| Inference function is one of important features of human being's intelligence, and computational intelligence is new important technique of realization of artificial intelligence. Fuzzy inferences are theory bases and kernels of fuzzy expert systems and fuzzy control systems, are also useful tools for fuzzy information processing and machine intelligence in information science, therefore, are significant research subjects of computer science, control science and decision-making science.Operator ∨λ, presented by Fung and Fu in 1975, is a generalized form of operator max and operator min, holds many good mathematical properties, and is realized easily in hardware form, its value can vary from min(x,y) to max(x,y), fuzzy inference with thiskind of operators is also easy to be transformed as fuzzy neural network, thus parameter A can be adjusted by learning algorithm of the corresponding network. Because operator ∨λ has not been paid enough attention to, so its properties are first investigated systemically for discussion of fuzzy inference in the paper.Benefited from operator ∨λ , fuzzy compositional operator "o" is generalized as "P1oP2" where p1,p2 ∈ [0.1], it is found that the operator holds many good properties,then the compositional rules of fuzzy inference (CRI for short) proposed by L.A.Zadeh is generalize as the parameterized compositional rules of fuzzy inference (CRIP for short). Due to introducing parameters, the value space of CRIP is greater than that of CRI, so that CRIP satisfies very easily the inference principle of consistency, and fuzzy implication operator of CRIP is no longer crucial, so the difficult problem of choice of appropriate implication operator for this inference algorithm can be almost avoided, especially the fuzzy inference with CRIP can be transformed easily as fuzzy neural network, the parameter λ can be easily determined by means of its learning algorithm, the new method makes self-adaptation function adhere to conventional CRI. The paper gives the method for adjusting parameters of CRIP, inference instances and comparisons between CRIP and other inference methods.A generalized form of Mamdani's method for fuzzy inference is proposed based on monolithic fuzzy neural network. The two fuzzy neural network models are constructed respectively for generalized modus ponens and modus tollens. The paper gives the properties, learning algorithms and inference instances of the two neural networks. And the paper also compares this generalized method with the other inference methods.Traditional compatibility measure between two interval-valued fuzzy sets is expressed as a complex formula, thus its some essences are often concealed by the complexity of its representation. Because some properties of the measure are inconsistent with human's intuition, concept of so-called coincidence measure between two interval-valued fuzzy sets, and comparison between the two measures, then sufficient and necessary conditions are given for compatibility measure and coincidence measure are equal to 1 respectively. For the first time, propagations of the two measures are discussed here.Based on t-norm and s-norm, Fl neuron model and F2 neuron model are proposed. The first model has high sensitivity and strong robustness, are more suitable to be applied to industry control systems. The second model has low sensitivity and weak robustness, are more suitable to be applied to decision-making fields. The sufficient and necessary conditions are given respectively for generalized AND/OR are T/S norm clusters, and a fuzzy neural network with Fl and F2 neurons is constructed for fuzzy inference, the new inference method is generalization of CRI, and holds better properties than CRI. The concept of weak-bound-triangular norm is proposed, it may be applied to fuzzy proposition computation in the case the information is not completed and relations among sub-propositions are complicated.The robustness concepts of a general fuzzy inference with perturbations of rules are presented, then influence of fuzzy implicatio...
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