Feng Feng, Fujita Hamido, Jun Young Bae, Khan Madad
Department of Applied Mathematics, School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
Faculty of Software and Information Science, Iwate Prefectural University, Iwate 020-0193, Japan.
ScientificWorldJournal. 2014 Jan 12;2014:902687. doi: 10.1155/2014/902687. eCollection 2014.
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.
模糊软集的概念是一种混合软计算模型，它将渐进性和参数化方法和谐地结合起来以处理不确定性。在不确定性下的决策方面，模糊软集的分解在理论和实际应用中都非常重要。本研究旨在探索具有有限值空间的模糊软集的分解。引入了模糊软集的标量单积和内积运算，并研究了一些相关性质。利用t - 水平软集，我们定义了水平等价关系，并表明由水平等价关系诱导的单位区间的商结构与由给定模糊软集的所有t - 水平软集组成的格同构。我们还引入了关键阈值和完全阈值集的概念。最后，建立了具有有限值空间的模糊软集的一些分解定理，并通过一个关于多媒体手机分类和评级的例子进行说明。由于每个模糊集都可以看作是具有单个参数的模糊软集，因此所得到的结果扩展了模糊集的一些经典分解定理。
