Improved Hardy,s inequality for fuzzy integral

In this paper, we prove a Hardy type inequality for fuzzy integrals.The theory of fuzzy measures and fuzzy integrals (also known as sugeno integral) was introduced by Sugeno [4] as a tool for modelling non-deterministic problems. The properties and applications of the Sugeno integral have been studied by many authors, among others, Ralescu and Adams [5] in the study of several equivalent definitions of fuzzy integrals, and Wang and Klir [7] in a general overview on fuzzy measurement and fuzzy integration theory. The study of the Hardy,s inequality for Sugeno integral was initiated by Romn-Flores et al. [6], and then followed by the others[1,3]. The purpose of this paper is to prove a Hardy,s inequality for the Sugeno integral[3,6]. Firstly, we introduce some basic notation and properties of the fuzzy integral.

کلیدواژه ها:

Fuzzy measure ، Sugeno integral ، Hardys inequality