Fuzzy soft mathematical morphology

Abstract

A new framework which extends the concepts of soft mathematical morphology into fuzzy sets is presented. Images can be considered as arrays of fuzzy singletons on the Cartesian grid. Based on this notion the definitions for the basic fuzzy soft morphological operations are derived. Compatibility with binary soft mathematical morphology as well as the algebraic properties of fuzzy soft operations are studied. Explanation of the defined operations is also provided through several examples and experimental results.