Induced and logarithmic distances with multi-region aggregation operators
Abstract
This paper introduces the induced ordered weighted logarithmic averaging IOWLAD and multiregion induced ordered weighted logarithmic averaging MR-IOWLAD operators. The distinctive characteristic of these operators lies in the notion of distance measures combined with the complex reordering mechanism of inducing variables and the properties of the logarithmic averaging operators. The main advantage of MR-IOWLAD operators is their design, which is specifically thought to aid in decision-making when a set of diverse regions with different properties must be considered. Moreover, the induced weighting vector and the distance measure mechanisms of the operator allow for the wider modeling of problems, including heterogeneous information and the complex attitudinal character of experts, when aiming for an ideal scenario. Along with analyzing the main properties of the IOWLAD operators, their families and specific cases, we also introduce some extensions, such as the induced generalized ordered weighted averaging IGOWLAD operator and Choquet integrals. We present the induced Choquet logarithmic distance averaging ICLD operator and the generalized induced Choquet logarithmic distance averaging IGCLD operator. Finally, an illustrative example is proposed, including real-world information retrieved from the United Nations World Statistics for global regions.
First published online 5 April 2019
Keyword : OWA, decision-making science, logarithmic OWA operators, multiregion AGOP, induced OWA operators, distance OWA operators, induced distance logarithmic AGOP
How to Cite
Alfaro-García, V. G., Merigó, J. M., Plata-Pérez, L., Alfaro-Calderón, G. G., & Gil-Lafuente, A. M. (2019). Induced and logarithmic distances with multi-region aggregation operators. Technological and Economic Development of Economy, 25(4), 664-692. https://doi.org/10.3846/tede.2019.9382
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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León-Castro, E., Avilés-Ochoa, E. A., & Gil-Lafuente, A. M. (2016). Exchange rate USD/MXN forecast through econometric models, time series and HOWMA operators. Economic Computation & Economic Cybernetics Studies & Research, 50(4), 135-150.
León-Castro, E., Avilés-Ochoa, E., Merigó, J. M., & Gil-Lafuente, A. M. (2018). Heavy moving averages and their application in econometric forecasting. Cybernetics and Systems, 49(1), 26-43. https://doi.org/10.1080/01969722.2017.1412883
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Lv, K., Yu, A., Gong, S., Wu, M., & Xu, X. (2017). Impacts of educational factors on economic growth in regions of China: a spatial econometric approach. Technological and Economic Development of Economy, 23(6), 827-847. https://doi.org/10.3846/20294913.2015.1071296
Maldonado, S., Merigó, J. M., & Miranda, J. (2018). Redefining support vector machines with the ordered weighted average. Knowledge-Based Systems, 148, 41-46. https://doi.org/10.1016/j.knosys.2018.02.025
Merigó, J. M., & Casanovas, M. (2011). Decision-making with distance measures and induced aggregation operators. Computers and Industrial Engineering, 60(1), 66-76. https://doi.org/10.1016/j.cie.2010.09.017
Merigó, J. M., & Gil-Lafuente, A. M. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085-2094. https://doi.org/10.1016/j.ins.2010.01.028
Merigó, J. M., Peris-Ortíz, M., Navarro-García, A., & Rueda-Armengot, C. (2016). Aggregation operators in economic growth analysis and entrepreneurial group decision-making. Applied Soft Computing Journal, 47, 141-150. https://doi.org/10.1016/j.asoc.2016.05.031
