Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0824.28015
Liu, Xuecheng; Zhang, Guangquan
Lattice-valued fuzzy measure and lattice-valued fuzzy integral. (English)
[J] Fuzzy Sets Syst. 62, No.3, 319-332 (1994). ISSN 0165-0114

Summary: In this paper, (1) the concepts of lattice-valued fuzzy measure (with no valuation property) and lower (resp. upper) lattice-valued fuzzy integral are proposed, which give the unified description to the fuzzy measures and fuzzy integrals studied by Delgado and Moral, Qiao, Ralescu, Adams, Sugeno, Wang, and Zhang; (2) some asymptotic structural characteristics of lattice-valued fuzzy measures are introduced, and some relations between them are given; (3) some concepts of convergences for lattice- valued functions are defined, and Riesz' theorem, Egoroff's theorem and Lebesgue's theorem for lattice-valued measurable functions are proved; (4) the monotone increasing (resp. decreasing) convergence theorem and almost (resp. pseudo almost) everywhere convergence theorem for lower (resp. upper) lattice-valued fuzzy integral are shown under some weak conditions.

MSC 2000:: *28E10 Fuzzy measures

Keywords: lattice-valued fuzzy measure; lattice-valued fuzzy integral; Riesz' theorem; Egoroff's theorem; Lebesgue's theorem; convergence

Cited in: Zbl 0896.28008

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]