Fuzzy Integrals

Zhenyuan Wang and George J. Klir
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Zhenyuan Wang: State University of New York at Binghamton
George J. Klir: State University of New York at Binghamton

Chapter Chapter 7 in Fuzzy Measure Theory, 1992, pp 131-162 from Springer

Abstract: Abstract In this chapter, we assume that (X, ℱ) is a measurable space, where X ∈ ℱ, μ : ℱ → [0, ∞] is a fuzzy measure (or a nonnegative monotone set function for Section 7.6), and that F is the class of all finite nonnegative measurable functions defined on (X, ℱ). For any given f ∈ F, we write F α = {x|f(x) ≥ α}, F α + = {x f(x) > α}, where α ∈ [0, ∞]. Let the sets F α and F α+ be called an α-cut and a strict α-cut of f, respectively.

Date: 1992
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DOI: 10.1007/978-1-4757-5303-5_7

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