直觉相似关系和直觉模糊子群

Intuitionific similarities and intuitionific fuzzy subgroups

研究集合S上的变换群的直觉模糊子群和S上的直觉相似关系之间的密切联系,证明了S上的变换群的任一直觉模糊子群可确定S上的一个直觉相似关系,反之,S上的任一个直觉相似关系可确定S上的变换群的一个直觉模糊子群.同时研究了直觉相似关系和伪度量之间的联系.利用这个联系进一步研究了直觉模糊子群和伪度量之间的联系,即由S上的变换群的直觉模糊子群可确定一个超伪度量,反之,由一个超伪度量可确定S上的变换群的直觉模糊子群.

In this paper we show strict relation between the intuitionific fuzzy groups of transformation group in S and intuitionfic similarities on S, i.e. any intuitionific fuzzy subgroup of transformation group on S is associated with an intuitionific similarity on S, and any intuitionific similarity on S is as- sociated with an intuitionific fuzzy subgroup of transformation group on S. And we show the relation between intuitionfic similarity and pseudometric. Further more, from such relation we study the relation between intuitionific fuzzy subgroup and pseudometric, i.e. intutionific fuzzy subgroup of transformation group on S is associated with a pseudometric and, conversely, pseudometric is asoociated with a intuitionific fuzzy subgroup of transformation group on S.