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

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

2010-10-21

arxiv.org/abs/1010.4561v2

Computer Science

Artificial Intelligence

11 pages, 20 figures, under review of SPRINGER (Fuzzy Optimization and Decision Making)

Scientific paper

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.

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