×

zbMATH — the first resource for mathematics

Fuzzy classification systems. (English) Zbl 1056.90077
Summary: In this paper it is pointed out that a classification is always made taking into account all the available classes, i.e., by means of a classification system. The approach presented in this paper generalizes the classical definition of fuzzy partition as defined by Ruspini, which is now conceived as a quite often desirable objective that can be usually obtained only after a long learning process. In addition, our model allows the evaluation of the resulting classification, according to several indexes related to covering, relevance and overlapping.

MSC:
90B50 Management decision making, including multiple objectives
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] A. Amo, J. Montero, V. Cutello, On the principles of fuzzy classification, In: Proceedings North American Fuzzy Information Processing Society Conference, 1999, pp. 675-679
[2] Amo, A.; Montero, J.; Biging, G., Classifying pixels by means of fuzzy relations, International journal of general systems, 29, 605-621, (2000) · Zbl 0952.62056
[3] Amo, A.; Montero, J.; Fernández, A.; López, M.; Tordesillas, J.; Biging, G., Spectral fuzzy classification: an application, IEEE transactions systems man and cybernautics (C), 32, 42-48, (2002)
[4] Amo, A.; Montero, J.; Molina, E., On the representation of recursive rules, European journal of operational research, 130, 29-53, (2001) · Zbl 1137.03322
[5] Ball, G.H.; Hall, D.J., ISODATA–A novel method of data analysis and pattern classification, (1965), Stanford Research Institute Menlo Park, CA
[6] Belton, V.; Hodgkin, J., Facilitators, decision makers, D.I.Y. users: Is intelligent multicriteria decision support for all feasible or desirable, European journal of operational research, 113, 247-260, (1999)
[7] Bezdek, J.C.; Harris, J.D., Fuzzy partitions and relations: an axiomatic basis for clustering, Fuzzy sets and systems, 1, 111-127, (1978) · Zbl 0442.68093
[8] Butnariu, D., Additive fuzzy measures and integrals, Journal of mathematical analysis and applications, 93, 436-452, (1983) · Zbl 0516.28006
[9] V. Cutello, J. Montero, Nondeterministic fuzzy classification systems, In: Proceedings FUZZ-IEEE Conference, 1997, pp. 1689-1694
[10] Cutello, V.; Montero, J., Recursive connective rules, International of journal of intelligent systems, 14, 3-20, (1999) · Zbl 0955.68103
[11] De Baets, B., Idempotent uninorms, European journal of operational research, 118, 631-642, (1999) · Zbl 0933.03071
[12] Dombi, J., Basic concepts for a theory of evaluation: the aggregative operator, European journal of operational research, 10, 282-293, (1982) · Zbl 0488.90003
[13] Dombi, J., A general class of fuzzy operators, Fuzzy sets and systems, 8, 149-163, (1982) · Zbl 0494.04005
[14] Dumitrescu, D., Fuzzy partitions with the connectives T∞, S∞, Fuzzy sets and systems, 47, 193-195, (1992) · Zbl 0755.04003
[15] Fodor, J.; Roubens, M., Valued preference structures, European journal of operational research, 79, 277-286, (1994) · Zbl 0812.90005
[16] Fodor, J.; Roubens, M., Fuzzy preference modelling and multicriteria decision support, (1994), Kluwer Dordrecht · Zbl 0827.90002
[17] Foody, G.M., The continuum of classification fuzziness in thematics mapping, Photogrammetric engineering and remote sensing, 65, 443-451, (1999)
[18] Iancu, I., Connectives for fuzzy partitions, Fuzzy sets and systems, 101, 509-512, (1999) · Zbl 0928.03062
[19] Matsakis, P.; Andrèfouët, S.; Capolsini, P., Evaluation of fuzzy partitions, Remote sensing of environment, 74, 516-533, (2000)
[20] R. Mesiar, Aggregation operators: Some classes and construction methods, In: Proceedings Eight International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2000, pp. 707-711
[21] R. Mesiar, B. De Baets, New construction methods for aggregation operators, In: Proceedings Eight International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2000, pp. 701-710
[22] Montero, J., Comprehensive fuzziness, Fuzzy sets and systems, 20, 86-89, (1986) · Zbl 0605.28019
[23] Montero, J., Extensive fuzziness, Fuzzy sets and systems, 21, 201-209, (1986) · Zbl 0605.28020
[24] Montero, J.; Tejada, J.; Cutello, V., A general model for deriving preference structures from data, European journal of operational research, 98, 98-110, (1997) · Zbl 0929.91014
[25] J. Montero, J. Yáñez, J. González-Pachón, Searching for the dimension of a fuzzy preference relation, EURO Conference Budapest, July 16-19, 2000
[26] Roubens, M., Pattern classification problems and fuzzy sets, Fuzzy sets and systems, 1, 239-253, (1978) · Zbl 0435.68064
[27] Roy, B., Decision science or decision-aid science, European journal of operational research, 66, 184-203, (1993)
[28] Ruspini, E.H., A new approach to clustering, Information and control, 15, 22-32, (1969) · Zbl 0192.57101
[29] Schwizer, B.; Sklar, A., Probabilistic metric spaces, (1983), North-Holland New York · Zbl 0546.60010
[30] Shafer, G., Savage revisited, Statistical science, 1, 463-501, (1990) · Zbl 0613.62002
[31] H. Thiele, A characterization of Ruspini-partitions by similarity relations, In: Proceedings International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, 1996, pp. 389-394
[32] H. Thiele, A characterization of arbitrary Ruspini-partitions by fuzzy similarity relations, In: Proceedings FUZZ-IEEE Conference, 1997, pp. 131-134
[33] Trillas, E., On negation functions in fuzzy set theory, (), 31-43
[34] Yager, R.R., On ordered weighted averaging aggregation operators in multi-criteria decision making, IEEE transactions on systems, man and cybernetics, 18, 183-190, (1988) · Zbl 0637.90057
[35] Yager, R.; Rybalov, A., Uninorm aggregation operators, Fuzzy sets and systems, 80, 111-120, (1996) · Zbl 0871.04007
[36] Yáñez, J.; Montero, J., A poset dimension algorihtm, Journal of algorithms, 30, 185-208, (1999) · Zbl 0914.68149
[37] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
[38] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE transactions on systems, man and cybernetics, 1, 28-44, (1973) · Zbl 0273.93002
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.