Decomposition of Fuzzy Soft Sets with Finite Value Spaces

Abstract EN

The notion of fuzzy soft sets is a hybrid soft computing model that integrates bothgradualness and parameterization methods in harmony to deal with uncertainty.

The decomposition of fuzzy soft sets is of great importance in both theory andpractical applications with regard to decision making under uncertainty.

This studyaims to explore decomposition of fuzzy soft sets with finite value spaces.

Scalaruni-product and int-product operations of fuzzy soft sets are introduced and somerelated properties are investigated.

Using t-level soft sets, we define level equivalentrelations and show that the quotient structure of the unit interval induced by levelequivalent relations is isomorphic to the lattice consisting of all t-level soft sets of agiven fuzzy soft set.

We also introduce the concepts of crucial threshold values andcomplete threshold sets.

Finally, some decomposition theorems for fuzzy soft setswith finite value spaces are established, illustrated by an example concerningthe classification and rating of multimedia cell phones.

The obtained results extendsome classical decomposition theorems of fuzzy sets, since every fuzzy set can beviewed as a fuzzy soft set with a single parameter.