Merigó, J. M., & Yager, R. R. (2013). Generalized moving averages, distance measures and OWA operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(04), 533-559. https://doi.org/10.1142/S0218488513500268
Mesiar, R. (1995). Choquet-like integrals. Journal of Mathematical Analysis and Applications, 194(2), 477-488. https://doi.org/10.1006/jmaa.1995.1312
Mesiar, R., Kolesárová, A., Bustince, H., Dimuro, G. P., & Bedregal, B. C. (2016). Fusion functions based discrete choquet-like integrals. European Journal of Operational Research, 252(2), 601-609. https://doi.org/10.1016/j.ejor.2016.01.027
Su, W., Zeng, S., & Ye, X. (2013). Uncertain group decision-making with induced aggregation operators and euclidean distance. Technological and Economic Development of Economy, 19(3), 431-447. https://doi.org/10.3846/20294913.2013.821686
Sucháček, J., Seďa, P., Friedrich, V., & Koutský, J. (2017). Regional aspects of the development of largest enterprises in the Czech Republic. Technological and Economic Development of Economy, 23(4), 649-666. https://doi.org/10.3846/20294913.2017.1318314
Tan, C., & Chen, X. (2010). Induced choquet ordered averaging operator and its application to group decision making. International Journal of Intelligent Systems, 25(1), 59-82. https://doi.org/10.1002/int.20388
United Nations. (2017). World Statistics Pocketbook 2017 edition (41st ed.). New York: United Nations Publications. https://doi.org/10.18356/c983bdf2-en
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Xian, S. D., Sun, W. J., Xu, S. H., & Gao, Y. Y. (2016). Fuzzy linguistic induced OWA minkowski distance operator and its application in group decision making. Pattern Analysis and Applications, 19(2), 325-335. https://doi.org/10.1007/s10044-014-0397-3
Xu, Z. S., & Chen, J. (2008). Ordered weighted distance measure. Journal of Systems Science and Systems Engineering, 17(4), 432-445. https://doi.org/10.1007/s11518-008-5084-8
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man and Cybernetics B, 18(1), 183-190. https://doi.org/10.1109/21.87068
Yager, R. R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59(2), 125-148. https://doi.org/10.1016/0165-0114(93)90194-M
Yager, R. R. (2003). Induced aggregation operators. Fuzzy Sets and Systems, 137(1), 59-69. https://doi.org/10.1016/S0165-0114(02)00432-3
Yager, R. R., & Filev, D. P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 29(2), 141-150. https://doi.org/10.1109/3477.752789
Zeng, S. (2017). Pythagorean fuzzy multiattribute group decision making with probabilistic information and owa approach. International Journal of Intelligent Systems, 32(11), 1136-1150. https://doi.org/10.1002/int.21886
Zeng, S., Llopis-Albert, C., & Zhang, Y. (2018). A novel induced aggregation method for intuitionistic fuzzy set and its application in multiple attribute group decision making. International Journal of Intelligent Systems, 33(11), 2175-2188. https://doi.org/10.1002/int.22009
Zeng, S., Su, W., & Zhang, C. (2016). Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making. Technological and Economic Development of Economy, 22(2), 177-193. https://doi.org/10.3846/20294913.2014.984253
Zeng, S., & Xiao, Y. (2018). A method based on topsis and distance measures for hesitant fuzzy multiple attibute decision making. Technological and Economic Development of Economy, 24(3), 969-983. https://doi.org/10.3846/20294913.2016.1216472
Zeng, S., & Su, W. H. (2011). Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems, 24(8), 1224-1232. https://doi.org/10.1016/j.knosys.2011.05.013
Zeng, S., & Weihua, S. (2012). Linguistic induced generalized aggregation distance operators and their application to decision making. Economic Computation and Economic Cybernetics Studies and Research, 46(2), 155-172.
