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UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification

Armin Salimi-Badr

TL;DR

The paper tackles the limitation of traditional FIS, where rules are forced to consider all input variables, by introducing UNFIS, which employs fuzzy selection neurons to form unstructured, input-subset rules for classification. A seven-layer neuro-fuzzy architecture enables selective antecedents, while a tailored GqLM learning algorithm optimizes multiclass cross-entropy within a trust-region framework. The approach yields competitive or superior accuracy with more interpretable, sparse rule sets across real-world datasets and demonstrates clear benefits in high-dimensional settings. This work advances interpretable, adaptable fuzzy classifiers and offers a practical training method for multiclass problems.

Abstract

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules defined based on evaluating all input variables. Indeed, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Therefore, this constraint limits the performance, generalization, and interpretability of the FIS. To address this issue, this paper presents a neuro-fuzzy inference system for classification applications that can select different sets of input variables for constructing each fuzzy rule. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, in this paper, the consequent part of the Takagi-Sugeno-Kang FIS is also changed properly to consider only the selected set of input variables. To learn the parameters of the proposed architecture, a trust-region-based learning method (General quasi-Levenberg-Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification problems. Based on these comparisons the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy.

UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification

TL;DR

The paper tackles the limitation of traditional FIS, where rules are forced to consider all input variables, by introducing UNFIS, which employs fuzzy selection neurons to form unstructured, input-subset rules for classification. A seven-layer neuro-fuzzy architecture enables selective antecedents, while a tailored GqLM learning algorithm optimizes multiclass cross-entropy within a trust-region framework. The approach yields competitive or superior accuracy with more interpretable, sparse rule sets across real-world datasets and demonstrates clear benefits in high-dimensional settings. This work advances interpretable, adaptable fuzzy classifiers and offers a practical training method for multiclass problems.

Abstract

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules defined based on evaluating all input variables. Indeed, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Therefore, this constraint limits the performance, generalization, and interpretability of the FIS. To address this issue, this paper presents a neuro-fuzzy inference system for classification applications that can select different sets of input variables for constructing each fuzzy rule. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, in this paper, the consequent part of the Takagi-Sugeno-Kang FIS is also changed properly to consider only the selected set of input variables. To learn the parameters of the proposed architecture, a trust-region-based learning method (General quasi-Levenberg-Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification problems. Based on these comparisons the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy.
Paper Structure (11 sections, 2 theorems, 29 equations, 4 figures, 5 tables, 1 algorithm)

This paper contains 11 sections, 2 theorems, 29 equations, 4 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Proposed Method
  3. Unstructured Fuzzy Rules
  4. Unstructured Neuro-Fuzzy Inference System (UNFIS)
  5. General quasi-Levenberg-Marquardt (GqLM) Algorithm
  6. Experiments
  7. Experimental Setup and Performance Criteria
  8. Real-world Classification Problems
  9. Illustrative Example for Proposed Feature Selection
  10. Studying the Performance of GqLM
  11. Conclusions

Key Result

Lemma 2.1

The membership value $\mu^{+i}_j$ is in range (0,1).

Figures (4)

  • Figure 1: The effect of changing value of selection parameter $\varsigma$ on the shape of a Gaussian membership function.
  • Figure 2: The architecture of the proposed Fuzzy Neural Network.
  • Figure 3: Samples of Iris dataset along with the extracted fuzzy sets for two fuzzy rules.
  • Figure 4: Comparison of the performance of the proposed learning algorithm (GqLM) with other methods including Levenberg-Marquardt (LM), Stochastic Gradient Descent (SGD), and Momentum.

Theorems & Definitions (4)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • proof