title: On some nonclassical algebraic properties of interval-valued fuzzy soft sets.
abstract: Interval-valued fuzzy soft sets realize a hybrid soft computing model in a general framework. Both Molodtsov's soft sets and interval-valued fuzzy sets can be seen as special cases of interval-valued fuzzy soft sets. In this study, we first compare four different types of interval-valued fuzzy soft subsets and reveal the relations among them. Then we concentrate on investigating some nonclassical algebraic properties of interval-valued fuzzy soft sets under the soft product operations. We show that some fundamental algebraic properties including the commutative and associative laws do not hold in the conventional sense, but hold in weaker forms characterized in terms of the relation = L . We obtain a number of algebraic inequalities of interval-valued fuzzy soft sets characterized by interval-valued fuzzy soft inclusions. We also establish the weak idempotent law and the weak absorptive law of interval-valued fuzzy soft sets using interval-valued fuzzy soft J-equal relations. It is revealed that the soft product operations ∧ and ∨ of interval-valued fuzzy soft sets do not always have similar algebraic properties. Moreover, we find that only distributive inequalities described by the interval-valued fuzzy soft L-inclusions hold for interval-valued fuzzy soft sets.
authors.affiliation: Department of Applied Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
authors.forename: Xiaoyan
authors.identifier: 0000-0002-8848-9220
authors.initials: X
authors.lastname: Liu
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: Mathematics and OR Section, Xi'an Research Institute of High-Tech Hongqing Town, Xi'an 710025, China.
authors.forename: Hui
authors.identifier: 0000-0003-4359-3355
authors.initials: H
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D017143:Fuzzy Logic; D008962:Models, Theoretical