Fuzzy interval logic is proposed, which is a logical system extended from fuzzy logic for the purpose of representing unknown or contradictory information added to true and false. In the fuzzy interval logic, any proposition can be allowed to take an interval truth value [n, p], which is a special case of a linguistic truth value or the general case of a numerical one, where n and p are any values in the closed interval [0,1]. In this paper, introducing two partial ordered relations on the set of truth values of fuzzy interval logic, concerning truth and ambiguity, basic logic operators are defined. Some fundamental properties of a fuzzy interval logic function represented by a logic formula consisting of these operators and variables are studied. Kleene's law, which holds in fuzzy logic, doesn't hold here. The necessary and sufficient condition for two fuzzy logic formulas being equivalent each other is given using the quantization theorem. This shows that two fuzzy interval logic functions are equivalent when they take same value at only four values {[0,0], [1,1], [0,1], [1,0]}, that is, fuzzy interval logic is essentially four valued logic.

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Concept of fuzzy flip-flop has been proposed based on 2 valued J-K flip-flop which is a fundamental element of ordinary computer memory module. By using the same number of fuzzy flip-flop's as the cardinal number of the universe of discourse, a notion of fuzzy register has been proposed. It is able to memorize any shaped membership function, to output a complement function and to operate a various kind of compositional rule of fuzzy inference. A notion of fuzzy shift register is also presented, where the right/left shiftoperation of the membership function is possible on the universe of discourse.

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It is easy to express the process of system failure qualitatively. From the following points of view, this paper emphasizes the need to apply the fuzzy theory to the analysis of system reliability based on the qualitative expression. 1) Many fuzzy terms are found in the qualitative expression. 2) It is uncertain whether equipment failure or human error leads to a system accident or not, especially in a complex and large scale system. 3) It is difficult to analyze equipment failure and human error in detail. It is necessary to analyze them not microscopically but macroscopically. Fuzziness is essential to the macroscopic analysis. This paper also discusses not only the AND and the OR operations of the failure possibility and the operation of dependence between equipment failures or human errors but also two other kinds of the operation which are necessary for the analysis of system reliability based on the qualitative expression of the system accident. As an example, the task, in which a human operator controls valves manually in order to increase the flow rate of the high pressure raw material, is considered. Failure in the task including equipment failure is analyzed based on the qualitative expression of failure in the task.

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A fuzzy logic controller with a built-in function for self-tuning of control characteristics has been applied to an automatic speed control device to create a robust system for production vehicles. The fuzzy control algorithm brings about a better riding comfort and control accuracy than that of conventional control algorithm. And fuzzy logic is employed to predict drivers' individual preferences for control characteristics when the vehicle speed is controlled to a set level by the automatic speed control device. The results arethen reflected in the control characteristics to provide the preferred speed control.

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