# Fuzzy Decision Trees

Malcolm J. Beynon (Cardiff University, UK)
DOI: 10.4018/978-1-59904-843-7.ch044

## Abstract

The first (crisp) decision tree techniques were introduced in the 1960s (Hunt, Marin, & Stone, 1966), their appeal to decision makers is due in no part to their comprehensibility in classifying objects based on their attribute values (Janikow, 1998). With early techniques such as the ID3 algorithm (Quinlan, 1979), the general approach involves the repetitive partitioning of the objects in a data set through the augmentation of attributes down a tree structure from the root node, until each subset of objects is associated with the same decision class or no attribute is available for further decomposition, ending in a number of leaf nodes. This article considers the notion of decision trees in a fuzzy environment (Zadeh, 1965). The first fuzzy decision tree (FDT) reference is attributed to Chang and Pavlidis (1977), which defined a binary tree using a branch-bound-backtrack algorithm, but limited instruction on FDT construction. Later developments included fuzzy versions of crisp decision techniques, such as fuzzy ID3, and so forth (see Ichihashi, Shirai, Nagasaka, & Miyoshi, 1996; Pal & Chakraborty, 2001) and other versions (Olaru & Wehenkel, 2003).

## Key Terms in this Chapter

Membership Function: Mathematical function to grade the association of a value to a set.

Inductive Learning: The process of analysis through working with samples, which infers generalizations from the information in the data.

Branch: Path down a decision tree from the root node to a leaf node.

Subsethood: The degree to which the set A is a subset of the set B.

Root Node: First (top) node in a decision tree, from which all branches of the tree start from.

Decision Tree: A tree-like way of representing a collection of hierarchical decision rules that lead to a class or value, starting from a root node ending in a series of leaf nodes.

Leaf Node: Node at the end of a branch that discerns which decision class the associated branch classifies to.

## Complete Chapter List

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Foreword
Jean-Charles Pomerol
Preface
Acknowledgment
Chapter 1
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Chapter 2
Zita Zoltay Paprika
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Chapter 3
John Wang, Chandana Chakraborty, Huanyu Ouyang
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Sven A. Carlsson
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Ricardo Colomo Palacios, Juan Miguel Gómez Berbís, Ángel García Crespo
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Maria Eugénia Captivo, João Clímaco, Sérgio Fernandes
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Amit V. Deokar, Omar F. El-Gayar
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Sergio F. Ochoa, José A. Pino
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Malcolm J. Beynon
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Thomas Madritsch, Michael May, Herwig Ostermann, Roland Staudinger
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Alexandre Gachet, Ralph Sprague
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Patrick Brézillon, Jean-Charles Pomerol
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Pascale Zaraté
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Dashboards for Management  (pages 116-123)
Werner Beuschel
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John Wang, James Yao, Qiyang Chen
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Patrick Humphreys
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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Ivan Bruha
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Viviane Barbosa Diniz, Marcos R.S. Borges, José Orlando Gomes, José H. Canós
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Udo Richard Averweg
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Patrick Humphreys
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Daniel J. Power
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James Yao, John Wang, Qiyang Chen, June Lu
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DS/AHP  (pages 278-285)
Malcolm J. Beynon
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David Sammon
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Simon Woodworth, Joe Cunningham
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G. Kouamou, C. Pettang
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Fátima C.C. Dargam
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Chapter 44
Fuzzy Decision Trees  (pages 382-390)
Malcolm J. Beynon
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P. Serra, R. A. Ribeiro, R. Marques Pereira, R. Steel, M. Niezette, A. Donati
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Games of Strategy  (pages 402-409)
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John Wang, Dajin Wang, Aihua Li
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Alexey Petrovsky
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Frédéric Adam, Jean-Charles Pomerol, Patrick Brézillon
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Marcelo Índio dos Reis, Marcos R.S. Borges, José Orlando Gomes
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Fergal Carton
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Manual Mora, Ovsei Gelman, Guisseppi Forgionne, Francisco Cervantes
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John McAvoy, Tom Butler
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Peter O’Donnell, Rob Meredith
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Knowledge Based DSS  (pages 565-575)
Michel R. Klein
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James D. Jones
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Camille Rosenthal-Sabroux, Michel Grundstein, Fernando Iafrate
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James D. Jones
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Csaba Csáki
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Brad Morantz, Thomas Whalen, G. Peter Zhang
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Chris Schlueter Langdon
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Manual Mora, Francisco Cervantes, Guisseppi Forgionne, Ovsei Gelman
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Tan Yigitcanlar, Omur Saygin
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João Carlos Namorado Clímaco, João Carlos Soares de Mello, Lidia Angulo Meza
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PROMETHEE  (pages 743-750)
Malcolm J. Beynon
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Malcolm J. Beynon
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Todd McElroy
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Edward Shinnick, Geraldine Ryan
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Rough Set Theory  (pages 783-789)
Malcolm J. Beynon
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Dorrie DeLuca, Joseph S. Valacich
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Software Agents  (pages 798-806)
Stanislaw Stanek, Maciej Gawinecki, Malgorzata Pankowska, Shahram Rahimi
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C.W. Holsapple
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Mattias Strand, Sven A. Carlsson
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Robert Fitzgerald, John Findlay
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Hanan Yaniv, Susan Crichton
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Hanan Yaniv
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Pat Finnegan, Jeremy Hayes
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Giusseppi Forgionne, Stephen Russell
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David Sammon
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David Sammon
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Giusseppi Forgionne, Stephen Russell
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Chapter 107