Abstract
Soft set theory was originally proposed by Molodtsov in 1999 as a general mathematical tool for dealing with uncertainty. However, it has been pointed out that classical soft set model is not appropriate to deal with imprecise and fuzzy problems. In order to handle these types of problems, some fuzzy extensions of soft set theory are presented, yielding fuzzy soft set theory. As a further research, in this work, we first propose concepts of interval fuzzy sets and interval fuzzy soft sets, define some operations on them and study some of their relevant properties, especially, the dual laws are discussed with respect to difference operation in interval fuzzy soft set theory. We then introduce a revised Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method and choice value method for interval fuzzy soft set which the weight information is completely unknown. Meanwhile, an analysis of computation complexity is employed, also the discriminative power of two methods are shown. Finally, two illustrative examples are employed to show that they can be successfully applied to problems that contain uncertainties.
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