A new measure of volatility using induced heavy moving averages
Abstract
The volatility is a dispersion technique widely used in statistics and economics. This paper presents a new way to calculate volatility by using different extensions of the ordered weighted average (OWA) operator. This approach is called the induced heavy ordered weighted moving average (IHOWMA) volatility. The main advantage of this operator is that the classical volatility formula only takes into account the standard deviation and the average, while with this formulation it is possible to aggregate information according to the decision maker knowledge, expectations and attitude about the future. Some particular cases are also presented when the aggregation information process is applied only on the standard deviation or on the average. An example in three different exchange rates for 2016 are presented, these are for: USD/MXN, EUR/MXN and EUR/USD.
Keyword : volatility, IHOWMA operator, exchange rate, moving average
How to Cite
León-Castro, E., Espinoza-Audelo, L. F., Aviles-Ochoa, E., Merigó, J. M., & Kacprzyk, J. (2019). A new measure of volatility using induced heavy moving averages. Technological and Economic Development of Economy, 25(4), 576-599. https://doi.org/10.3846/tede.2019.9374
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Avilés-Ochoa, E., Perez-Arellano, L. A., León-Castro, E., & Merigó, J. M. (2017). Prioritized induced probabilistic distances in transparency and access to information laws. Fuzzy Economic Review, 22(1). https://doi.org/10.25102/fer.2017.01.04
Belles-Sampera, J., Merigó, J. M., Guillén, M., & Santolino, M. (2014). Indicators for the characterization of discrete Choquet integrals. Information Sciences, 267, 201-216. https://doi.org/10.1016/j.ins.2014.01.047
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(3), 2033-2050. https://doi.org/10.3233/JIFS-161640
Blanco-Mesa, F., Merigó, J. M., & Kacprzyk, J. (2016). Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory. Knowledge-Based Systems, 111, 217-227. https://doi.org/10.1016/j.knosys.2016.08.016
Carr, P., & Wu, L. (2008). Variance risk premiums. The Review of Financial Studies, 22(3), 1311-1341. https://doi.org/10.1093/rfs/hhn038
Della Corte, P., Ramadorai, T., & Sarno, L. (2016). Volatility risk premia and exchange rate predictability. Journal of Financial Economics, 120(1), 21-40. https://doi.org/10.1016/j.jfineco.2016.02.015
Emrouznejad, A., & Marra, M. (2014). Ordered weighted averaging operators 1988–2014: A citation‐based literature survey. International Journal of Intelligent Systems, 29(11), 994-1014. https://doi.org/10.1002/int.21673
Ethier, W. (1973). International trade and the forward exchange market. The American Economic Review, 63(3), 494-503.
Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. Journal of business, 67-78. https://doi.org/10.1086/296072
Grossmann, A., Love, I., & Orlov, A. G. (2014). The dynamics of exchange rate volatility: A panel VAR approach. Journal of International Financial Markets, Institutions and Money, 33, 1-27. https://doi.org/10.1016/j.intfin.2014.07.008
He, Y., He, Z., & Chen, H. (2015). Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE transactions on cybernetics, 45(1), 116-128. https://doi.org/10.1109/TCYB.2014.2320910
Héricourt, J., & Poncet, S. (2015). Exchange rate volatility, financial constraints, and trade: empirical evidence from Chinese firms. The World Bank Economic Review, 29(3), 550-578. https://doi.org/10.1093/wber/lht035
Herrera-Viedma, E., Cabrerizo, F. J., Kacprzyk, J., & Pedrycz, W. (2014). A review of soft consensus models in a fuzzy environment. Information Fusion, 17, 4-13. https://doi.org/10.1016/j.inffus.2013.04.002
Hooghe, M., & Kern, A. (2015). Party membership and closeness and the development of trust in political institutions: An analysis of the European Social Survey, 2002–2010. Party Politics, 21(6), 944-956. https://doi.org/10.1177/1354068813509519
Kacprzyk, J. (1986). Group decision making with a fuzzy linguistic majority. Fuzzy sets and systems, 18(2), 105-118. https://doi.org/10.1016/0165-0114(86)90014-X
Kacprzyk, J. (2015). Fuzzy dynamic programming for the modeling of sustainable regional development (Survey). Applied and Computational Mathematics, 14(2), 107-124.
