The problem of upgrade has been emphsised with the development of fuzzy mathematics. The problem of upgrade on algebraic structure was considered in paper[1], and the concept of the hypergroup was raised, And then, th...The problem of upgrade has been emphsised with the development of fuzzy mathematics. The problem of upgrade on algebraic structure was considered in paper[1], and the concept of the hypergroup was raised, And then, the works were carried out in the paper [2]—[6]. This paper gives some further description for hypergroup. The main work is concluded as follows: (1) Solving the structure of hypergroup on the cyclical group. (2)Relationship amang the associative hypergroups for group, normal subgroup and factor group is considered. (3)Relationship between hypergroup and ordinary group is descriped. (4)The problem of existence on maximal, maximun, minimun element for the hypergroup which satisfys certain restricted condition is considered.展开更多
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
文摘The problem of upgrade has been emphsised with the development of fuzzy mathematics. The problem of upgrade on algebraic structure was considered in paper[1], and the concept of the hypergroup was raised, And then, the works were carried out in the paper [2]—[6]. This paper gives some further description for hypergroup. The main work is concluded as follows: (1) Solving the structure of hypergroup on the cyclical group. (2)Relationship amang the associative hypergroups for group, normal subgroup and factor group is considered. (3)Relationship between hypergroup and ordinary group is descriped. (4)The problem of existence on maximal, maximun, minimun element for the hypergroup which satisfys certain restricted condition is considered.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
