Document Type : Research Paper
Department of Computer Sciences, Tbilisi State University, Georgia.
The Ordered Weighted Averaging (OWA) operator was introduced by Yager  to provide a method for aggregating inputs that lie between the max and min operators. In this article we continue to present some extensions of OWA-type aggregation operators. Several variants of the generalizations of the fuzzy-probabilistic OWA operator-FPOWA (introduced by Merigo , ) are presented in the environment of fuzzy uncertainty, where different monotone measures (fuzzy measure) are used as uncertainty measures. The considered monotone measures are: possibility measure, Sugeno additive measure, monotone measure associated with Belief Structure and Choquet capacity of order two. New aggregation operators are introduced: AsFPOWA and SA-AsFPOWA. Some properties of new aggregation operators and their information measures are proved. Concrete faces of new operators are presented with respect to different monotone measures and mean operators. Concrete operators are induced by the Monotone Expectation (Choquet integral) or Fuzzy Expected Value (Sugeno Integral) and the Associated Probability Class (APC) of a monotone measure. New aggregation operators belong to the Information Structure I6 (see Part I, Section 3). For the illustration of new constructions of AsFPOWA and SA-AsFPOWA operators an example of a fuzzy decision-making problem regarding the political management with possibility uncertainty is considered. Several aggregation operators (“classic” and new operators) are used for the comparing of the results of decision making.
- Mean aggregation operators
- Fuzzy aggregations
- Fuzzy measure
- Associated probabilities
- Fuzzy numbers
- Fuzzy decision making
- de Campos Ibañez, L. M., & Carmona, M. J. B. (1989). Representation of fuzzy measures through probabilities. Fuzzy sets and systems, 31(1), 23-36.
- Choquet, G. (1954). Theory of In Annales de l'institut Fourier(Vol. 5, pp. 131-295). DOI : https://doi.org/10.5802/aif.53
- Dubois, D., Marichal, J. L., Prade, H., Roubens, M., & Sabbadin, R. (2001). The use of the discrete Sugeno integral in decision-making: A survery. International journal of uncertainty, fuzziness and knowledge-based systems, 9(05), 539-561.
- Dubois, D., & Prade, H. (2007). Possibility theory. Scholarpedia, 2(10), 2074.
- Grabisch, M., Sugeno, M., & Murofushi, T. (2010). Fuzzy measures and integrals: theory and applications. Heidelberg: Physica.
- Kaufman, A., & Gupta, M. M. (1991). Introduction to fuzzy arithmetic. New York: Van Nostrand Reinhold Company.
- Klir, G. J. (2013). Architecture of systems problem solving. Springer Science & Business Media.
- Klir, G. J., & Folger, T. A. (1988). Fuzzy sets: uncertainty and information, prentice. New York: Prentice-Hall, Englewood Cliffs.
- Klir, G. J., & Wierman, M. J. (2013). Uncertainty-based information: elements of generalized information theory(Vol. 15). Physica.
- Marichal, J. L. (2000). An axiomatic approach of the discrete Choquet integral as a tool to aggregate interacting criteria. IEEE transactions on fuzzy systems, 8(6), 800-807.
- Marichal, J. L. (2000). On Choquet and Sugeno integrals as aggregation functions. Fuzzy measures and integrals-theory and applications, 247-272.
- Marichal, J. L. (2000). On Sugeno integral as an aggregation function. Fuzzy sets and systems, 114(3), 347-365.
- Merigo, J. M. (2011). The uncertain probabilistic weighted average and its application in the theory of expertons. African journal of business management, 5(15), 6092-6102.
- Merigó, J. M. (2011). Fuzzy multi-person decision making with fuzzy probabilistic aggregation operators. International journal of fuzzy systems, 13(3), 163-174.
- Merigó, J. M., & Casanovas, M. (2011). The uncertain induced quasi‐arithmetic OWA operator. International journal of intelligent systems, 26 (1), 1-24. https://doi.org/10.1002/int.20444
- Merigó, J. M., & Casanovas, M. (2010). Fuzzy generalized hybrid aggregation operators and its application in fuzzy decision making. International journal of fuzzy systems, 12(1), 15-24.
- Merigo, J. M., & Casanovas, M. (2010). The fuzzy generalized OWA operator and its application in strategic decision making. Cybernetics and systems: an international journal, 41(5), 359-370.
- Sirbiladze, G. (2012). Extremal fuzzy dynamic systems: Theory and applications(Vol. 28). Springer Science & Business Media.
- Sirbiladze, G. (2005). Modeling of extremal fuzzy dynamic systems. Part I. Extended extremal fuzzy measures. International journal of general systems, 34(2), 107-138.
- Sirbiladze, G., & Gachechiladze, T. (2005). Restored fuzzy measures in expert decision-making. Information sciences, 169(1-2), 71-95.
- Sirbiladze, G., Ghvaberidze, B., Latsabidze, T., & Matsaberidze, B. (2009). Using a minimal fuzzy covering in decision-making problems. Information sciences, 179(12), 2022-2027.
- Sirbiladze, G., & Sikharulidze, A. (2003). Weighted fuzzy averages in fuzzy environment: Part I. Insufficient expert data and fuzzy averages. International journal of uncertainty, fuzziness and knowledge-based systems, 11(02), 139-157.
- Sirbiladze, G., Sikharulidze, A., Ghvaberidze, B., & Matsaberidze, B. (2011). Fuzzy-probabilistic aggregations in the discrete covering problem. International journal of general systems, 40(02), 169-196.
- Sugeno, M. (1974). Theory of fuzzy integrals and its applications (Doctoral Thesis, Tokyo Institute of technology). Retrieved from https://ci.nii.ac.jp/naid/10017209011/
- Torra, V. (1997). The weighted OWA operator. International journal of intelligent systems, 12(2), 153-166.
- Yager, R. R. (2009). On the dispersion measure of OWA operators. Information sciences, 179(22), 3908-3919.
- Yager, R. R. (2007). Aggregation of ordinal information. Fuzzy optimization and decision making, 6(3), 199-219.
- Yager, R. R. (2004). Generalized OWA aggregation operators. Fuzzy optimization and decision making, 3(1), 93-107.
- Yager, R. R. (2002). On the evaluation of uncertain courses of action. Fuzzy optimization and decision making, 1(1), 13-41.
- Yager, R. R. (2002). Heavy OWA operators. Fuzzy optimization and decision making, 1(4), 379-397.
- Yager, R. R. (2002). On the cardinality index and attitudinal character of fuzzy measures. International journal of general systems, 31(3), 303-329.
- Yager, R. R. (2000). On the entropy of fuzzy measures. IEEE transactions on fuzzy systems, 8(4), 453-461.
- Yager, R. R. (1999). A class of fuzzy measures generated from a Dempster–Shafer belief structure. International journal of intelligent systems, 14(12), 1239-1247.
- Yager, R. R. (1988). On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE transactions on systems, man, and cybernetics, 18(1), 183-190.
- Yager, R. R., & Kacprzyk, J. (Eds.). (2012). The ordered weighted averaging operators: theory and applications. Springer Science & Business Media.
- Yager, R. R., Kacprzyk, J., & Beliakov, G. (Eds.). (2011). Recent developments in the ordered weighted averaging operators: theory and practice(Vol. 265). Springer.
- Sirbiladze, G., Badagadze, O., & Tsulaia, G. (2012). New fuzzy aggregations. Part II: associated probabilities in the aggregations of the POWA operator. International journal of control systems and robotics, 1, 73-85.