview of operators for aggregating information. Int. J. Intell. Syst. 2003, 18(9):953–969. 10.1002/int.10127
Yager RR, Kacprzyk J: The ordered weighted averaging operator: theory and applications. Kluwer, Boston; 1997.
Yager RR: On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Trans. Syst. Man Cybern. B Cybern. 1988, 18(1):183–190. 10.1109/21.87068
Bordonga G, Fedrizzi M, Passi G: A linguistic modelling of consensus in group decision making based on OWA operators. IEEE Trans. Syst. Man Cybern. Syst. Hum 1997, 27(1):126–132. 10.1109/3468.553232
Chen H, Liu C, Sheng Z: Induced ordered weighted harmonic averaging (IOWHA) operator and its application to combination forecasting method. Chin. J. Manage. Sci. 2004, 12: 35–40.
Chiclana F, Herrera F, Viedma EH: The ordered weighted geometric operator: properties and applications. In Proceedings of the 8th International Conference on Information Processing and Management of Uncertainty in Knowledge Based Systems. Madrid, Spain; 2000:985–991.
Fodor J, Marichal JL, Roubens M: Characterization of the ordered weighted averaging operators. IEEE Trans. Fuzzy Syst. 1995, 3(2):236–240. 10.1109/91.388176
Merigó JM: A unified model between the weighted average and the induced OWA operator. Expert Syst. Appl. 2011, 8(9):11560–11572.
Merigó JM, Gil-Lafuente AM: The induced generalized OWA operator. Inf. Sci. 2009, 179(6):729–741. 10.1016/j.ins.2008.11.013
Merigó JM, Casanovas M: The fuzzy generalized OWA operator and its application in strategic decision making. Cybern. Syst. 2010, 41(5):359–370. 10.1080/01969722.2010.486223
Merigó JM, Casanovas M: Induced and uncertain heavy OWA operators. Comp. Ind. Eng. 2011, 60(1):106–116. 10.1016/j.cie.2010.10.005
Merigó JM, Casanovas M: The uncertain induced quasi-arithmetic OWA operator. Int. J. Intell. Syst. 2011, 26(1):1–24. 10.1002/int.20444
Merigó JM, Casanovas M, Martìnez L: Linguistic aggregation operators for linguistic decision making based on the Dempster-Shafer theory of evidence. International Journal Uncertainty, Fuzziness and Knowledge Based Systems 2010, 18(3):287–304. 10.1142/S0218488510006544
Wang XR, Fan ZP: Fuzzy ordered weighted averaging operator and its applications. Fuzzy Syst. Math. 2003, 17(4):67–72.
Wei GW: FIOWHM operator and its application to multiple attribute group decision making. Expert Syst. Appl. 2011, 38(4):2984–2989. 10.1016/j.eswa.2010.08.087
Xu ZS: Fuzzy ordered weighted geometric operator and its applications in fuzzy AHP. Syst. Eng. Electron. 2002, 31(4):855–858.
Xu ZS, QL D: The ordered weighted geometric averaging operators. Int. J. Intell. Syst. 2002, 17(7):709–716. 10.1002/int.10045
Xu ZS: A priority method for triangular fuzzy number complementary judgment matrix. Syst. Eng. Theor. Pract. 2003, 23(10):86–89.
Xu ZS: EOWA and EOWG operators for aggregating linguistic labels based on linguistic preference relations. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 2004, 12(6):791–810. 10.1142/S0218488504003211
Xu ZS: An approach based on the uncertain LOWG and induced uncertain LOWG operators to group decision making with uncertain multiplicative linguistic preference relations. Decis. Support. Syst. 2006, 41(2):488–499. 10.1016/j.dss.2004.08.011
Xu ZS, Xia G, Chen M, Wang L: Induced generalized intuitionistic fuzzy OWA operator for multi-attribute group decision making. Expert Syst. Appl. 2012, 39(2):1902–1910. 10.1016/j.eswa.2011.08.057
Yager RR: Families of OWA operators. Fuzzy Sets Syst. 1993, 59(2):125–148. 10.1016/0165-0114(93)90194-M
Yager RR: Quantifier guided aggregation using OWA operators. Int. J. Intell. Syst. 1996, 11(1):49–73. 10.1002/(SICI)1098-111X(199601)11:1<49::AID-INT3>3.3.CO;2-L
Yager RR: Generalized OWA aggregation operators. Fuzzy Optim. Decis. Making 2004, 3(1):93–107.
Yager RR: Centered OWA operators. Soft. Comput. 2007, 11(7):631–639. 10.1007/s00500-006-0125-z
Yager RR, Kacprzyk J, Beliakov G: Recent developments in the ordered weighted averaging operator: theory and practice. Springer, Heidelberg; 2011.
Dyckhoff H, Pedrycz W: Generalized means as model of compensative connectives. Fuzzy Sets Syst. 1984, 14(2):143–154. 10.1016/0165-0114(84)90097-6
Herrera F, Martínez L: An approach for combining numerical and linguistic information based on the 2-tuple fuzzy linguistic representation model in decision making. Int.J. Uncertainty Fuzziness Knowl. Based Syst. 2000, 8(5):539–562. 10.1142/S0218488500000381
Xu ZS: Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment. Inf. Sci. 2004, 168(1–4):171–184.
Wei GW: Uncertain linguistic hybrid geometric mean operator and its application to group decision making under uncertain linguistic environment. Int. J. Uncertainty Fuzziness Knowl. Based Syst. 2009, 17(2):251–267. 10.1142/S021848850900584X
Xu ZS: Group decision making with triangular fuzzy linguistic variables. Springer, Berlin, Heidelberg; 2007:17–26.
Xu ZS: An approach based on similarity measure to multiple attribute decision making with trapezoid fuzzy linguistic variables. Springer, Berlin, Heidelberg; 2005:110–117.
Liang XC, Chen SF: Multiple attribute decision making method based on trapezoid fuzzy linguistic variables. J. Southeast Univ. (English Edition) 2008, 24(4):478–481.
Wei GW, Yi WD: Trapezoid fuzzy linguistic weighted geometric averaging operator. In Proceedings of the 4th International Conference on Fuzzy System and Knowledge Discovery. Haikou; 2007:300–304.
Liu P, Su Y: The multiple attribute decision making method based on the TFLHOWA operator. Comput. Math. Appl. 2010, 60(9):2609–2615. 10.1016/j.camwa.2010.08.087
Liu P, Su Y: Multiple attribute decision making method based on the trapezoid fuzzy linguistic hybrid harmonic averaging operator. Informatica 2012, 36(1):83–90.
Bonferroni C: Sulle medie multiple di potenze. Bollettino dell’Unione Matematica Italiana 1950, 5(3):267–270.
Liu P, Jin Y: The trapezoid fuzzy linguistic Bonferroni mean operators and their application to multiple attribute decision making. Scientia Iranica 2012, 19(6):1947–1959. 10.1016/j.scient.2012.06.028
Liu P, Wu X: Multiple attribute decision making method based on the generalized aggregation operators in trapezoid fuzzy linguistic variables. J. Comput. Anal. Appl. 2013, 15(5):807–816.
Yager RR: Prioritized aggregation operators. Int. J. Approx. Reason. 2008, 48(1):263–274. 10.1016/j.ijar.2007.08.009
Yager RR: Prioritized OWA aggregation. Fuzzy Optim. Decis. Making 2009, 8(3):245–262. 10.1007/s10700-009-9063-4