We prove a general form of Chebyshev type inequality for generalized upper Sugeno integral in the form of necessary and sufficient condition. A key role in our considerations is played by the class of m-positively dependent functions which includes comonotone functions as a proper subclass. As a consequence, we state an equivalent condition for Chebyshev type inequality to be true for all comonotone functions and any monotone measure. Our results generalize many others obtained in the framework of q-integral, seminormed fuzzy integral and Sugeno integral on the real half-line. Some further consequences of these results are obtained, among others Chebyshev type inequality for any functions. We also point out some flaws in existing results and provide their improvements. * Mathematics Subject Classification (2010): Primary 28A25, 28E10, Secondary 91B06, 60E05
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