Zhou, L., & Chen, H. (2010). Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. International Journal of Intelligent Systems, 25(7), 683-707. https://doi.org/10.1002/int.20419
Zhou, L., Chen, H., & Liu, J. (2012). Generalized logarithmic proportional averaging operators and their applications to group decision making. Knowledge-Based Systems, 36, 268-279. https://doi.org/10.1016/j.knosys.2012.07.006
Zhou, L., Tao, Z., Chen, H., & Liu, J. (2014). Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making. Soft Computing, 19(3), 715-730. https://doi.org/10.1007/s00500-014-1295-8
Zwick, R., Carlstein, E., & Budescu, D. V. (1987). Measures of similarity among fuzzy concepts: a comparative analysis. International Journal of Approximate Reasoning, 1(2), 221-242. https://doi.org/10.1016/0888-613X(87)90015-6
Alfaro-García, V. G., Gil-Lafuente, A. M., & Merigó, J. M. (2016). Induced generalized ordered weighted logarithmic aggregation operators. In 2016 IEEE Symposium Series on Computational Intelligence (SSCI) (pp. 1-7). Athens, Greece. https://doi.org/10.1109/SSCI.2016.7850012
Alfaro-García, V. G., Merigó, J. M., Gil-Lafuente, A. M., & Kacprzyk, J. (2018). Logarithmic aggregation operators and distance measures. International Journal of Intelligent Systems, 33(7), 1488-1506. https://doi.org/10.1002/int.21988
Avilés-Ochoa, E., León-Castro, E., Perez-Arellano, L. A., & Merigó, J. M. (2018). Government transparency measurement through prioritized distance operators. Journal of Intelligent & Fuzzy Systems, 34(4), 2783-2794. https://doi.org/10.3233/JIFS-17935
Batabyal, A. A., & Yoo, S. J. (2018). Schumpeterian creative class competition, innovation policy, and regional economic growth. International Review of Economics and Finance, 55, 86-97. https://doi.org/10.1016/j.iref.2018.01.016
Beliakov, G., Bustince, H., & Calvo, T. (2016). A practical guide to averaging functions (Vol. 329). Springer International Publishing. https://doi.org/10.1007/978-3-319-24753-3
Beliakov, G., Pradera, A., & Calvo, T. (2007). Aggregation functions: a guide for practitioners (Vol. 221). Springer Berlin Heidelberg.
Blanco-Mesa, F., León-Castro, E., & Merigó, J. M. (2018). Bonferroni induced heavy operators in ERM decision-making: A case on large companies in Colombia. Applied Soft Computing, 72, 371-391. https://doi.org/10.1016/j.asoc.2018.08.001
Blanco-Mesa, F., Merigó, J. M., & Gil-Lafuente, A. M. (2017). Fuzzy decision making: A bibliometric-based review. Journal of Intelligent & Fuzzy Systems, 32, 2033-2050. https://doi.org/10.3233/JIFS-161640
Bolton, J., Gader, P., & Wilson, J. N. (2008). Discrete choquet integral as a distance metric. IEEE Transactions on Fuzzy Systems, 16(4), 1107-1110. https://doi.org/10.1109/TFUZZ.2008.924347
Chen, S. J., & Chen, S. M. (2003). A new method for handling multicriteria fuzzy decision-making problems using FN-IOWA operators. Cybernetics and Systems, 34(2), 109-137. https://doi.org/10.1080/01969720302866
Chiclana, F., Herrera-Viedma, E., Herrera, F., & Alonso, S. (2007). Some induced ordered weighted averaging operators and their use for solving group decision-making problems based on fuzzy preference relations. European Journal of Operational Research, 182(1), 383-399. https://doi.org/10.1016/j.ejor.2006.08.032
Choquet, G. (1954). Theory of capacities. Annales de l’institut Fourier, 5, 131-295. https://doi.org/10.5802/aif.53
Florida, R. (2002). The rise of the creative class. New York: Basic Books.
Florida, R. (2005). The flight of the creative class. New York: Harper Business. https://doi.org/10.4324/9780203997673
Florida, R., Gulden, T., & Mellander, C. (2008). The rise of the mega-region. Cambridge Journal of Regions, Economy and Society, 1(3), 459-476. https://doi.org/10.1093/cjres/rsn018
Florida, R., Mellander, C., & Stolarick, K. (2008). Inside the black box of regional development - human capital, the creative class and tolerance. Journal of Economic Geography, 8(5), 615-649. https://doi.org/10.1093/jeg/lbn023
Grossman, G. M., & Helpman, E. (1993). Innovation and growth in the global economy. Cambridge: MIT Press.
