Showing papers on "Fuzzy logic published in 1974"

Application of fuzzy algorithms for control of simple dynamic plant

Abstract: The paper describes a scheme in which a fuzzy algorithm is used to control plant, in this case, a laboratory-built steam engine. The algorithm is implemented as an interpreter of a set of rules expressed as fuzzy conditional statements. This implementation on a digital computer is used online, to control the plant. The merit of such a controller is discussed in the light of the results obtained.

Fuzzy Relations in Group Decision Theory

Abstract: This paper develops the notion of fuzzy preference orderings for individuals and groups, on the basis of the theory of fuzzy (binary) relations as developed by L. A. Zadeh [4]. This concept is illustrated with well known methods of group decision-making and some of its formal properties are investigated. Finally an algorithm to map fuzzy orderings on non-fuzzy ones is proposed to guide the decision-maker in reaching decisions which reflect the fuzziness of the preferences over the available options.

Concept representation in natural and artificial languages: Axioms, extensions and applications for fuzzy sets

Abstract: This paper reports research related to mathematics, philosophy, computer science and linguistics. It gives a system of axioms for a relatively simple form of fuzzy set theory, and uses these axioms to consider the accuracy of representing concepts in various ways by fuzzy sets. By-products of this approach include a number of new operations and laws for fuzzy sets, parallel to those for ordinary sets, and a demonstration that all the basic operations are intrinsically determined. In addition, the paper explores both hierarchical and algorithmic extensions of fuzzy sets, and then applications to problems in natural language semantics and combinatorics. Finally, the paper returns to the problem of representing concepts, and discusses some implications for artificial intelligence.

Some Recent Investigations of a New Fuzzy Partitioning Algorithm and its Application to Pattern Classification Problems

Abstract: Recent results pertaining to a newly developed fuzzy partitioning algorithm are surveyed. The algorithm has potential value as a heuristic tool for identifying clusters within large finite data sets, and more specifically, for estimating the parameters in a mixture of unimodal probability densities, given a finite sample drawn from the mixture. The topics treated are: fuzzy partitions, conventional clustering algorithms, fuzzy clustering algorithms, asymptotic behavior of optimal fuzzy partitions with increasing cluster separation, scalar measures of partition fuzziness, and unsupervised learning and parameter estimation.

Fuzzy Sets and Neural Networks

Abstract: It is possible that a better model for the behavior of a nerve cell may be provided by what might be called a fuzzy neuron, which is a generalization of the McCulloch-Pitts model. The concept of a fuzzy neuron employs some of the concepts and techniques of the theory of fuzzy sets which was introduced by Zadeh [2, 3] and applied to the theory of automaton by Wee and Fu [6], Tanaka et al. [7], Santo [8] and others. In effect, the introduction of fuzziness into the model of a neuron makes it better adapted to the study of the behavior of systems which are imprecisely defined by virtue of their high degree of complexity. Many of the biological systems, economic systems, urban systems and more generally, large-scale systems fall into this category. In the nearly three decades since its publication, the pioneering work of McCulloch and Pitts [1], has had a profound influence on the development of the theory of neural nets, in addition to stimulating much of the early work in automata theory and regula...

On the Precision of Adjectives Which Denote Fuzzy Sets

Abstract: The characteristic function of a fuzzy set denoted by a phrase “much larger than 5,” or “heavy,” is investigated experimentally. The S-shaped curve for the characteristic function is derived from some plausible assumptions involving a differential equation, and its parameters are estimated statistically. It was found that the precision of the fuzzy set–measured by the maximum slope of the characteristic function–denoted by “much greater than 5” is less than that denoted by “very much greater than 5.” When the subject is allowed to be fuzzy in his response about grade of membership, there is greater consistency in the response. Anchoring was also found to make an adjective denoting fuzzy set more precise.

Large systems

Abstract: It is argued that we need theories of large systems. This is particularly so since society is composed of large systems, and since without applicat.ions, control theory will be sterile. Some typical large systems are economics, education, urban systems, transportation, energy, and the environment. Observe that these systems are not independent. This makes the associated problems more interesting and difficult. It is noted that the fuzzy set theory of Lotfi Zadeh appears promising in this area since all of the concepts associated with large systems are imprecise or fuzzy.

Fuzzy sets in the theory of measurement of incompatible observables

Abstract: The notion of fuzzy event is introduced in the theory of measurement in quantum mechanics by indicating in which sense measurements can be considered to yield fuzzy sets. The concept of probability measure on fuzzy events is defined, and its general properties are deduced from the operational meaning assigned to it. It is pointed out that such probabilities can be derived from the formalism of quantum mechanics. Any such probability on a given fuzzy set is related to the frequency of occurrence within that set of points in a random sample, where the sample points are themselves fuzzy sets obtained as outcomes of measurements of, in general, incompatible observables on replicas of the system in the same prepared state.

