Abstract not found

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

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.

Fuzzy rules have been advocated as a key tool for expressing pieces of knowledge in "fuzzy logic". However, there does not exist a unique kind of fuzzy rules, nor is there only one type of "fuzzy logic". This diversity has caused many a misunderstanding in the literature of fuzzy control. The paper is a survey of different possible semantics for a fuzzy rule and shows how they can be captured in the framework of fuzzy set and possibility theory. It is pointed out that the interpretation of fuzzy rules dictates the way the fuzzy rules should be combined. The various kinds of fuzzy rules considered in the paper (gradual rules, certainty rules, possibility rules, and others) have different inference behaviors and correspond to various intended uses and applications. The representation of fuzzy unless-rules is briefly investigated on the basis of their intended meaning. The problem of defining and checking the coherence of a block of parallel fuzzy rules is also briefly addressed. This iss...

This papers aims at clarifying the meaning of different interpretations of the Max-Min or, more generally, the Max-t-norm rule in fuzzy systems. It turns out that basically two distinct approaches play an important role in fuzzy logic and its applications: fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information. Keywords: Fuzzy logic; fuzzy control; Max-Min rule, fuzzy interpolation. 1 Introduction This is a synthesizing paper which returns to the question, what is the role of the Max-Min (Max-t-norm) rule in fuzzy logic from the viewpoint of logical inference. We aim at demonstrating that two basic, more or less complementary approaches in fuzzy logic and its applications can be distinguished, namely: fuzzy interpolation of a fuzzily specified precise function and logical inference in the presence of fuzzy information. The first task is solved using the Max-t-norm rule which essentially leads to search of a fuzzy...

We define fuzzy constraint networks and prove a theorem about their relationship to fuzzy logic. Then we introduce Khayyam, a fuzzy constraint-based programming language in which any sentence in the first-order fuzzy predicate calculus is a well-formed constraint statement. Finally, using Khayyam to address an equipment selection application, we illustrate the expressive power of fuzzy constraint-based languages.

. Rational inference relations were introduced by Lehmann and Magidor as the ideal systems for drawing conclusions from a conditional base. However, there has been no simple characterization of these relations, other than its original representation by preferential models. In this paper, we shall characterize them with a class of total preorders of formulas by improving and extending Gardenfors and Makinson's results for expectation inference relations. A second representation is application-oriented and is obtained by considering a class of consequence operators that grade sets of defaults according to our reliance on them. The finitary fragment of this class of consequence operators has been employed by recent default logic formalisms based on maxiconsistency. Keywords: foundations of knowledge representation, nonmonotonic reasoning, nonmonotonic consequence relations, orderings of formulas. 1 Introduction A recent breakthrough in nonmonotonic logic is the beginning of study of nonm...

Partner selection continues to be one of the most important activity in industries. Selecting manufacturing partners in the new emerging world of agile manufacturing is an endeavor that is beset with the complexity and dynamics of the market driven by customer needs as well as the inherent subjectivity of the selection process. Traditional vendor selection methodologies do not lend themselves as a ready solution to these needs of agile environment. This paper develops a flexible optimization framework for optimal manufacturing partner selection in such an environment. 1. INTRODUCTION In face of fierce global competition and the brief moments of opportunity, manufacturing factories have become more focused, increasing the dependence on vendors in product realization. A multi-partnership manufacturing environment has thus emerged in which partner selection has become critical and is governed by market specific needs. `Agile Manufacturing' is a new concept that subsumes characteristics ...

It is well known that the theory of probability can be treated and developed in a consistent and uniform way using the classical theory of measure and integration. Indeed, the Russian scientist Kolmogorov identified probability with normalized classical measures and used the Lebesgue theory of integration to give a logically consistent and unifying account of probability theory. In this paper, we indicate how, in an analogous way, a unified and consistent treatment of possibility theory can be given. Using seminormed fuzzy integrals, a generalization of Sugeno's fuzzy integrals ideally suited for working with our possibility measures, we discuss how a theory of possibility can be developed along the same formal lines as the theory of probability. 1. Introduction Early in this century, the Russian scientist A. N. Kolmogorov 17 showed how the theory of probability could be consistently formulated in a unifying measure- and integral-theoretic framework. As a result of his work, probab...

this paper discusses some of the empirical problems connected with natural languages' essentially varying and vague meanings, how these can be analysed statistically from discourse data, and represented formally as fuzzy system of vocabulary mappings. Some examples computed from East- and West-German newspaper texts will be to illustrate the approach's feasibility. 1 INTRODUCTION