Grossman, G. M., & Helpman, E. (2015). Globalization and growth. American Economic Review, 105(5), 100-104. https://doi.org/10.1257/aer.p20151068
Hamming, R. W. (1950). Error-detecting and error-correcting codes. Bell System Technical Journal, 29, 147-160. https://doi.org/10.1002/j.1538-7305.1950.tb00463.x
He, X. R., Wu, Y. Y., Yu, D., & Merigó, J. M. (2017). Exploring the ordered weighted averaging operator knowledge domain: A bibliometric analysis. International Journal of Intelligent Systems, 32, 1151-1166. https://doi.org/10.1002/int.21894
León-Castro, E., Avilés-Ochoa, E. A., & Gil-Lafuente, A. M. (2016). Exchange rate USD/MXN forecast through econometric models, time series and HOWMA operators. Economic Computation & Economic Cybernetics Studies & Research, 50(4), 135-150.
León-Castro, E., Avilés-Ochoa, E., Merigó, J. M., & Gil-Lafuente, A. M. (2018). Heavy moving averages and their application in econometric forecasting. Cybernetics and Systems, 49(1), 26-43. https://doi.org/10.1080/01969722.2017.1412883
Li, Z., Sun, D., & Zeng, S. (2018). Intuitionistic fuzzy multiple attribute decision-making model based on weighted induced distance measure and its application to investment selection. Symmetry, 10(7), 261. https://doi.org/10.3390/sym10070261
Lv, K., Yu, A., Gong, S., Wu, M., & Xu, X. (2017). Impacts of educational factors on economic growth in regions of China: a spatial econometric approach. Technological and Economic Development of Economy, 23(6), 827-847. https://doi.org/10.3846/20294913.2015.1071296
Maldonado, S., Merigó, J. M., & Miranda, J. (2018). Redefining support vector machines with the ordered weighted average. Knowledge-Based Systems, 148, 41-46. https://doi.org/10.1016/j.knosys.2018.02.025
Merigó, J. M., & Casanovas, M. (2011). Decision-making with distance measures and induced aggregation operators. Computers and Industrial Engineering, 60(1), 66-76. https://doi.org/10.1016/j.cie.2010.09.017
Merigó, J. M., & Gil-Lafuente, A. M. (2010). New decision-making techniques and their application in the selection of financial products. Information Sciences, 180(11), 2085-2094. https://doi.org/10.1016/j.ins.2010.01.028
Merigó, J. M., Peris-Ortíz, M., Navarro-García, A., & Rueda-Armengot, C. (2016). Aggregation operators in economic growth analysis and entrepreneurial group decision-making. Applied Soft Computing Journal, 47, 141-150. https://doi.org/10.1016/j.asoc.2016.05.031
Merigó, J. M., & Yager, R. R. (2013). Generalized moving averages, distance measures and OWA operators. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 21(04), 533-559. https://doi.org/10.1142/S0218488513500268
Mesiar, R. (1995). Choquet-like integrals. Journal of Mathematical Analysis and Applications, 194(2), 477-488. https://doi.org/10.1006/jmaa.1995.1312
Mesiar, R., Kolesárová, A., Bustince, H., Dimuro, G. P., & Bedregal, B. C. (2016). Fusion functions based discrete choquet-like integrals. European Journal of Operational Research, 252(2), 601-609. https://doi.org/10.1016/j.ejor.2016.01.027
Su, W., Zeng, S., & Ye, X. (2013). Uncertain group decision-making with induced aggregation operators and euclidean distance. Technological and Economic Development of Economy, 19(3), 431-447. https://doi.org/10.3846/20294913.2013.821686
Sucháček, J., Seďa, P., Friedrich, V., & Koutský, J. (2017). Regional aspects of the development of largest enterprises in the Czech Republic. Technological and Economic Development of Economy, 23(4), 649-666. https://doi.org/10.3846/20294913.2017.1318314
Tan, C., & Chen, X. (2010). Induced choquet ordered averaging operator and its application to group decision making. International Journal of Intelligent Systems, 25(1), 59-82. https://doi.org/10.1002/int.20388
