Bulgarian Academy of Sciences

The theory of fuzzy measures and fuzzy integrals was introduced by S u g e n o [16] and intensively studied. Monographs [15] and [18] are dedicated to this topic. Recently, several classical inequalities were generalized to fuzzy integral. F l o r e sF r a n u l i č and R o m á n-F l o r e s [11] provided a Chebyshev type inequality for fuzzy integral of continuous and strictly monotone functions based on Lebesgue measure, then O u y a n g, F a n g and W a n g [13] generalized the result and obtained a Chebyshev type inequality for fuzzy integral of monotone functions based on an arbitrary fuzzy measure. The series of papers on this topic was recently closed by M e s i a r and O u y a n g ([14]) with a general version of Chebyshev inequality for the Sugeno integral on an abstract fuzzy measure space, based on a product-like operation. The theory of intuitionistic fuzzy measures was developed in the last years (see [38]). In this contribution we use the theorem of decomposition of the Sugeno integral with respect to intuitionistic fuzzy-valued fuzzy measures ([8]) and the general result