Kacprzyk, J., & Fedrizzi, M. (1988). A ‘soft’measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research, 34(3), 316-325. https://doi.org/10.1016/0377-2217(88)90152-X
Kacprzyk, J., & Fedrizzi, M. (1989). A ‘human-consistent’degree of consensus based on fuzzy login with linguistic quantifiers. Mathematical Social Sciences, 18(3), 275-290. https://doi.org/10.1016/0165-4896(89)90035-8
Kacprzyk, J., & Straszak, A. (1984). Determination of “stable” trajectories of integrated regional development using fuzzy decision models. IEEE Transactions on Systems, Man, and Cybernetics, 14(2), 310-313. https://doi.org/10.1109/TSMC.1984.6313215
Kacprzyk, J., Fedrizzi, M., & Nurmi, H. (1992). Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems, 49(1), 21-31. https://doi.org/10.1016/0165-0114(92)90107-F
Kacprzyk, J., Romero, R. A., & Gomide, F. A. (1999). Involving objective and subjective aspects in multistage decision making and control under fuzziness: dynamic programming and neural networks. International Journal of Intelligent Systems, 14(1), 79-104. https://doi.org/10.1002/(SICI)1098-111X(199901)14:1<79::AID-INT6>3.0.CO;2-6
Kacprzyk, J., Zadrożny, S., & Raś, Z. W. (2010). How to support consensus reaching using action rules: a novel approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(04), 451-470. https://doi.org/10.1142/S0218488510006647
Kenney, J., & Keeping, E. (1962). Moving Averages. Princeton: Van Nostrand.
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 and Economic Cybernetics Studies and Research, 50(4), 135-150.
León‐Castro, E., Avilés‐Ochoa, E., & Merigó, J. M. (2018). Induced heavy moving averages. International Journal of Intelligent Systems, 33(9), 1823-1839. https://doi.org/10.1002/int.21916
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
Liu, H. C., You, J. X., You, X. Y., & Su, Q. (2016). Fuzzy Petri nets using intuitionistic fuzzy sets and ordered weighted averaging operators. IEEE Transactions on Cybernetics, 46(8), 1839-1850. https://doi.org/10.1109/TCYB.2015.2455343
Liu, P., & Chen, S. M. (2017). Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Transactions on Cybernetics, 47(9), 2514-2530. https://doi.org/10.1109/TCYB.2016.2634599
Merigó, J. M., & Casanovas, M. (2011). Decision-making with distance measures and induced aggregation operators. Computers & Industrial Engineering, 60(1), 66-76. https://doi.org/10.1016/j.cie.2010.09.017
Merigó, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179(6), 729-741. https://doi.org/10.1016/j.ins.2008.11.013
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
Merigó, J. M., Guillén, M., & Sarabia, J. M. (2015). The ordered weighted average in the variance and the covariance. International Journal of Intelligent Systems, 30(9), 985-1005. https://doi.org/10.1002/int.21716
Merigó, J. M., Xu, Y., & Zeng, S. (2013). Group decision making with distance measures and probabilistic information. Knowledge-Based Systems, 40, 81-87. https://doi.org/10.1016/j.knosys.2012.11.014
Minton, B. A., & Schrand, C. (1999). The impact of cash flow volatility on discretionary investment and the costs of debt and equity financing. Journal of Financial Economics, 54(3), 423-460. https://doi.org/10.1016/S0304-405X(99)00042-2
Mueller, P., Vedolin, A., & Yen, Y. M. (2012). Bond variance risk premia. Financial Markets Group, London School of Economics and Political Science.
Officer, R. R. (1973). The variability of the market factor of the New York Stock Exchange. The Journal of Business, 46(3), 434-453. https://doi.org/10.1086/295551
Pérez-Arellano, L. A., León-Castro, E., Avilés-Ochoa, E., & Merigó, J. M. (2017). Prioritized induced probabilistic operator and its application in group decision making. International Journal of Machine Learning and Cybernetics, 1-12.
