Molodtsov introduced soft sets as a mathematical tool to handle uncertainty associated with real world data based problems. In this paper we propose some new concepts which generalize existing comparable notions. We introduce the concept of generalized soft equality (denoted as $g$-soft equality) of two soft sets and prove that the so called lower and upper soft equality of two soft sets imply $g$-soft equality but the converse does not hold. Moreover we give tolerance or dependence relation on the collection of soft sets and soft lattice structures. Examples are provided to illustrate the concepts and results obtained herein.