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This chapter gives a basic idea of fuzzy calculus meant for the uninitiated researcher. The principal definitions of fuzzy order logic along with practical realizations are discussed. Concepts of fuzzy logic control and fuzzy state space and transfer functions are introduced along with stability and frequency domain representation of fuzzy systems. The notions of fuzzy controllers, delay fuzzy systems and fuzzy fractional calculus are briefly reviewed. In the present work we explore the possibility of combining fuzzy inference with neural networks implemented on memristive devices which significantly improve the computational efficiency. In this chapter, we introduce a novel method, based on fuzzy inference, to reduce the computational burden of memristive networks. At the end of this work, many ideas are mentioned which could be addressed in future investigations.