Proposes a technique to map data fluctuations into the parameter space of multivariate models, after an average model using the average data is constructed. This mapping preserves the relative positions of individuals in data as well as the average in data. The idea is applied to factor analysis and a quantifying method.
The portion of the new product development cycle between when work on a new idea could start and when it actually starts—the so-called Fuzzy Front End—is often lengthy, typically poorly understood, and usually full of opportunities for improvement. Consequently, there are substantial benefits to analyzing this stage quantitatively. In particular, such analysis sheds light on many important decisions regarding the structural design of the early development process. A key implication of such analysis is that front-end process structure should differ depending on the underlying economics of the specific situation. This in turn suggests that there are no universally applicable "best practices" for optimizing the Fuzzy Front End.
Using existing data from a certain type of gravity-wave detector, a researcher has been able to set significant bounds on proposed quantum properties of space-time, suggesting that the fuzziness of space-time is experimentally accessible.
In vascular plants there are at least eight ways to develop polymerous whorls, i.e., whorls with four or more leaves. Six ways are presented and compared with literature to estimate organ identity (morphological significance) of the leaflike whorl members. New shoots (also seedlings) may start with dimerous or trimerous whorls. Then leaf number per whorl rises as follows: (1) Many taxa add more leaves per whorl continuously with increasing size of the apical meristem (e.g., , ). (2) Taxa provided with interpetiolar stipules replace their stipules by leaves (e.g., and allies). (3) Taxa with the capacity to form compound leaves shift basal leaflets around the whole node (e.g., , probably also ). Various whorled plants start shoot development with leaf inception along a helix, which is continued into the whorled region. Then polymerous whorls develop as follows: (4) forms helically arranged fascicles instead of single leaves before the production of complete whorls. (5) and add supernumerary leaves between a first series of helically arranged leaves. (6) produces an annular bulge around the node of each first‐formed leaf. All additional leaves of a whorl arise on this annular bulge. Leaf identity of whorl members cannot be defined unequivocally in whorls with asynchronous (i.e., nonsimultaneous) development, dorsoventral distribution of lateral buds, and/or fewer vascular traces than leaves per node. It is heuristically stimulating to accept structural categories (e.g., shoot, leaf, leaflet, stipule) as fuzzy concepts, as developmental pathways that may overlap to some degree, leading to developmental mosaics (intermediates). For example, the whorled leaves of resemble whole shoots, corroborating Arber's partial‐shoot theory.
This article investigates various constructs on a set of classical effects (measurable fuzzy sets or fuzzy events). We begin by studying the properties of a connective box with bottom missing and its dual connective box with top missing which seem to have been neglected in the literature. The importance of these connectives for fuzzy probability theory is pointed out. We then introduce and investigate the properties of a commutator which can be employed to define a degree of relative fuzziness. A special case of this commutator defines a degree of fuzziness. The expectation of the commutator provides a relative entropy whose properties are delineated and the expectation of the special case gives an entropy function that has been previously studied as a measure of fuzziness. (C) 1999 Elsevier Science B.V. All rights reserved.
Current needs of industry required the development of advanced database models like active mobile database systems. An active mobile database system can be designed by incorporation of triggering rules into a mobile computing environment in which the users are able to access a collection of database services using mobile and non-mobile computers at any location. Fuzzy concepts are adapted to the field of databases in order to deal with ambiguous, uncertain data. Fuzziness comes into picture in active mobile databases especially with spatial queries on moving objects. Incorporating fuzziness into rules would also improve the effectiveness of active mobile databases as it provides much flexibility in defining rules for the supported application. In this paper we present some methods to adapt the concepts developed for fuzzy systems to active mobile databases.
Ishibuchi et al. (1996) have proposed a linguistic rule extraction method from trained neural networks for pattern classification problems. In the method, antecedent linguistic values such as "small" and "large" are used as inputs to a multilayer feedforward neural network for determining the consequent part of linguistic rules. Since the linguistic input values are handled as fuzzy numbers, the corresponding outputs from the neural network are also calculated as fuzzy numbers by fuzzy arithmetic. The accurate calculation of the fuzzy outputs is very important because the determination of the consequent part is based on the calculated fuzzy outputs. It is, however, well-known that fuzzy arithmetic involves excess fuzziness. In this paper, we illustrate how subdivision methods can decrease the excess fuzziness. We also examine the effect of those methods on the performance of our rule extraction method.
When a fuzzy input vector is presented to a multi-layer feedforward neural network, the corresponding fuzzy output vector is calculated by fuzzy arithmetic. It is well known that fuzzy arithmetic involves excess fuzziness; we employ subdivision methods of interval input vectors for decreasing excess fuzziness included in fuzzy outputs from neural networks. First we examine a simple subdivision method where each level set of a fuzzy input vector is subdivided into many cells with the same size by uniformly subdividing all elements of the level set into multiple intervals. Next we examine a hierarchical subdivision method where each level set is subdivided into many cells with different sizes by iteratively subdividing a single element of a cell into two intervals. Finally we modify the hierarchical subdivision method for efficiently decreasing excess fuzziness.