马学玲,詹建明.$M$-半群的直觉$(S,T)$-模糊$M$-子半群的性质[J].数学研究及应用,2007,27(3):455~468 |
$M$-半群的直觉$(S,T)$-模糊$M$-子半群的性质 |
Intuitionistic $(S,T)$-Fuzzy $M$-Subsemigroups of an $M$-Semigroup |
投稿时间:2006-04-16 修订日期:2006-07-02 |
DOI:10.3770/j.issn:1000-341X.2007.03.002 |
中文关键词: $M$-半群 (虚)直觉$(S,T)$-模糊$M$-子半群 直觉$(S,T)$-直积. |
英文关键词:$M$-semigroup (imaginable) intuitionistic fuzzy $M$-subsemigroup intuitionistic $(S,T)$-direct product. |
基金项目:国家自然科学基金(60474022); 湖北省教育厅重点科研基金(2004Z002; D200529001) |
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中文摘要: |
K.T. Atanassov 在1986年首先引入直觉模糊集的概念. 本文利用$s$-范数和$t$-范数, 引入$M$-半群的直觉$(S,T)$-模糊$M$-子半群的概念, 刻画其性质和特征. 我们再进一步给出了直觉$(S,T)$-直积的概念, 并由此探讨了一些有意义的相关结论. |
英文摘要: |
Intuitionistic fuzzy sets are generalized fuzzy sets which were first introduced by Atanassov in 1986. In this paper, we introduce the concept of intuitionistic fuzzy $M$-subsemigroups of an $M$-semigroup $M$ with respect to an $s$-norm $S$ and a $t$-norm $T$ on intuitionistic fuzzy sets and study their properties. In particular, intuitionistic $(S,T)$-direct products of $M$-semigroups are considered and some recent results of fuzzy $M$-subsemigroups of $M$-semigroups obtained by Zhan and Tan$^{[21]}$ are extended and generalized to intuitionistic $(S,T)$-fuzzy $M$-subsemigroups over $M$-semigroups. |
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