Results of the Chebyshev type inequality for Pseudo-integral

results of the chebyshev type inequality for pseudo-integral

in this paper, some results of the chebyshev type integral inequality for the pseudo-integral are proven. the obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. finally, we applied our results  to the case of comonotone functions.

Results of the Chebyshev Type Inequality for Pseudo-integral

In this paper, some results of the Chebyshev type integral inequality for the pseudo-integral are proven. The obtained results, are related to the measure of a level set of the maximum and the sum of two non-negative integrable functions. Finally, we applied our results to the case of comonotone functions.

Extensions of Chebyshev inequality for fuzzy integral and applications⋆

The theory of fuzzy measures and fuzzy integrals was introduced by Sugeno [24] as a tool for modeling nondeterministic problems. Sugeno’s integral is analogous to Lebesgue integral which has been studied by many authors, including Pap [18], Ralescu and Adams [19] and, Wang and Klir [25], among others. RománFlores et al [9, 20–23], started the studies of inequalities for Sugeno integral, and the...

Chebyshev type inequalities for pseudo-integrals

General Chebyshev type inequalities for universal integral

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed in...

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.