新型软域

New type of soft fields

为获得新型软域的新概念,采用与传统软代数不同的定义方法,将软集的参数集赋予域的代数结构。并且得到了新型软域的充要条件。利用软集运算中的限制交运算,得到了2个新型软域的限制交仍是新型软域。运用对偶软集的方法给出了新型软域的等价刻画。最后利用域的同态映射诱导出软集的同态像与原像,并得到了新型软域的同态像和原像仍是新型软域的性质。以这种方式得到的新型软域比通常的软域有更深刻的结果,为今后新型软代数的研究提供了基础。

To develop a concept for a new type of soft field, we introduce a method that endows a parameter set with a field algebra structure that differs from that of traditional soft algebras. We then obtain the necessary and sufficient condition of a new type of soft field. By performing a soft-set intersection operation, we prove that the intersection operation of two new soft-field types still represents a new type of soft field. In addition, we provide equivalent characterizations of this new type of soft field by applying dual soft sets. Finally, we induce homomorphic and inverse images of these soft sets by homomorphically mapping the fields and deriving the properties of the homomorphic and inverse images of this new type of soft field. Using this method to achieve this new type of soft field, we achieve more profound results when compared with ordinary soft fields and lay the foundation for future research into this new type of soft algebra.