Aggregation of ordinal information
Our interest is with the fusion of information which has an ordinal structure. Information fusion in this environment requires the availability of ordinal aggregation operations. Basic ordinal operations are first introduced. Next we investigate conjunctive and disjunction aggregations of ordinal information. The idea of a pseudo-log in the ordinal environment is presented. We discuss the introduction of a zero like point on an ordinal scale along with the related ideas of bipolarity (positive and negative values) and uni-norm aggregation operators. We introduce mean like aggregation operators as well weighted averages on a ordinal scale. The problem of selecting between ordinal models is considered.
KeywordsAggregation operations information fusion ordinal operators linguistic values uni-norm ordinal weighted average
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- De Baets B. (1998). Uninorms: The known classes. In: Ruan D., Abderrahim H.A., D’hondt P., Kerre E. (eds) Fuzzy logic and intelligent technologies for nuclear science and industry. Singapore, World Scientific, pp.21–28Google Scholar
- De Baets, B., & Fodor, J. (1997). On the structure of uninorms and their residual implicators. Proc. Eighteenth Linz Seminaron Fuzzy Set Theory: Linz, Austria, pp. 81–87.Google Scholar
- Dubois, D., Kaci, S., & Prade, H. (2004). Bipolarity in reasoning and decision—an introduction. The case of the possibility framework. In Proc. of the 10th International Conf. on Information processing and the management of uncertainty in knowledge-based systems (IPMU) (pp. 959–966). Perugia, Italy.Google Scholar
- Murofushi, T., & Sugeno, M. (2000). Fuzzy measures and fuzzy integrals. In Grabisch, M., Murofushi, T., & Sugeno, M. (Eds.) Fuzzy measures and integrals. Heidelberg, Physica-Verlag, pp. 3–41Google Scholar
- Yager R.R. (1996). Structures generated from weighted fuzzy intersection and union. Journal of the Chinese Fuzzy Systems Association 2, 37–58Google Scholar
- Yager R.R. (2002). Ordinal decision making with a notion of acceptable: Denoted ordinal scales. In Lin T.Y., Yao Y.Y. & Zadeh L.A. (eds). Data mining, rough sets and granular computing. Heidelberg, Physica-Verlag, pp. 98–413Google Scholar
- Zadeh L.A. (2000). Toward a logic of perceptions based on fuzzylogic. In: Novak W., Perfilieva I. (eds). Discovering the world with fuzzy logic. Heidelberg, Physica-Verlag, pp. 4–28Google Scholar
- Zaruda J.M. (1992). Introduction to artificial neural systems. St Paul, MN, West Publishing Co.Google Scholar