AN APPROACH TO THE THEORETICAL FOUNDATIONS OF ELECTRONIC CIRCUIT DESIGN: SHEFFER STROKE HILBERT ALGEBRAS AND FUZZY SETS WITH THRESHOLDS

The Sheffer Stroke (also known as the NAND operator) is an important logical operator used in digital circuits based on the theory of fuzzy sets. The concept of fuzzy subalgebras (or fuzzy ideals) with thresholds in Sheffer Stroke Hilbert algebras is introduced. Several properties of these fuzzy subalgebras (fuzzy ideals) are discussed, and their generalizations are proven. Furthermore, the relationships between fuzzy subalgebras (fuzzy ideals) with thresholds and their level subsets are explored in detail.