United Nations. (2017). World Statistics Pocketbook 2017 edition (41st ed.). New York: United Nations Publications. https://doi.org/10.18356/c983bdf2-en
Wei, G., & Zhao, X. (2012). Some induced correlated aggregating operators with intuitionistic fuzzy information and their application to multiple attribute group decision making. Expert Systems with Applications, 39(2), 2026-2034. https://doi.org/10.1016/j.eswa.2011.08.031
Xian, S. D., Sun, W. J., Xu, S. H., & Gao, Y. Y. (2016). Fuzzy linguistic induced OWA minkowski distance operator and its application in group decision making. Pattern Analysis and Applications, 19(2), 325-335. https://doi.org/10.1007/s10044-014-0397-3
Xu, Z. S., & Chen, J. (2008). Ordered weighted distance measure. Journal of Systems Science and Systems Engineering, 17(4), 432-445. https://doi.org/10.1007/s11518-008-5084-8
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Transactions on Systems, Man and Cybernetics B, 18(1), 183-190. https://doi.org/10.1109/21.87068
Yager, R. R. (1993). Families of OWA operators. Fuzzy Sets and Systems, 59(2), 125-148. https://doi.org/10.1016/0165-0114(93)90194-M
Yager, R. R. (2003). Induced aggregation operators. Fuzzy Sets and Systems, 137(1), 59-69. https://doi.org/10.1016/S0165-0114(02)00432-3
Yager, R. R., & Filev, D. P. (1999). Induced ordered weighted averaging operators. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 29(2), 141-150. https://doi.org/10.1109/3477.752789
Zeng, S. (2017). Pythagorean fuzzy multiattribute group decision making with probabilistic information and owa approach. International Journal of Intelligent Systems, 32(11), 1136-1150. https://doi.org/10.1002/int.21886
Zeng, S., Llopis-Albert, C., & Zhang, Y. (2018). A novel induced aggregation method for intuitionistic fuzzy set and its application in multiple attribute group decision making. International Journal of Intelligent Systems, 33(11), 2175-2188. https://doi.org/10.1002/int.22009
Zeng, S., Su, W., & Zhang, C. (2016). Intuitionistic fuzzy generalized probabilistic ordered weighted averaging operator and its application to group decision making. Technological and Economic Development of Economy, 22(2), 177-193. https://doi.org/10.3846/20294913.2014.984253
Zeng, S., & Xiao, Y. (2018). A method based on topsis and distance measures for hesitant fuzzy multiple attibute decision making. Technological and Economic Development of Economy, 24(3), 969-983. https://doi.org/10.3846/20294913.2016.1216472
Zeng, S., & Su, W. H. (2011). Intuitionistic fuzzy ordered weighted distance operator. Knowledge-Based Systems, 24(8), 1224-1232. https://doi.org/10.1016/j.knosys.2011.05.013
Zeng, S., & Weihua, S. (2012). Linguistic induced generalized aggregation distance operators and their application to decision making. Economic Computation and Economic Cybernetics Studies and Research, 46(2), 155-172.
Zhou, L., & Chen, H. (2010). Generalized ordered weighted logarithm aggregation operators and their applications to group decision making. International Journal of Intelligent Systems, 25(7), 683-707. https://doi.org/10.1002/int.20419
Zhou, L., Chen, H., & Liu, J. (2012). Generalized logarithmic proportional averaging operators and their applications to group decision making. Knowledge-Based Systems, 36, 268-279. https://doi.org/10.1016/j.knosys.2012.07.006
Zhou, L., Tao, Z., Chen, H., & Liu, J. (2014). Generalized ordered weighted logarithmic harmonic averaging operators and their applications to group decision making. Soft Computing, 19(3), 715-730. https://doi.org/10.1007/s00500-014-1295-8
Zwick, R., Carlstein, E., & Budescu, D. V. (1987). Measures of similarity among fuzzy concepts: a comparative analysis. International Journal of Approximate Reasoning, 1(2), 221-242. https://doi.org/10.1016/0888-613X(87)90015-6