## Abstract

Earlier clustering techniques such as the modified learning vector quantization (MLVQ) and the fuzzy Kohonen partitioning (FKP) techniques have focused on the derivation of a certain set of parameters so as to define the fuzzy sets in terms of an algebraic function. The fuzzy membership functions thus generated are uniform, normal, and convex. Since any irregular training data is clustered into uniform fuzzy sets (Gaussian, triangular, or trapezoidal), the clustering may not be exact and some amount of information may be lost. In this paper, two clustering techniques using a Kohonen-like self-organizing neural network architecture, namely, the unsupervised discrete clustering technique (UDCT) and the supervised discrete clustering technique (SDCT), are proposed. The UDCT and SDCT algorithms reduce this data loss by introducing nonuniform, normal fuzzy sets that are not necessarily convex. The training data range is divided into discrete points at equal intervals, and the membership value corresponding to each discrete point is generated. Hence, the fuzzy sets obtained contain pairs of values, each pair corresponding to a discrete point and its membership grade. Thus, it can be argued that fuzzy membership functions generated using this kind of a discrete methodology provide a more accurate representation of the actual input data. This fact has been demonstrated by comparing the membership functions generated by the UDCT and SDCT algorithms against those generated by the MLVQ, FKP, and pseudofuzzy Kohonen partitioning (PFKP) algorithms. In addition to these clustering techniques, a novel pattern classifying network called the Yager fuzzy neural network (FNN) is proposed in this paper. This network corresponds completely to the Yager inference rule and exhibits remarkable generalization abilities. A modified version of the pseudo-outer product (POP)-Yager FNN called the modified Yager FNN is introduced that eliminates the drawbacks of the earlier network and yields superior performance. Extensive experiments have been conducted to test the effectiveness of these two networks, using various clustering algorithms. It follows that the SDCT and UDCT clustering algorithms are particularly suited to networks based on the Yager inference rule.

Original language | English |
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Pages (from-to) | 625-644 |

Number of pages | 20 |

Journal | IEEE Transactions on Neural Networks |

Volume | 19 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2008 |

Externally published | Yes |

## Keywords

- Anderson's Iris data
- Automatic derivation
- Fuzzy Kohonen partitioning (FKP)
- Fuzzy clustering
- Fuzzy pattern classification
- Membership function
- Modified learning vector quantization (MLVQ)
- Noise modeling and cancellation
- Normal and convex fuzzy sets
- Pseudofuzzy partition
- Self-organizing feature maps
- Supervised and unsupervised learning
- Traffic prediction and modeling
- Triangular and trapezoidal fuzzy sets
- Yager inference rule
- Yager rule network

## ASJC Scopus subject areas

- Software
- Computer Science Applications
- Computer Networks and Communications
- Artificial Intelligence