# Deep Fuzzy Systems

## TL;DR

This paper explores the structure and representation of deep fuzzy systems, focusing on recursive fuzzy systems, fuzzy chains, and connection matrices to model complex fuzzy logic processes.

## Contribution

It introduces a formal framework for representing deep fuzzy systems using recursive calls, fuzzy chains, and connection matrices, advancing the understanding of their structure.

## Key findings

- Recursive fuzzy systems are modeled as sequences of fuzzy memberships.
- Connection matrices effectively represent recursive calls in fuzzy systems.
- The framework enables systematic analysis of deep fuzzy system architectures.

## Abstract

An investigation of deep fuzzy systems is presented in this paper. A deep fuzzy system is represented by recursive fuzzy systems from an input terminal to output terminal. Recursive fuzzy systems are sequences of fuzzy grade memberships obtained using fuzzy transmition functions and recursive calls to fuzzy systems. A recursive fuzzy system which calls a fuzzy system n times includes fuzzy chains to evaluate the final grade membership of this recursive system. A connection matrix which includes recursive calls are used to represent recursive fuzzy systems.

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Source: https://tomesphere.com/paper/1906.08222