Computing, in its usual sense, is centered on manipulation of numbers and symbols. In contrast, computing with words, or CW for short, is a methodology in which the objects of computation are words and propositions drawn from a natural language, e.g., small, large, far, heavy, not very likely, the price of gas is low and declining, Berkeley is near San Francisco, it is very unlikely that there will be a significant increase in the price of oil in the near future, etc. Computing with words is inspired by the remarkable human capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Familiar examples of such tasks are parking a car, driving in heavy traffic, playing golf, riding a bicycle, understanding speech and summarizing a story. Underlying this remarkable capability is the brain’s crucial ability to manipulate perceptions – perceptions of distance, size, weight, color, speed, time, direction, force, number, truth, likelihood and other characteristics of physical and mental objects. Manipulation of perceptions plays a key role in human recognition, decision and execution processes. As a methodology, computing with words provides a foundation for a computational theory of perceptions – a theory which may have an important bearing on how humans make – and machines might make – perception-based rational decisions in an environment of imprecision, uncertainty and partial truth. A basic difference between perceptions and measurements is that, in general, measurements are crisp whereas perceptions are fuzzy. One of the fundamental aims of science has been and continues to be that of progressing from perceptions to measurements. Pursuit of this aim has led to brilliant successes. We have sent men to the moon; we can build computers

With the development of the semantic web activity, ontologies become widely used to represent the conceptualization of a domain. However, none of the existing ontology languages provides a means to capture uncertainty about the concepts, properties and instances in a domain. Probability theory is a natural choice for dealing with uncertainty. Incorporating probability theory into existing ontology languages will provide these languages additional expressive power to quantify the degree of the overlap or inclusion between two concepts, support probabilistic queries such as finding the most probable concept that a given description belongs to, and make more accurate semantic integration possible. One approach to provide such a probabilistic extension to ontology languages is to use Bayesian networks, a widely used graphic model for knowledge representation under uncertainty. In this paper, we present our on-going research on extending OWL, an ontology language recently proposed by W3C’s Semantic Web Activity. First, the language is augmented to allow additional probabilistic markups, so probabilities can be attached with individual concepts and properties in an OWL ontology. Secondly, a set of translation rules is defined to convert this probabilistically annotated OWL ontology into a Bayesian network. Our probabilistic extension to OWL has clear semantics: the Bayesian network obtained will be associated with a joint probability distribution over the application domain. General Bayesian network inference procedures (e.g., belief propagation or junction tree) can be used to compute P(C | e): the degree of the overlap or inclusion between a concept C and a concept represented by a description e. We also provide a similarity measure that can be used to find the most probable concept that a given description belongs to. 1.

Traditional database query systems allow users to construct complicated database queries from specialized database language primitives. While powerful and expressive, such systems are not easy to use, especially for browsing or exploring the data. Information visualization systems address this problem by providing graphical presentations of the data and direct manipulation tools for exploring the data. Recent work in this area has reported the value of dynamic queries coupled with two-dimensional data representations for progressive refinement of user queries. However, the queries generated by these systems are limited to conjunctions of global ranges of parameter values. In this paper, we extend dynamic queries by encoding each operand of the query as a Magic Lens filter. Compound queries can be constructed by overlapping the lenses. Each lens includes a slider and a set of buttons to control the value of the filter function and to define the compostion operation generated by overlapp...

Illustrations play a major role in the education process. Whether used to teach a surgical or radiologic procedure, to illustrate normal or aberrant anatomy, or to explain the functioning of a technical device, illustration significantly impacts learning. Although many specimens are readily available as volumetric data sets, particularly in medicine, illustrations are commonly produced manually as static images in a time-consuming process. Our goal is to create a fully dynamic three-dimensional illustration environment which directly operates on volume data. Single images have the aesthetic appeal of traditional illustrations, but can be interactively altered and explored. In this paper we present methods to realize such a system which combines artistic visual styles and expressive visualization techniques. We introduce a novel concept for direct multi-object volume visualization which allows control of the appearance of inter-penetrating objects via two-dimensional transfer functions. Furthermore, a unifying approach to efficiently integrate many non-photorealistic rendering models is presented. We discuss several illustrative concepts which can be realized by combining cutaways, ghosting, and selective deformation. Finally, we also propose a simple interface to specify objects of interest through three-dimensional volumetric painting. All presented methods are integrated into VolumeShop, an interactive hardware-accelerated application for direct volume illustration.

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This paper deals with the application of fuzzy logic in a relational database environment with the objective of capturing more meaning of the data. It is shown that with suitable interpretations for the fuzzy membership functions, a fuzzy relational data model can be used to represent ambiguities in data values as well as impreciseness in the association among them. Relational operators for fuzzy relations have been studied, and applicability of fuzzy logic in capturing integrity constraints has been investigated. By introducing a fuzzy resemblance measure EQUAL for comparing domain values, the definition of classical functional dependency has been generalized to fuzzy functional dependency (ffd). The implication problem of ffds has been examined and a set of sound and complete inference axioms has been proposed. Next, the problem of lossless join decomposition of fuzzy relations for a given set of fuzzy functional dependencies is investigated. It is proved that with a suitable restriction on EQUAL, the design theory of a classical relational database with functional dependencies can be extended to fuzzy relations satisfying fuzzy functional dependencies.

To Mom, Dad, and Susan, for their support and encouragement.

(IRS) defined using an ordinal fuzzy linguistic approach is proposed. The ordinal fuzzy linguistic approach is presented, and its use for modeling the imprecision and subjectivity that appear in the user-IRS interaction is studied. The user queries and IRS responses are modeled linguistically using the concept of fuzzy linguistic variables. The system accepts Boolean queries whose terms can be weighted simultaneously by means of ordinal linguistic values according to three possible semantics: asymmetrical threshold semantic, aquantitativesemantic,andanimportancesemantic.Thefirstone identifies a new threshold semantic used to express qualitative restrictions on the documents retrieved for a given term. It is monotone increasing in index term weight for the threshold values that are on the right of the mid-value, and decreasing for the threshold values that are on the left of the mid-value. The second one is a new semantic proposal introduced to express quantitative restrictions on the documents retrieved for aterm, i.e., restrictions on the number of documents that must be retrieved containing that term. The last one is the usual semantic of relative importance that has an effect when the term is in aBoolean expression. Abottom-up evaluation mechanism of queries is presented that coherently integrates the use of the three semantics and satisfies the separability property. The advantage of this IRS with respect to others is that users can express linguistically different semantic restrictions on the desired documents simultaneously, incorporating more flexibility in the user–IRS interaction.

Assume that each object in a database has m grades, or scores, one for each of m attributes.

A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineering design. This imprecision is represented using the fuzzy calculus. Calculations can be performed using this method, to produce (imprecise) performance parameters from imprecise (input) design parameters. The Fuzzy Weighted Average technique is used to perform these calculations. A new metric, called the γ-level measure, is introduced to determine the relative coupling between imprecise inputs and outputs. The background and theory supporting this approach are presented, along with one example. 1.