Notes on a model for fuzzy computing

TL;DR

This paper proposes a formal framework for fuzzy computing that aligns with the structures of boolean and quantum computing, emphasizing their underlying similarities.

Contribution

It introduces a unified formal setting for fuzzy computing inspired by established computation theories, highlighting common patterns among them.

Findings

Identifies formal similarities between fuzzy, boolean, and quantum computing

Proposes a common pattern underlying these theories

Contributes to the theoretical foundation of fuzzy computing

Abstract

In these notes we propose a setting for fuzzy computing in a framework similar to that of well-established theories of computation: boolean, and quantum computing. Our efforts have been directed towards stressing the formal similarities: there is a common pattern underlying these three theories. We tried to conform our approach, as much as possible, to this pattern. This work was part of a project jointly with Professor Vittorio Cafagna. Professor Cafagna passed away unexpectedly in 2007. His intellectual breadth and inspiring passion for mathematics is still very well alive.