Title of article :
Diaz-Metcalf type inequality for Sugeno and pseudo-integrals
Author/Authors :
Karimzadeh ، M. R. Department of Mathematics - University of Maragheh , Daraby ، B. Department of Mathematics - University of Maragheh , Rahimi ، A. Department of Mathematics - University of Maragheh
Abstract :
In this paper, we have proved Diaz-Metcalf inequality for fuzzy integrals. More precisely: If f, g : [0, 1] → R are continuous and strictly increasing functions, then the fuzzy integral inequality − ∫ 1 0 fsdμ · − ∫ 1 0 gsdμ ≤ − ∫ 1 0 (f · g)s dμ, holds, where s 1 and μ is the Lebesgue measure on R. In addition, we have shown this inequality for pseudo-integrals.
Keywords :
Diaz , Metcalf type inequality , fuzzy integral , integral inequality , pseudo integral.
Journal title :
Iranian Journal of Fuzzy Systems (IJFS)
Journal title :
Iranian Journal of Fuzzy Systems (IJFS)