Pilbeam, K., & Langeland, K. N. (2015). Forecasting exchange rate volatility: GARCH models versus implied volatility forecasts. International Economics and Economic Policy, 12(1), 127-142. https://doi.org/10.1007/s10368-014-0289-4
Rabbani, A. G., Grable, J. E., Heo, W., Nobre, L., & Kuzniak, S. (2017). Stock market volatility and changes in financial risk tolerance during the great recession. Journal of Financial Counseling and Planning, 28(1), 140. https://doi.org/10.1891/1052-3073.28.1.140
Ren, P., Xu, Z., & Hao, Z. (2017). Hesitant fuzzy thermodynamic method for emergency decision making based on prospect theory. IEEE Transactions on Cybernetics, 47(9), 2531-2543. https://doi.org/10.1109/TCYB.2016.2638498
Zeng, S., & Xiao, Y. (2018). A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making. Technological and Economic Development of Economy, 24(3), 969-983. https://doi.org/10.3846/20294913.2016.1216472
Van Biezen, I., Mair, P., & Poguntke, T. (2012). Going, going,... gone? The decline of party membership in contemporary Europe. European Journal of Political Research, 51(1), 24-56. https://doi.org/10.1111/j.1475-6765.2011.01995.x
Xu, Z. (2006). Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2), 231-238. https://doi.org/10.1016/j.inffus.2004.06.005
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183-190. https://doi.org/10.1109/21.87068
Yager, R. R. (1996). On the inclusion of variance in decision making under uncertainty. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4(05), 401-419. https://doi.org/10.1142/S0218488596000238
Yager, R. R. (2002). Heavy OWA operators. Fuzzy Optimization and Decision Making, 1(4), 379-397. https://doi.org/10.1023/A:1020959313432
Yager, R. R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3(1), 93-107. https://doi.org/10.1023/B:FODM.0000013074.68765.97
Yager, R. R. (2006). Generalizing variance to allow the inclusion of decision attitude in decision making under uncertainty. International Journal of Approximate Reasoning, 42(3), 137-158. https://doi.org/10.1016/j.ijar.2005.09.001
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
Yager, R. R., Kacprzyk, J., & Beliakov, G. (Eds.). (2011). Recent developments in the ordered weighted averaging operators: theory and practice (Vol. 265). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-17910-5
Zeng, S., Chen, J., & Li, X. (2016). A hybrid method for pythagorean fuzzy multiple-criteria decision making. International Journal of Information Technology & Decision Making, 15(02), 403-422. https://doi.org/10.1142/S0219622016500012
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
Zhou, L. G., & Chen, H. Y. (2011). Continuous generalized OWA operator and its application to decision making. Fuzzy Sets and Systems, 168(1), 18-34. https://doi.org/10.1016/j.fss.2010.05.009
Avilés-Ochoa, E., León-Castro, E., Gil-Lafuente, A. M., & Merigó, J. M. (2018). Forgotten effects in exchange rate forecasting models. In Complex systems: solutions and challenges in economics, management and engineering (pp. 423-437). Cham: Springer.
Avilés-Ochoa, E., Perez-Arellano, L. A., León-Castro, E., & Merigó, J. M. (2017). Prioritized induced probabilistic distances in transparency and access to information laws. Fuzzy Economic Review, 22(1). https://doi.org/10.25102/fer.2017.01.04
Belles-Sampera, J., Merigó, J. M., Guillén, M., & Santolino, M. (2014). Indicators for the characterization of discrete Choquet integrals. Information Sciences, 267, 201-216. https://doi.org/10.1016/j.ins.2014.01.047
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(3), 2033-2050. https://doi.org/10.3233/JIFS-161640
Blanco-Mesa, F., Merigó, J. M., & Kacprzyk, J. (2016). Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory. Knowledge-Based Systems, 111, 217-227. https://doi.org/10.1016/j.knosys.2016.08.016
Carr, P., & Wu, L. (2008). Variance risk premiums. The Review of Financial Studies, 22(3), 1311-1341. https://doi.org/10.1093/rfs/hhn038
Della Corte, P., Ramadorai, T., & Sarno, L. (2016). Volatility risk premia and exchange rate predictability. Journal of Financial Economics, 120(1), 21-40. https://doi.org/10.1016/j.jfineco.2016.02.015
Emrouznejad, A., & Marra, M. (2014). Ordered weighted averaging operators 1988–2014: A citation‐based literature survey. International Journal of Intelligent Systems, 29(11), 994-1014. https://doi.org/10.1002/int.21673
Ethier, W. (1973). International trade and the forward exchange market. The American Economic Review, 63(3), 494-503.
Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. Journal of business, 67-78. https://doi.org/10.1086/296072
Grossmann, A., Love, I., & Orlov, A. G. (2014). The dynamics of exchange rate volatility: A panel VAR approach. Journal of International Financial Markets, Institutions and Money, 33, 1-27. https://doi.org/10.1016/j.intfin.2014.07.008
He, Y., He, Z., & Chen, H. (2015). Intuitionistic fuzzy interaction Bonferroni means and its application to multiple attribute decision making. IEEE transactions on cybernetics, 45(1), 116-128. https://doi.org/10.1109/TCYB.2014.2320910
Héricourt, J., & Poncet, S. (2015). Exchange rate volatility, financial constraints, and trade: empirical evidence from Chinese firms. The World Bank Economic Review, 29(3), 550-578. https://doi.org/10.1093/wber/lht035
Herrera-Viedma, E., Cabrerizo, F. J., Kacprzyk, J., & Pedrycz, W. (2014). A review of soft consensus models in a fuzzy environment. Information Fusion, 17, 4-13. https://doi.org/10.1016/j.inffus.2013.04.002
Hooghe, M., & Kern, A. (2015). Party membership and closeness and the development of trust in political institutions: An analysis of the European Social Survey, 2002–2010. Party Politics, 21(6), 944-956. https://doi.org/10.1177/1354068813509519
Kacprzyk, J. (1986). Group decision making with a fuzzy linguistic majority. Fuzzy sets and systems, 18(2), 105-118. https://doi.org/10.1016/0165-0114(86)90014-X
Kacprzyk, J. (2015). Fuzzy dynamic programming for the modeling of sustainable regional development (Survey). Applied and Computational Mathematics, 14(2), 107-124.
Kacprzyk, J., & Fedrizzi, M. (1988). A ‘soft’measure of consensus in the setting of partial (fuzzy) preferences. European Journal of Operational Research, 34(3), 316-325. https://doi.org/10.1016/0377-2217(88)90152-X
Kacprzyk, J., & Fedrizzi, M. (1989). A ‘human-consistent’degree of consensus based on fuzzy login with linguistic quantifiers. Mathematical Social Sciences, 18(3), 275-290. https://doi.org/10.1016/0165-4896(89)90035-8
Kacprzyk, J., & Straszak, A. (1984). Determination of “stable” trajectories of integrated regional development using fuzzy decision models. IEEE Transactions on Systems, Man, and Cybernetics, 14(2), 310-313. https://doi.org/10.1109/TSMC.1984.6313215
Kacprzyk, J., Fedrizzi, M., & Nurmi, H. (1992). Group decision making and consensus under fuzzy preferences and fuzzy majority. Fuzzy Sets and Systems, 49(1), 21-31. https://doi.org/10.1016/0165-0114(92)90107-F
Kacprzyk, J., Romero, R. A., & Gomide, F. A. (1999). Involving objective and subjective aspects in multistage decision making and control under fuzziness: dynamic programming and neural networks. International Journal of Intelligent Systems, 14(1), 79-104. https://doi.org/10.1002/(SICI)1098-111X(199901)14:1<79::AID-INT6>3.0.CO;2-6
Kacprzyk, J., Zadrożny, S., & Raś, Z. W. (2010). How to support consensus reaching using action rules: a novel approach. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 18(04), 451-470. https://doi.org/10.1142/S0218488510006647
Kenney, J., & Keeping, E. (1962). Moving Averages. Princeton: Van Nostrand.
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 and Economic Cybernetics Studies and Research, 50(4), 135-150.
León‐Castro, E., Avilés‐Ochoa, E., & Merigó, J. M. (2018). Induced heavy moving averages. International Journal of Intelligent Systems, 33(9), 1823-1839. https://doi.org/10.1002/int.21916
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
Liu, H. C., You, J. X., You, X. Y., & Su, Q. (2016). Fuzzy Petri nets using intuitionistic fuzzy sets and ordered weighted averaging operators. IEEE Transactions on Cybernetics, 46(8), 1839-1850. https://doi.org/10.1109/TCYB.2015.2455343
Liu, P., & Chen, S. M. (2017). Group decision making based on Heronian aggregation operators of intuitionistic fuzzy numbers. IEEE Transactions on Cybernetics, 47(9), 2514-2530. https://doi.org/10.1109/TCYB.2016.2634599
Merigó, J. M., & Casanovas, M. (2011). Decision-making with distance measures and induced aggregation operators. Computers & Industrial Engineering, 60(1), 66-76. https://doi.org/10.1016/j.cie.2010.09.017
Merigó, J. M., & Gil-Lafuente, A. M. (2009). The induced generalized OWA operator. Information Sciences, 179(6), 729-741. https://doi.org/10.1016/j.ins.2008.11.013
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
Merigó, J. M., Guillén, M., & Sarabia, J. M. (2015). The ordered weighted average in the variance and the covariance. International Journal of Intelligent Systems, 30(9), 985-1005. https://doi.org/10.1002/int.21716
Merigó, J. M., Xu, Y., & Zeng, S. (2013). Group decision making with distance measures and probabilistic information. Knowledge-Based Systems, 40, 81-87. https://doi.org/10.1016/j.knosys.2012.11.014
Minton, B. A., & Schrand, C. (1999). The impact of cash flow volatility on discretionary investment and the costs of debt and equity financing. Journal of Financial Economics, 54(3), 423-460. https://doi.org/10.1016/S0304-405X(99)00042-2
Mueller, P., Vedolin, A., & Yen, Y. M. (2012). Bond variance risk premia. Financial Markets Group, London School of Economics and Political Science.
