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We prove a~general form of Chebyshev type inequality for generalized upperSugeno integral in the form of necessary and sufficient condition. A key rolein our considerations is played by the~class of $m$-positively dependentfunctions which includes comonotone functions as a~proper subclass. Asa~consequence, we state an equivalent condition for Chebyshev type inequalityto be true for all comonotone functions and any monotone measure. Our resultsgeneralize many others obtained in the framework of q-integral, seminormedfuzzy integral and Sugeno integral on the real half-line. Some furtherconsequences of these results are obtained, among others Chebyshev typeinequality for any functions. We also point out some flaws in existing resultsand provide their improvements.

General form of Chebyshev type inequality for generalized Sugeno integral