# Multi-Valued Neural Networks I A Multi-Valued Associative Memory

## TL;DR

This paper introduces a novel multi-valued associative memory model using lattice theory, expanding fuzzy neural network concepts to handle elements or subsets of a lattice for classification tasks.

## Contribution

It generalizes fuzzy associative memory to multi-valued cases without numerical representations, providing new properties and a learning algorithm for such networks.

## Key findings

- Defined conditions for storing pattern pairs in the memory
- Developed a learning algorithm for multi-valued networks
- Applied the model to classify aircraft/spacecraft trajectories

## Abstract

A new concept of a multi-valued associative memory is introduced, generalizing a similar one in fuzzy neural networks. We expand the results on fuzzy associative memory with thresholds, to the case of a multi-valued one: we introduce the novel concept of such a network without numbers, investigate its properties, and give a learning algorithm in the multi-valued case. We discovered conditions under which it is possible to store given pairs of network variable patterns in such a multi-valued associative memory. In the multi-valued neural network, all variables are not numbers, but elements or subsets of a lattice, i.e., they are all only partially-ordered. Lattice operations are used to build the network output by inputs. In this paper, the lattice is assumed to be Brouwer and determines the implication used, together with other lattice operations, to determine the neural network output. We gave the example of the network use to classify aircraft/spacecraft trajectories.