Abstract
In the introduction we examine Dombi aggregative operators, uninorms, strict t-norms and t-conorms.We give a certain class of weighted aggregative operators (weighted representable uninorms). After, we focus on a specific form of the aggregative operator. Using Dombi’s generator function, we show that this form is the same as that for the aggregation of expert probability values, and we can get this operator via Bayes’ theorem. These two theorems shed new light on the class of aggregative operators.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aczél, J.: Lectures on functional equations and their applications. Academic Press, New York (1966)
Bordley, R.F.: A multiplicative formula for aggregating probability assessments. Management Science 28, 1137–1148 (1982)
Calvo, T., Baets, B.D., Fodor, J.: The functional equations of frank and alsina for uninorms and nullnorms. Fuzzy Sets and Systems 120, 385–394 (2001)
Dombi, J.: Basic concepts for a theory of evaluation: the aggregative operator. European Journal of Operations Research 10, 282–293 (1982)
Fodor, J., Yager, R.R., Rybalov, A.: Structure of uninorms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 5(4), 411–427 (1997)
Hu, S.-K., Li, Z.-F.: The structure of continuous uni-norms. Fuzzy Sets and Systems 124, 43–52 (2001)
Genest, C., Zidek, J.V.: Combining Probability Distributions: A Critique and an Annotated Bibliography. Statistical Science 1(1), 114–135 (1986)
Gilardoni, G.L.: On irrevelance of alternatives and opinion pooling. Brazilian Journal of Probability and Statistics 16, 87–98
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer (2000)
Klement, E.P., Mesiar, R., Pap, E.: On the relationship of associative compensatory operators to triangular norms and conorms. Uncertainty, Fuzziness and Knowledge-Based Systems 4, 129–144 (1996)
Li, Y.-M., Shi, Z.-K.: Weak uninorm aggregation operators. Information Sciences 124, 317–323 (2000)
Li, Y.M., Shi, Z.K.: Remarks on uninorms aggregation operators. Fuzzy Sets and Systems 114, 377–380 (2000)
Li, J., Mesiar, R., Struk, P.: Pseudo-optimal measures. Information Sciences 180(20), 4015–4021 (2010)
Mas, M., Mayor, G., Torrens, J.: The distributivity condition for uninorms and t-operators. Fuzzy Sets and Systems 128, 209–225 (2002)
Monserrat, M., Torrens, J.: On the reversibility of uninorms and t-operators. Fuzzy Sets and Systems 131, 303–314 (2002)
Yager, R.R.: Uninorms in fuzzy systems modeling. Fuzzy Sets and Systems 122, 167–175 (2001)
Yager, R.R., Rybalov, A.: Uninorm aggregation operators. Fuzzy Sets and Systems 80(1), 111–120 (1996)
Ramoni, M., Sebastiani, P.: Robust Bayes classifiers. Artificial Intelligence 125, 209–226 (2001)
Frank, E., Trigg, L., Holmes, G., Witten, I.H.: Technical note: Naive Bayes for regression. Machine Learning 41, 5–25 (2000)
Friedman, J.H.: On bias, variance, 0/1 loss, and the curse-of-dimensionality. Data Mining and Knowledge Discovery 1, 55–77 (1997)
Friedman, J.H., Geiger, D., Goldszmidt, M.: Bayesian network classifiers. Machine Learning 29, 131–163 (1997)
Triangular Norms. Kluwer, Dordrecht (2000)
Ortiz, J.M., Deutsch, C.V.: Indicator simulationAccounting for Multiple-Point Statistics. Mathematical Geology 36(5), 545–565 (2004)
Fodor, J., De Baets, B.: A single-point characterization of representable uninorms. Fuzzy Sets and Systems 202, 89–99 (2012)
Jenei, S., Montagna, F.: Strongly involutive uninorm algebras. Journal of Logic and Computation (2012), doi:10.1093/logcom/exs019
Jenei, S.: Structural description of a class of involutive uninorms via skew symmetrization. Journal of Logic and Computation 21(5), 729–737 (2011)
Jenei, S., Montagna, F.: Classification of absorbent-continuous, sharp FL e algebras over weakly real chains (under review process)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dombi, J. (2013). Bayes Theorem, Uninorms and Aggregating Expert Opinions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-39165-1_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39164-4
Online ISBN: 978-3-642-39165-1
eBook Packages: EngineeringEngineering (R0)