Fuzzy classification context for the responsive and formal design process

Abstract

This paper presents an application of a fuzzy relation in system modeling (from requirements) to be used for a Systems Engineering (SE) methodology. We define fuzzy classifications (models for distributed systems), extract component and system theories (sets of logical expressions), and ensure consistency of requirements for the Responsive and Formal Design (RFD) Process. The RFD process is a SE methodology that relates a set of requirements, associated models, simulations, and the relationship between them, by integrating Model-Based Systems Engineering (MBSE) to manage system modeling complexity with formal methods to ensure that designs are verifiably correct against their requirements. To translate informal requirements to logical expressions in the RFD process, we first model requirements using a 3-tuple structure called a classification formulated from Barwise and Seligman's channel theory. A classification consists of (observed situations) and (situation features) and a binary relation classifying tokens with types. However, classifying tokens using types as present (represented as ‘1’) or absent (represented as ‘0’) as used in channel theory is not always possible (since it involves vagueness and imprecission) and the representation lacks expressiveness to reason about relations among such types (vague situation features). Hence, a binary classification doesn't capture uncertainity. In this paper, we consider a degree of truth in the relation between tokens and types to define a fuzzy classification. We then develop an algorithm that extracts a theory from a fuzzy classification. This helps in formal proof for checking consistency (no contradiction) and deducing to requirements (verifying properties). We demonstrate our development using three small satellites measurement system whose goal is to image the colorful auroral ovals seen around Earth's magnetic poles.