Fritz Carlson’s inequality for fuzzy integrals

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.

General Fritz Carlson’s Type Inequality for Sugeno Integrals

Recently, the study of fuzzy integral inequalities has gained much attention. The most popular method is using the Sugeno integral 1 . The study of inequalities for Sugeno integral was initiated by Román-Flores et al. 2, 3 and then followed by the others 4–11 . Now, we introduce some basic notation and properties. For details, we refer the reader to 1, 12 . Suppose that Σ is a σ-algebra of subs...

Quadrature Rules for Fuzzy Integrals

Stolarsky Type Inequality for Sugeno Integrals on Fuzzy Convex Functions

Recently, Flores-Franulič et al. [A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 208 (2008) 55-59] proved the Stolarsky’s inequality for the Sugeno integral on the special class of continuous and strictly monotone functions. This result can be generalized to a general class of fuzzy convex functions in this paper. We also give a fuzzy integral inequal...

Minkowski's Inequality for Integrals

The following inequality is a generalization of Minkowski's inequality C12.4 to double integrals. In some sense it is also a theorem on the change of the order of iterated integrals, but equality is only obtained if p = 1. 13.14 Theorem (Minkowski's inequality for integrals) Let XX and YY be-finite measure spaces and u u X × Y → ¯ be ⊗-measurable. Then X Y uuxx yy dyy p dxx 1/p Y X uuxx yy p dx...