On the minimization of incompletely specified fuzzy functions

Abstract: This article is concerned with the study of fuzziness in incompletely specified combinational networks by means of a suitable fuzzy algebra. For completely specified fuzzy functions, minimal sets have been obtained using the definition of fuzzy consensus. Using the basic properties of fuzzy logic, the concepts of fuzzy prime implicant, essential fuzzy prime implicant, and fuzzy iterated consensus are used to find the minimal sum-of-products expression of an incompletely specified fuzzy function.

On the Properties of Fuzzy Switching Functions

Abstract: A strictly binary approach to the treatment of switching circuits today is not always adequate to describe systems in the real world. This approach is partly due, to the relative simplicity of designing binary switching systems, and to the fact that basic switching modules in common use are two-positional. Consequently, every variable in Boolean logic is assumed to be two-valued. However, because of real-world constraints, the attributes of system variables are often ambiguously defined. In other words, quite often variables might have values other than falsehood and truth. Cases with such attributes arise, for example in artifical intelligence and related subjects. Ever since Zadeh introduced the idea of fuzzy set theory [11 by utilizing the concept of membership grade, a number of authors have been concerned with the analysis and applications of fuzzy models. Especially, the relation of fuzzy to switching systems have been discussed in [2]–[12] and by other researchers in relation to other topi...

Application of fuzzy logic to the detection of static hazards in combinational switching systems

Abstract: In this paper the fuzzy set as discussed by Zadeh is viewed as a multivalued logic with a continuum of truth values in the interval [0,1]. The concept of static hazard in combinational switching systems is related to fuzzy logic and various properties of this relation are established. The paper derives the necessary and sufficient conditions for a fuzzy function to adequately describe the steady-state and static hazard behavior of a combinational system, by extending the ternary method discussed by Yoeli and Rinon and using the resolution principle of mechanical theorem-proving.

Fuzzy Syntax-Directed Translations

Abstract: Fuzzy syntax-directed translation based on syntax-directed translation schemata is introduced as a model of the mapping of strings from one imprecise language into another. The “max-min” requirement is used, and regular translations as performed by a fuzzy finite transducer are examined.

Fuzzy Notions in Nonlinear System Classification

Abstract: Pattern Recognition methods like the A-nearest neighbor technique and clustering have been successfully used to classify nonlinear systems to a predetermined set of well separated classes, demonstrating similarities in their input-output behavior. The cross-correlation function has been used as a feature vector which yielded a classification with a relatively small misclassification error. Further categorization of the nonlinearity within a class is not possible through the above approach. However, a membership factor in a fuzzy sense can be assigned to each nonlinear system within a certain class. This factor is dependent on the coefficients of the polynomial expansion of the nonlinearity involved and may be obtained through the cross-correlation vector. This way, every class of nonlinear systems may be defined as a fuzzy set. The investigation of the properties of such a set as well as its contribution to the further classification of nonlinear systems is discussed in this paper.

The Effect of Logic Operations on Fuzzy Logic Distributions

Abstract: The variables in a fuzzy logic system may be assigned any truth value in the closed interval [0,1]. Assuming independent logic value assignments with known probability distributions, the effects of subsequent logic operations are examined.

A Note on the Simplification of Fuzzy Switching Functions

Abstract: This note is concerned with the modification of the definition of fuzzy consensus. The modified version is used to find the set of all fuzzy prime implicants of a fuzzy switching function as defined previously. The fuzzy algebra used to derive these functions satisfies the set of axioms of a distributive lattice with unique identities under the operators of maximum and minimum as described earlier.

A Methodology for Interactive Systems

Abstract: In the recent activities in the fields of applied computer science such as Artificial Intelligence, Information Retrieval, Pattern Recognition etc., a methodology of interactive systems is one of the most important problems in designing a system for the above-mentioned purposes. A basic condition which we have to consider in designing an interactive system is that the dialogue partner of a machine is always a man who uses the interactive system and who evaluates its performance on the basis of his different characteristics of information processing. In this respect, it is obvious that the machine part of such an interactive system should be designed so that the human characteristics are also taken into account in terms of performance criterion. In the following brief note, a basic scheme of interactive systems is discussed focusing on the problems which basically come from human ambiguous or fuzzy expression1.

Evaluation Model of Humanistic Systems by Fuzzy Multiple Integral and Fuzzy Correlation

Abstract: We have proposed a mathematical model of subjective evaluation on the basis of fuzzy integral. In particular, we have developed the evaluating method of complex systems composed of several subsystems by virtue of fuzzy multiple integral. Furthermore, for the sake of identifying the preference measure, that is fuzzy measure , effectively, we have introduced the fuzzy correlation.