This paper focuses on the fuzzy Volterra integro-differential equation of nth order of the second-kind with nonlinear fuzzy kernel and initial values. The derived integral equations are solvable, the solutions of which are unique under certain conditions. The existence and uniqueness of the solutions are investigated in a theorem and an upper boundary is found for solutions. Comparison of the e...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

The binary states, i.e., success or failed state assumptions used in conventional reliability are inappropriate for reliability analysis of complex industrial systems due to lack of sufficient probabilistic information. For large complex systems, the uncertainty of each individual parameter enhances the uncertainty of the system reliability. In this paper, the concept of fuzzy reliability...