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This paper presents the design of a VLSI fuzzy processor, which is capable of dealing with complex fuzzy inference systems, i.e., fuzzy inferences that include rule chaining. The architecture of the processor is based on a computational model whose main features are: the capability to cope effectively with complex fuzzy inference systems; a detection phase of the rule with a positive degree of activation to reduce the number of rules to be processed per inference; parallel computation of the degree of activation of active rules; and representation of membership functions based on α-level sets. As the fuzzy inference can be divided into different processing phases, the processor is made up of a number of stages which are pipelined. In each stage several inference processing phases are performed parallelly. Its performance is in the order of 2 MFLIPS with 256 rules, eight inputs, two chained variables, and four outputs and 5.2 MFLIPS with 32 rules, three inputs, and one output with a clock frequency of 66 MHz