Contamination-Free Measures and Algebraic Operations

TL;DR

This paper introduces new methods and semantics for managing contaminated operations in rough algebraic systems, aiming to preserve rough evolution and ensure consistency across different semantic domains.

Contribution

It develops a novel approach to handle contaminated operations and structured bigness within rough Y-systems, enhancing the comparison of rough algebraic semantics.

Findings

Proposed methods effectively handle contaminated operations.

Semantics developed improve consistency across semantic domains.

Enhances the formal framework of rough Y-systems.

Abstract

An open concept of rough evolution and an axiomatic approach to granules was also developed recently by the present author. Subsequently the concepts were used in the formal framework of rough Y-systems (RYS) for developing on granular correspondences by her. These have since been used for a new approach towards comparison of rough algebraic semantics across different semantic domains by way of correspondences that preserve rough evolution and try to avoid contamination. In this research paper, new methods are proposed and a semantics for handling possibly contaminated operations and structured bigness is developed. These would also be of natural interest for relative consistency of one collection of knowledge relative other.