On Induced Soft Sets and Topology for the Parameter Set of a Soft Set

Soft sets can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we introduce the concept of induced soft set based on point-set mapping, some operations on induced soft sets are discussed, and the algebraic structures of induced soft sets, e.g., the lattice structure and the soft quotient algebra, are established. Based on a soft set and its induced soft set, we construct a reflexive and transitive relation on the parameter set E of the soft set, moreover, establish a topology for the parameter set of the soft set. The conclusions may be used in such as environmental science and social science.