Weighted Means of Subjective Evaluations
In this article, we recall different student evaluation methods based on fuzzy set theory. The problem arises is the aggregation of this fuzzy information when it is presented as a fuzzy number. Such aggregation problem is becoming present in an increasing number of areas: mathematics, physic, engineering, economy, social sciences, etc. In the previously quoted methods the fuzzy numbers awarded by each evaluator are not directly aggregated. They are previously defuzzycated and then a weighted mean or other type of aggregation function is often applied. Our aim is to aggregate directly the fuzzy awards (expressed as discrete fuzzy numbers) and to get like a fuzzy set (a discrete fuzzy number) resulting from such aggregation, because we think that in the defuzzification process a large amount of information and characteristics are lost. Hence, we propose a theoretical method to build n-dimensional aggregation functions on the set of discrete fuzzy number. Moreover, we propose a method to obtain the group consensus opinion based on discrete fuzzy weighted normed operators.
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- 4.Casasnovas, J., Vincente Riera, J.: Maximum and Mininum of Discrete Fuzzy numbers. In: Frontiers in Artificial Intelligence and Applications: Artificial Intelligence Research and Development, vol. 163, pp. 273–280. IOS Press (2007)Google Scholar
- 5.Casasnovas, J., Vincente Riera, J.: Lattice properties of discrete fuzzy numbers under extended min and max. In: Proceedings IFSA-EUSFLAT, Lisbon, pp. 647–652 (July 2009)Google Scholar
- 6.Casasnovas, J., Vincente Riera, J.: Extension of discrete t-norms and t-conorms to discrete fuzzy numbers. In: Fuzzy Sets and Systems, doi:10.1016/j.fss.2010.09.016Google Scholar
- 11.Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic (Theory and applications). Prentice-Hall (1995)Google Scholar
- 14.Mayor, G., Torrens, J.: Triangular norms on discrete settings. In: Klement, E.P., Mesiar, R. (eds.) Logical, Algebraic, Analytic, and Probabilistic Aspects of Triangular Norms. Elsevier (2005)Google Scholar
- 15.Mayor, G., Soto, A.R., Suñer, J., Trillas, E.: Multi-dimensional Aggregation of Fuzzy Numbers Through the Extension Principle. In: Data mining, Rough sets and Granular computing. Studies in Fuzziness and Soft Computing, pp. 350–363. Physica-VerlagGoogle Scholar