title: Decomposition of fuzzy soft sets with finite value spaces.
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.
authors.affiliation: Department of Applied Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
authors.forename: Feng
authors.identifier: 0000-0002-8876-3090
authors.initials: F
authors.lastname: Feng
authors.affiliation: Faculty of Software and Information Science, Iwate Prefectural University, Iwate 020-0193, Japan.
authors.forename: Hamido
authors.identifier: 0000-0001-5256-210X
authors.initials: H
authors.lastname: Fujita
authors.affiliation: Department of Mathematics Education (and RINS), Gyeongsang National University, Jinju 660-701, Republic of Korea.
authors.forename: Young Bae
authors.initials: YB
authors.lastname: Jun
authors.affiliation: Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad 22060, Pakistan.
authors.forename: Madad
authors.identifier: 0000-0003-0044-961X
authors.initials: M
authors.lastname: Khan
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical