一致凸模糊映射及其有關(guān)性質(zhì)

包玉娥,吳梅花

(內(nèi)蒙古民族大學(xué)數(shù)學(xué)學(xué)院,內(nèi)蒙古通遼 028043)

一致凸模糊映射及其有關(guān)性質(zhì)

包玉娥,吳梅花

(內(nèi)蒙古民族大學(xué)數(shù)學(xué)學(xué)院,內(nèi)蒙古通遼 028043)

討論了模糊映射的一致凸性及其有關(guān)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(xué)規(guī)劃、數(shù)理經(jīng)濟和最優(yōu)控制論等學(xué)科發(fā)展的需要,凸性理論日益受到人們的重視.許多學(xué)者對模糊映射在凸集上的廣義凸性及其在數(shù)學(xué)規(guī)劃中的應(yīng)用方面進行了不少的研究工作,極大地豐富了數(shù)學(xué)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(yīng)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

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

[7]張萍,黃虎,王早.預(yù)不變凸模糊集的一些性質(zhì)[J].純粹數(shù)學(xué)與應(yīng)用數(shù)學(xué),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(xué).

2000MSC:03E72