A fuzzy numeric inference strategy for classification and regression problems

Article type: Research Article

Authors: Crockett, K.^{; *} | Bandar, Z. | O'Shea, J. | Fowdar, J.

Affiliations: The Intelligent Systems Group, Department of Computing and Mathematics, The Manchester Metropolitan University, Chester Street, Manchester, M15 9GD, UK

Correspondence: [*] Corresponding author. Tel.: +44 161 247 1497; Fax: +44 161 247 1483; E-mail: K.Crockett@mmu.ac.uk

Abstract: This paper introduces a novel Fuzzy Numeric Inference Strategy (FNIS) which induces fuzzy trees that can be applied to data domains where the outcome can be either numeric or discrete. The methodology applies the principles of fuzzy theory to pre-generated crisp decision trees in order to soften the sharp decision boundaries that are inherent in such induction techniques. Introducing fuzziness around a tree node allows classification knowledge to be represented more naturally and in-line with human thinking thus creating more robust trees when handling imprecise or conflicting information. The FNIS methodology first extrapolates rules from crisp decision trees. Each attribute is then fuzzified using a Genetic Algorithm (GA) to determine the size of the fuzzy partitions around each tree node automatically. A fuzzy decision tree is then created using a one-to-one mapping and a genetically optimised pre-selected fuzzy inference technique is used to combine all information throughout the tree. FNIS uses two strategies for defuzzification, depending on the type of the outcome variable. For discrete values the traditional centre of gravity approach is adopted, whilst for predicting numeric outcomes a novel method of defuzzification is proposed. CHAID is a successfully proven algorithm for inducing decision trees which can solve both classification and regression problems. It is used to illustrate the creation of fuzzy trees through the proposed strategy. A series of experiments is carried out to compare the performance of crisp trees with FNIS induced fuzzy trees, using real world datasets. The results are shown to compare favourably with other fuzzy and crisp decision tree algorithms. The fuzzy trees are also shown to be more robust leading to improved classification/prediction over crisp trees.

DOI: 10.3233/KES-2008-12401

Journal: International Journal of Knowledge-based and Intelligent Engineering Systems, vol. 12, no. 4, pp. 255-269, 2008