Affiliations: [a] Center for Radio Administration and Technology Development, Xihua University, Chengdu, Sichuan, China
| [b] School of Information Science and Technology, Southwest Jiaotong University, Chengdu, Sichuan, China
| [c] BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME), University of Salamanca, Salamanca, Spain
Abstract: This paper reviews and compares theories of fuzzy sets and soft sets from the perspective of transformation, and we prove that every fuzzy set on a universe U can be considered as a soft set, and show that any soft set can be regarded as even a fuzzy set. This paper presents two mapping methods to implement the transformation, namely, the methods of the binary-coded genetic algorithm (BCGA) and the ordered weighted averaging (OWA) operators. In practical applications, it can be used to establish the membership function of fuzzy sets, and it can also be applied to pattern recognition, decision-making, etc. In general, it provides a new perspective to observe the relationship between soft sets and fuzzy sets, and it can be regarded as a general strategy to establish the membership function of fuzzy sets. Further, it reveals that the transformation method is similar to the process of building neurons, which opens a door to machine learning for soft set theory.
