Abstract
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter.
Highlights
With the development of modern science and technology, modelling various uncertainties has become an important task for a wide range of applications including data mining, pattern recognition, decision analysis, machine learning, and intelligent systems
We have investigated the decomposition of fuzzy soft sets with finite value spaces
It has been shown that the collection L(S) of all t-level soft sets of a given fuzzy soft set S forms a sublattice of the lattice (SA(U), ∪̃, ∩̃)
Summary
With the development of modern science and technology, modelling various uncertainties has become an important task for a wide range of applications including data mining, pattern recognition, decision analysis, machine learning, and intelligent systems. The concept of uncertainty is too complicated to be captured within a single mathematical framework In response to this situation, a number of approaches including probability theory, fuzzy sets [1], and rough sets [2] have been developed. Decomposition of fuzzy soft sets is a topic of both theoretical and practical value Motivated by this consideration, Feng et al investigated some basic. The Scientific World Journal properties of level soft sets based on variable thresholds and obtained some decomposition theorems of fuzzy soft sets by considering variable thresholds [25]. In this study, we shall follow the research line above and concentrate on decomposition of fuzzy soft sets with finite value spaces. The last section summarizes the study and suggests possible directions for future work
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