Fuzzy Membrane Systems: Handling Inexactitude in Computations

Title: Fuzzy Membrane Systems: Handling Inexactitude in Computations

Abstract: This research explores the use of fuzzy set theory to introduce uncertainty in membrane computing, specifically focusing on the inexactitude of reactives involved in biochemical reactions. The study proposes a fuzzy version of symport/antiport membrane systems, where threshold functions determine whether a rule can be applied based on the degree of accuracy of objects to the reactives specified in the rule. The results show that these fuzzy membrane systems can generate exactly the recursively enumerable finite-valued fuzzy subsets of N, proving their universality. This work opens up new possibilities for handling uncertainty and approximations in membrane computing, paving the way for more accurate and realistic models of cellular processes.

Main Research Question: How can fuzzy set theory be used to introduce uncertainty and inexactitude in membrane computing?

Methodology: The study introduces a fuzzy version of symport/antiport membrane systems. These systems handle possibly inexact copies of reactives and are endowed with threshold functions that determine whether a rule can be applied or not, depending on the degree of accuracy of objects to the reactives specified in the rule.

Results: The research demonstrates that fuzzy membrane systems can generate exactly the recursively enumerable finite-valued fuzzy subsets of N, establishing their universality. This implies that these systems can effectively model and compute with approximate values, making them more suitable for representing and simulating real-world cellular processes where inexactitude is common.

Implications: The introduction of fuzzy set theory in membrane computing opens up new avenues for research and applications. By allowing for the handling of inexactitude, these systems can provide more accurate and realistic models of cellular processes, leading to advancements in various fields such as biology, chemistry, and computer science. Additionally, the fuzzy approach offers a new perspective on the universality of membrane computing systems, contributing to a better understanding of their computational capabilities.

Link to Article: https://arxiv.org/abs/0403027v1 Authors: arXiv ID: 0403027v1