On Union and Intersection of Fuzzy Soft Set

Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. Maji et al. have further initiated several basic notions of soft set theory. They have also introduced the concept of fuzzy soft set, a more generalized concept, which is a combination of fuzzy set and soft set. They introduced some properties regarding fuzzy soft union, intersection, complement of a fuzzy soft set, DeMorgan Laws etc. These results were further revised and improved by Ahmad and Kharal. They defined arbitrary fuzzy soft union and intersection and proved DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory. In this paper, we give some propositions on fuzzy soft union and intersection with proof and examples. Using the definition of arbitrary fuzzy soft union and intersection proposed by Ahmad and Kharal, we are giving two more propositions with proof and examples. We further give the proof of DeMorgan Laws for a family of fuzzy soft sets in a fuzzy soft class proposed by Ahmad and Kharal and verify these laws with examples.