We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

We define the concept of a mapping on classes of fuzzy soft sets and study the properties of fuzzy soft images and fuzzy soft inverse images of fuzzy soft sets, and support them with examples and counterexamples.

Using intuitionistic fuzzy set theory, Sanchez's approach to medical diagnosis has been applied to the problem of selection of single remedy from homeopathic repertorization. Two types of Intuitionistic Fuzzy Relations (IFRs) and three types of selection indices are discussed. I also propose a new repertory exploiting the benefits of soft-intelligence.