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We consider fuzzy differential systems, or differential equations with fuzzy inputs and fuzzy initial conditions. Using a fuzzy sample path approach, we derive partial differential equations for the resulting membership functions. We also demonstrate sufficient continuity conditions under which the solutions exist and are fuzzy convex. The membership functions are shown to be identical to those...
Sigmoidal theory is a new theory that defines and analyzes a new family of functions called sigmoidal functions. A number of theorems proved show that there is an infinite number of classes of sigmoidal functions and provide us with a method of constructing those classes. Subsequently, multi-sigmoidal functions can be constructed using classes of sigmoidal functions. The applications of sigmoidal...
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