Extensions to the fuzzy pointing set and its application to artificial intelligence

The extension of the fuzzy pointing set S=R ∪ {*}, where * represents a nonreal background or uncertain value to the set S_n=R ∪ {*₁,. . .,* _n}, where *₁,. . .,*_n are nonreal values representing information with varying degrees of uncertainty, is considered. This extended pointing set casts the algebraic structure of S into a more general and intuitive environment. First, binary operations on S are extended to S_n, and the algebraic properties induced by them are studied. The extensions are shown to preserve the rich algebraic structure in S. In addition, a set of extended morphological operations on images in S_n² are presented, and the properties and applications attributed to the pointing set are shown to have analogs in the more general environment. Practical interpretations for S _n in artificial intelligence, and image and digital signal processing are given