Metric spaces of fuzzy sets

被引：40

作者：

Diamond, P ^{[1
]}

Kloeden, P

机构：

[1] Univ Queensland, Dept Math, St Lucia, Qld 4067, Australia

[2] Murdoch Univ, Sch Math & Phys Sci, Murdoch, WA 6150, Australia

来源：

FUZZY SETS AND SYSTEMS | 1999年 / 100卷

关键词：

fuzzy sets; L-p metrics; compact; locally compact;

D O I：

10.1016/S0165-0114(99)80007-4

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Two classes of metrics are introduced for spaces of fuzzy sets. Their equivalence is discussed and basic properties established. A characterisation of compact and locally compact subsets is given in terms of boundedness and p-mean equileft-continuity, and the spaces shown to be locally compact, complete and separable metric spaces.

引用

页码：63 / 71

页数：9

共 10 条

[1] CHARACTERIZATION OF COMPACT SUBSETS OF FUZZY-SETS [J].

DIAMOND, P ;

KLOEDEN, P .

FUZZY SETS AND SYSTEMS, 1989, 29 (03) :341-348

[2]

GRAVES LM, 1946, THEORY FUNCTIONS REA

[3] FUZZY DIFFERENTIAL-EQUATIONS [J].

KALEVA, O .

FUZZY SETS AND SYSTEMS, 1987, 24 (03) :301-317

[4] LIMIT-THEOREMS FOR FUZZY RANDOM-VARIABLES [J].

KLEMENT, EP ;

PURI, ML ;

RALESCU, DA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1986, 407 (1832) :171-182

[5] FUZZY DYNAMICAL-SYSTEMS [J].

KLOEDEN, PE .

FUZZY SETS AND SYSTEMS, 1982, 7 (03) :275-296

[6]

KLOEDEN PE, 1987, P 2 IFSA C TOK JUL, V1, P368

[7]

Lay Steven R., 1982, Pure and Applied Mathematics

[8]

LYASHENKO N. N., 1983, J SOVIET MATH, V21, P76

[9] THE CONCEPT OF NORMALITY FOR FUZZY RANDOM-VARIABLES [J].

PURI, ML ;

RALESCU, DA .

ANNALS OF PROBABILITY, 1985, 13 (04) :1373-1379

[10] LP METRICS FOR COMPACT, CONVEX-SETS [J].

VITALE, RA .

JOURNAL OF APPROXIMATION THEORY, 1985, 45 (03) :280-287

← 1 →