Using Quality Measures in the Intelligent Fusion of Probabilistic Information
Our objective here is to obtain quality-fused values from multiple sources of probabilistic distributions, where quality is related to the lack of uncertainty in the fused value and the use of credible sources. We first introduce a vector representation for a probability distribution. With the aid of the Gini formulation of entropy, we show how the norm of the vector provides a measure of the certainty, i.e., information, associated with a probability distribution. We look at two special cases of fusion for source inputs, those that are maximally uncertain and certain. We provide a measure of credibility associated with subsets of sources. We look at the issue of finding the highest-quality fused value from the weighted aggregation of source-provided probability distributions.
KeywordsQuality measures Information fusion Entropy Credibility Choquet integral
Ronald Yager was supported in part by an ONR grant award. Fred Petry would like to thank the Naval Research Laboratory’s Base Program, Program Element No. 0602435N for their sponsorship.
- 1.R. Pirsig, Zen and the Art of Motorcycle Maintenance: An Inquiry into Values (HarperCollins, New York, 1999)Google Scholar
- 2.J. Evans, W. Lindsay, The Management and Control of Quality (South-Western College Publications, Cincinnati, 1999)Google Scholar
- 8.M.R. Spiegal, D. Lipschutz, D. Spellman, Vector Analysis (John Wiley, Hoboken, 2009)Google Scholar
- 9.R.R. Yager, N. Alajlan, An intelligent interactive approach to group aggregation of subjective probabilities, Technical report MII-3502, Machine Intelligence Institute, Iona College, New Rochelle, NY, 2015Google Scholar
- 11.B. Buck, Maximum Entropy in Action: A Collection of Expository Essays (Oxford University Press, New York, 1991)Google Scholar
- 13.R.R. Yager, K. Engemann, Entropy measures in sports. Int. J. Syst. Meas. Decis. 1, 67–72 (1981)Google Scholar
- 15.D.G. Luenberger, Information Science (Princeton University Press, Princeton, 2006)Google Scholar
- 16.C. Gini, Variabilità e mutabilità,” Reprinted in Memorie di Metodologica Statistica, ed. by E. Pizetti, T. Salvemini (Libreria Eredi Virgilio Veschi, Rome, 1955Google Scholar
- 29.J.L. Marichal, M. Roubens, “Entropy of discrete fuzzy measures,” in Proceedings of Third International Workshop on Preferences and Decisions, Trento, pp. 135–148, 2000Google Scholar
- 30.T. Murofushi, A technique for reading fuzzy measures (i): the Shapely value with respect to a fuzzy measure, in Proceedings Second Fuzzy Workshop, Nagaoka, Japan (in Japanese), pp. 39–48, 1992Google Scholar