×

zbMATH — the first resource for mathematics

\(T\)-generable indistinguishability operators and their use for feature selection and classification. (English) Zbl 1423.68497
Summary: \(T\)-generable indistinguishability operators are operators \(E\) that can be expressed in the form \(E = T(E_{\mu_1}, E_{\mu_2},\dots, E_{\mu_m})\), where \(T\) is a t-norm and \(E_\mu\) is the fuzzy relation generated by the fuzzy subset \(\mu\). In this paper, we analyse their relation with powers with respect to the t-norm \(T\) and with quasi-arithmetic means. For non-strict continuous Archimedean t-norms they are completely characterised as generable by crisp equivalence relations. These fuzzy relations are used to define a method, called JADE, useful for feature selection and classification tasks. JADE is based on minimising the distance between two indistinguishability measures: the one given by weighting the attribute-values describing the domain objects and the other one given by the correct classification taken as an equivalence relation. The preliminary experiments we carried out with JADE are promising concerning the accuracy in solving classification tasks. We also report some issues of the method that could be improved in the future.

MSC:
68T37 Reasoning under uncertainty in the context of artificial intelligence
68T05 Learning and adaptive systems in artificial intelligence
68T10 Pattern recognition, speech recognition
Software:
UCI-ml; C4.5
PDF BibTeX Cite
Full Text: DOI
References:
[1] Valverde, L., On the structure of f-indistinguishability operators, Fuzzy Sets Syst., 17, 313-328, (1985) · Zbl 0609.04002
[2] Jacas, J.; Recasens, J., Aggregation of t-transitive relations, Int. J. Intell. Syst., 18, 1193-1214, (2003) · Zbl 1101.68812
[3] Pradera, A.; Trillas, E.; Castiñeira, E., On the aggregation of some classes of fuzzy relations, (Technologies for Constructing Intelligent Systems 2. Studies in Fuzziness and Soft Computing, vol 90. Physica, Heidelberg, (2002), Springer Verlag), 125-136 · Zbl 1015.68193
[4] Pradera, A.; Trillas, E., A note on pseudometrics aggregation, Int. J. Gen. Syst., 31, 41-51, (2002) · Zbl 1160.93307
[5] Bezdek, J.; Harris, J., Fuzzy partitions and relations; an axiomatic basis for clustering, Fuzzy Sets Syst., 1, 111-127, (1978) · Zbl 0442.68093
[6] Jacas, J.; Recasens, J., Aggregation operators based on indistinguishability operators, Int. J. Intell. Syst., 37, 857-873, (2006) · Zbl 1112.68122
[7] Klement, E.; Mesiar, R.; Pap, E., Triangular Norms, (2000), Kluwer Academic Publisher: Kluwer Academic Publisher Dordrecht, The Netherlands · Zbl 0972.03002
[8] Walker, C. L.; Walker, E., Powers of t-norms, Fuzzy Sets Syst., 129, 1-28, (2002) · Zbl 1001.03050
[9] Zadeh, L., Similarity relations and fuzzy orderings, Inf. Sci., 3, 2, 177-200, (1971) · Zbl 0218.02058
[10] Trillas, E.; Valverde, L., An inquiry into indistinguishability operators, (Aspects of Vagueness, (1984), Springer: Springer Netherlands, Dordrecht), 231-256 · Zbl 0564.03027
[11] De Soto, A. R.; Recasens, J., Some sets of indistinguishability operators as multiresolution families, Inf. Sci., 319, 38-55, (2015) · Zbl 1390.68645
[12] Massenet, J. R.S.; Torrens, J. J., Fuzzy implication functions based on powers of continuous t-norms, Int. J. Approx. Reason., 83, 265-279, (2017) · Zbl 1404.03024
[13] Boixader, D.; Recasens, J., Powers with respect to t-norms and t-conorms and aggregation functions, (Fuzzy Logic and Information Fusion, Studies in Fuzziness and Soft Computing, (2016), Springer-Verlag)
[14] Dasarathy, B. V., Data mining tasks and methods: classification: nearest-neighbor approaches, (Handbook of Data Mining and Knowledge Discovery, (2002), Oxford University Press, Inc.: Oxford University Press, Inc. New York, NY, USA), 288-298
[15] Aamodt, A.; Plaza, E., Case-based reasoning: foundational issues, methodological variations, and system approaches, AI Commun., 7, 1, 39-59, (1994)
[16] Quinlan, J. R., C4.5: Programs for Machine Learning, (1993), Morgan Kaufmann
[17] Kira, K.; Rendell, L., The feature selection problem: traditional methods and a new algorithm, (AAAI, (1992), AAAI Press and MIT Press), 129-134
[18] Rodriguez-Lujan, I.; Huerta, R.; Elkan, C.; Cruz, C., Quadratic programming feature selection, J. Mach. Learn. Res., 11, 1491-1516, (2010) · Zbl 1242.68245
[19] Zhang, L.; Coenen, F.; Leng, P., An attribute weight setting method for k-NN based binary classification using quadratic programming, (van Harmelen, F., ECAI, (2002), IOS Press), 325-329
[20] Bazaraa, M.; Sherali, H.; Shetty, C., Nonlinear Programming: Theory and Algorithms, Wiley-Interscience Series in Discrete Mathematics and Optimization, (1993), Wiley · Zbl 0774.90075
[21] Asuncion, A.; Newman, D., UCI machine learning repository, (2007)
[22] M. Hall, E. Frank, G. Holmes, B. Pfahringer, P. Reutemann, I. Witten.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.