The structure of soft set in digital images and soft continuity in digital images

In this thesis study, at first some fundamental notions related with Soft Set Theory is mentioned. In this thesis a finite subset of integers with kappa adjacency relation is considered a digital image. The definition of soft set is given by using a parameter set in digital images. Then soft contuniuty and soft homeomorphism is defined on this structure and examples of digital soft continuous function and digital soft homeomorphism is presented by using 4 adjacency and 8 adjacency in 2 dimensional digital images. Also properties of digital soft continuous mappings is proved. Defining the digital soft continuity and proving the properties of digital soft contunuity create infrastructure for defining soft homotopy in digital images. Hence digital soft retraction and digital soft homotopy is defined for kappa adjacent digital images. Then the examples of soft retraction and soft homotopy in digital images are given by using 2 adjacency in 1 dimensional digital images and 4 , 8 adjacency in 2 dimensional digital images. Also some properties of soft retractions and soft homotopy is proved in digital images. Finally it is shown that 'soft homotopy in digital images' is an equivalence relation.