Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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FUZZY LINEARITY OF THE FUZZY INTEGRAL

  • Kim, Mi Hye (Department of Mathematics Chungbuk National University) ;
  • Shin, Seung Soo (Department of Mathematics Chungbuk National University)
  • Received : 1998.05.19
  • Published : 1999.07.31
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Abstract

We introduce a concept of fuzzy linearity: A function $F:L^0(X){\rightarrow}\mathbb{R}$ is fuzzy linear if $F[({\alpha}{\wedge}f){\vee}(b{\wedge}g)]=[a{\wedge}F(f)]{\vee}[b{\wedge}F(g)]$ for $f,g{\in}L^0(X)$ and a, b > 0. We show that a fuzzy integral is fuzzy linear if the measure is fuzzy c-additive.

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