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STRUCTURAL CHARACTERISTICS OF FUZZY MEASURE ON S-COMPACT SPACES

1990; Taylor & Francis; Volume: 17; Issue: 4 Linguagem: Inglês

10.1080/03081079008935114

1563-5104

Wang Zhenyuan,

Fuzzy Systems and Optimization

Abstract In systems research, the fuzzy measures we encounter most often are finite and established on S-compact spaces, which contain finite and infinitely countable measurable spaces. The structural characteristics of set function, such as null-additivity, autocontinuity, and uniform autocontinuity, are very important for the researches in fuzzy integral. For a fuzzy measure, the null-additivity is a quite weak requirement added on it, but the autocontinuity and the uniform autocontinuity are very powerful properties. In this paper, we prove that the null-additivity is equivalent to the uniform autocontinuity for the finite fuzzy measures on S-compact spaces. INDEX TERMS: Fuzzy measurestructural characteristics of set functionS-compact space. Additional informationNotes on contributorsWANG ZHENYUAN On leave from the Department of Mathematics, Hebei University, Baoding, Hebei, China.