New S-norm and T-norm Operators for Active Learning Method

TL;DR

This paper introduces two novel morphological operators for Active Learning Method that function as fuzzy S-norm and T-norm, satisfying De Morgan's laws and enhancing the analytical capabilities of ALM.

Contribution

The paper proposes new morphological operators serving as fuzzy S-norm and T-norm, addressing a gap in ALM's analytical expression and logical completeness.

Findings

Operators satisfy De Morgan's laws

Operators are validated through mathematical, geometric, and fuzzy logic analysis

Enhances ALM's modeling and control capabilities

Abstract

Active Learning Method (ALM) is a soft computing method used for modeling and control based on fuzzy logic. All operators defined for fuzzy sets must serve as either fuzzy S-norm or fuzzy T-norm. Despite being a powerful modeling method, ALM does not possess operators which serve as S-norms and T-norms which deprive it of a profound analytical expression/form. This paper introduces two new operators based on morphology which satisfy the following conditions: First, they serve as fuzzy S-norm and T-norm. Second, they satisfy Demorgans law, so they complement each other perfectly. These operators are investigated via three viewpoints: Mathematics, Geometry and fuzzy logic.