Officer, R. R. (1973). The variability of the market factor of the New York Stock Exchange. The Journal of Business, 46(3), 434-453. https://doi.org/10.1086/295551
Pérez-Arellano, L. A., León-Castro, E., Avilés-Ochoa, E., & Merigó, J. M. (2017). Prioritized induced probabilistic operator and its application in group decision making. International Journal of Machine Learning and Cybernetics, 1-12.
Pilbeam, K., & Langeland, K. N. (2015). Forecasting exchange rate volatility: GARCH models versus implied volatility forecasts. International Economics and Economic Policy, 12(1), 127-142. https://doi.org/10.1007/s10368-014-0289-4
Rabbani, A. G., Grable, J. E., Heo, W., Nobre, L., & Kuzniak, S. (2017). Stock market volatility and changes in financial risk tolerance during the great recession. Journal of Financial Counseling and Planning, 28(1), 140. https://doi.org/10.1891/1052-3073.28.1.140
Ren, P., Xu, Z., & Hao, Z. (2017). Hesitant fuzzy thermodynamic method for emergency decision making based on prospect theory. IEEE Transactions on Cybernetics, 47(9), 2531-2543. https://doi.org/10.1109/TCYB.2016.2638498
Zeng, S., & Xiao, Y. (2018). A method based on TOPSIS and distance measures for hesitant fuzzy multiple attribute decision making. Technological and Economic Development of Economy, 24(3), 969-983. https://doi.org/10.3846/20294913.2016.1216472
Van Biezen, I., Mair, P., & Poguntke, T. (2012). Going, going,... gone? The decline of party membership in contemporary Europe. European Journal of Political Research, 51(1), 24-56. https://doi.org/10.1111/j.1475-6765.2011.01995.x
Xu, Z. (2006). Induced uncertain linguistic OWA operators applied to group decision making. Information Fusion, 7(2), 231-238. https://doi.org/10.1016/j.inffus.2004.06.005
Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18(1), 183-190. https://doi.org/10.1109/21.87068
Yager, R. R. (1996). On the inclusion of variance in decision making under uncertainty. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 4(05), 401-419. https://doi.org/10.1142/S0218488596000238
Yager, R. R. (2002). Heavy OWA operators. Fuzzy Optimization and Decision Making, 1(4), 379-397. https://doi.org/10.1023/A:1020959313432
Yager, R. R. (2004). Generalized OWA aggregation operators. Fuzzy Optimization and Decision Making, 3(1), 93-107. https://doi.org/10.1023/B:FODM.0000013074.68765.97
Yager, R. R. (2006). Generalizing variance to allow the inclusion of decision attitude in decision making under uncertainty. International Journal of Approximate Reasoning, 42(3), 137-158. https://doi.org/10.1016/j.ijar.2005.09.001
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
Yager, R. R., Kacprzyk, J., & Beliakov, G. (Eds.). (2011). Recent developments in the ordered weighted averaging operators: theory and practice (Vol. 265). Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-642-17910-5
Zeng, S., Chen, J., & Li, X. (2016). A hybrid method for pythagorean fuzzy multiple-criteria decision making. International Journal of Information Technology & Decision Making, 15(02), 403-422. https://doi.org/10.1142/S0219622016500012
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
Zhou, L. G., & Chen, H. Y. (2011). Continuous generalized OWA operator and its application to decision making. Fuzzy Sets and Systems, 168(1), 18-34. https://doi.org/10.1016/j.fss.2010.05.009