The fussy "roots" of quantum mechanics are traced directly to the Hamilton-Jacobi equation of classical mechanics. It is shown that the Shroedinger equation can be derived from the Hamilton-Jacobi equation. A deep underlying unity of both equations lies in the fact that a unique trajectory of a classical particle is "selected" out of many-continuum paths according to the Principle of least action. We can say that a classical particle has a membership in every path of the above set, which collapses to the winning single trajectory of a real motion. At the same time it can also be said that a quantum mechanical "particle" has different degrees of membership in a set of many-continuum paths where all of them contribute to the dynamics of the quantum mechanical particle. This allows one to provide an interpretation of the wave function as a parameter describing deterministic entity endowed by a fuzzy character. As a logical consequence of such an interpretation the complimentarity principle and the wave-particle duality concept can be abandoned in favor of a fuzzy deterministic microobject. This idea leads to a possibility of a quantum mechanical computer based on the fuzzy logic.
Communication systems are real-time deterministic, well defined systems that transport voice/data signals from point A to point B reliably. However, the transmitted signal is subject to significant distortion by the very harsh environment, the medium, and the system itself. Despite this, data reaches its destination crisply or error-free. To achieve the high quality of error-free data, mechanisms that affect the quality of signal are addressed a priori and countermeasures are developed so that the potentially "fuzzifiers" are removed or "de-fuzzified". Here, the fuzzification-defuzzification process of the signal in real-time communication systems is addressed in the context of temporal fuzziness or fuzziness in the time domain. Temporal fuzzy factors that affect the operation of communication systems and their signal transmission are illustrated, analyzed, and the de-fuzzification process is discussed.
The motivations for qualitative modelling and fuzzy modelling are almost identical: to cope with the complexities in the modelling of real systems. However, their developments have been independent, distinct and complementary. The synthesis of these techniques has required a re-appraisal of exactly what model properties are used in these techniques. We argue that precision and uncertainty are distinct concepts. Qualitative modelling deals with abstract imprecise models whilst fuzzy modelling copes with uncertain imprecise or precise models, With this clarification we have developed a fuzzy qualitative simulation system, an outline of which is given in this paper. We believe that such combinations of fuzzy and qualitative methods are the natural development of Zadeh's original proposal for intelligent reasoning about complex systems.
Like the fields of probability and statistics, fuzzy set theory is characterized by a variety of viewpoints. Adherents of fuzzy methods, however, consistently maintain that probability is not necessarily the optimal representation of uncertainty. We rebut this view.
Epsilon Serializability (ESR) has been proposed to manage and control inconsistency in extending the classic transaction processing. ESR increases system concurrency by tolerating a bounded amount of inconsistency. In this paper, we present multiversion divergence control (mvDC) algorithms that support ESR with not only value but also time fuzziness in multiversion databases. Unlike value fuzziness, accumulating time fuzziness is semantically different. A simple summation of the length of two time intervals may either underestimate the total time fuzziness, resulting in incorrect execution, or overestimate the total time fuzziness, unnecessarily degrading the effectiveness of mvESR. We present a new operation, called TimeUnion, to accurately accumulate the total time fuzziness. Because of the accurate control of time and value fuzziness by the mvDC algorithm, mvESR is very suitable for the use of multiversion databases for real-time applications that may tolerate a limited degree of data inconsistency but prefer more data recency.
The implementation of the fuzziness index in measuring response style in psychosocial questions was examined, The fuzziness index revealed significant individual differences in response styles in psychological questionnaires, Significant correlations between the fuzziness in psychosocial behaviors and intellectual abilities were presented. The study highlighted the future possibility in modeling the degree and location of fuzziness in order to better understand enormously diverse human characteristics and psychological systems.
First, this paper reviews several well known measures of fuzziness for discrete fuzzy sets. Then new multiplicative and additive classes are defined. We show that each class satisfies five well-known axioms for fuzziness measures, and demonstrate that several existing measures are relatives of these classes. The multiplicative class is based on nonnegative, monotone increasing concave functions. The additive class requires only nonnegative concave functions. Some relationships between several existing and the new measures are established, and some new properties are derived. The relative merits and drawbacks of different measures for applications are discussed. A weighted fuzzy entropy which is flexible enough to incorporate subjectiveness in the measure of fuzziness is also introduced. Finally, we comment on the construction of measures that may assess all of the uncertainties associated with a physical system.
This paper presents a method for controlling excessive fuzziness in a fuzzy classifier system. The proposed method uses multiple stimulus-response type classifier systems and is capable of handling complex control tasks. Simulations are done to show the effectiveness of the proposed method for acquiring control knowledge.