包玉娥,吴从炘.半模糊凸模糊映射[J].数学研究及应用,2010,30(4):571~580
半模糊凸模糊映射
Semistrictly Convex Fuzzy Mappings
投稿时间:2008-06-06  最后修改时间:2008-07-07
DOI:10.3770/j.issn:1000-341X.2010.04.001
中文关键词:  凸性  严格凸性  半严格凸性  下半连续  模糊映射.
英文关键词:convexity  strict convexity  semistrict convexity  lower semicontinuity  fuzzy mapping.
基金项目:国家自然科学基金(No.10271035),内蒙古教育厅科研基金资助项目(Grant No.NJ06088).
作者单位
包玉娥 内蒙古民族大学数学学院, 内蒙古 通辽 028043 
吴从炘 哈尔滨工业大学数学系, 黑龙江 哈尔滨 150001 
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中文摘要:
      本文引入了一类新的凸模糊映射一半严格凸模糊映射的概念,并讨论了它的一些性质.特别是,证明了它的局部性最小值就是整体性最小值,还讨论了它与凸性及严格凸性之间的关系,得到凸性和严格凸性成为半严格凸性的几个充分条件.
英文摘要:
      In this paper, a new class of fuzzy mappings called semistrictly convex fuzzy mappings is introduced and we present some properties of this kind of fuzzy mappings. In particular, we prove that a local minimum of a semistrictly convex fuzzy mapping is also a global minimum. We also discuss the relations among convexity, strict convexity and semistrict convexity of fuzzy mapping, and give several sufficient conditions for convexity and semistrict convexity.
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