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Formal Rules for Fuzzy Causal Analyses and Fuzzy Inferences

Causal inference is one of the central capabilities of the natural intelligence that plays a crucial role in thinking, perception, and problem solving. Fuzzy inferences are an extended form of formal inferences that provide a denotational mathematical means for rigorously dealing with degrees of matters, uncertainties, and vague semantics of linguistic variables, as well as for rational reasoning the semantics of fuzzy causalities. This paper presents a set of formal rules for causal analyses and fuzzy inferences such as those of deductive, inductive, abductive, and analogical inferences. Rules and methodologies for each of the fuzzy inferences are formally modeled and illustrated with real-world examples and cases of applications. The formalization of fuzzy inference methodologies enables machines to mimic complex human reasoning mechanisms in cognitive informatics, cognitive computing, soft computing, abstract intelligence, and computational intelligence.