包玉娥,吳梅花

(內(nèi)蒙古民族大學數(shù)學學院,內(nèi)蒙古通遼 028043)

一致凸模糊映射及其有關性質(zhì)

包玉娥,吳梅花

(內(nèi)蒙古民族大學數(shù)學學院,內(nèi)蒙古通遼 028043)

討論了模糊映射的一致凸性及其有關性質(zhì),給出了模糊映射為一致凸的幾個判別準則,并得到了可微一致凸模糊映射在某一點達到最小值的充分條件.

模糊數(shù);模糊映射;一致凸性

1 引言

隨著數(shù)學規(guī)劃、數(shù)理經(jīng)濟和最優(yōu)控制論等學科發(fā)展的需要,凸性理論日益受到人們的重視.許多學者對模糊映射在凸集上的廣義凸性及其在數(shù)學規(guī)劃中的應用方面進行了不少的研究工作,極大地豐富了數(shù)學規(guī)劃的研究內(nèi)容.由于一致凸函數(shù)在非線性最優(yōu)化算法中經(jīng)常被應用,因此對它的研究受到最優(yōu)化研究人員的重視,本文將要討論模糊映射在凸集上的一致凸性問題.

2 基本概念

3 模糊映射的一致凸性

[1]Katsaras A K,Voxman W.Topological properties of fuzzy numbers[J].Fuzzy Sets and Systems,1983,10:87-99.

[2]Zalinescu C.On uniform convex functions[J].J.Math.Anal.Appl.,1983,95:344-374.

[3]Bao Yu-e,Wu Congxin.Convexity and semicontinuity of fuzzy mappings[J].Computers and Mathematics with Applications,2006,51:1809-1816.

[4]Syau Y R.Differentiability and convexity of fuzzy mappings[J].Computers and Mathematics with Applications,2001,41:73-81.

[5]楊新民.一致凸函數(shù)的幾個性質(zhì)[J].重慶師范學院學報,1998,3:1-3.

[6]包玉娥,吳從炘.關于模糊映射的凸性與嚴格凸性[J].哈爾濱工業(yè)大學學報,2007,4:639-641.

[7]張萍,黃虎,王早.預不變凸模糊集的一些性質(zhì)[J].純粹數(shù)學與應用數(shù)學,2006,3:355-359.

Uniformly convex fuzzy mappings and its properties

BAO Yu-e,WU Mei-hua
(College of Mathematics,Inner Mogolia National University,Tongliao028043,China)

In this paper,uniformly convexity and concerning properties of fuzzy mappings are studied,some criterions for the uniformly convex fuzzy mapping are obtained,the sufficient condition that differential uniformly convex fuzzy mapping reach minimum are obtained.

fuzzy numbers,fuzzy mapping,uniformly convexity

O159.2

A

1008-5513(2009)04-0725-06

2008-04-21.

內(nèi)蒙古教育廳科研基金(NJ06088).

包玉娥(1962-),博士,教授,研究方向：凸性理論與模糊數(shù)學.

2000MSC:03E72