Showing papers on "Fuzzy logic published in 1975"

Fuzzy metrics and statistical metric spaces

Abstract: The adjective "fuzzy" seems to be a very popular and very frequent one in the contemporary studies concerning the logical and set-theoretical foundations of mathematics. The main reason of this quick development is, in our opinion, easy to be understood. The surrounding us world is full of uncertainty, the information we obtain from the environment, the notions we use and the data resulting from our observation or measurement are, in general, vague and incorrect. So every formal description of the real world or some of its aspects is, in every case, only an approxima­ tion and an idealization of the actual state. The notions like fuzzy sets, fuzzy orderings, fuzzy languages etc. enable to handle and to study the degree of uncertainty mentioned above in a purely mathematic and formal way. A very brief survey of the most interest­ ing results and applications concerning the notion of fuzzy set and the related ones can be found in [l]. The aim of this paper is to apply the concept of fuzziness to the clasical notions of metric and metric spaces and to compare the obtained notions with those resulting from some other, namely probabilistic statistical, generalizations of metric spaces. Our aim is to write this paper on a quite self-explanatory level the references being necessary only for the reader wanting to study these matters in more details.

Optimal Fuzzy Partitions: A Heuristic for Estimating the Parameters in a Mixture of Normal Distributions

Abstract: An algorithm is described for generating fuzzy partitions which extremize a fuzzy extension of the k-means squared-error criterion function on finite data sets X. It is shown how this algorithm may be applied to the problem of estimating the parameters (a priori probabilities, means, and covariances) of mixture of multivariate normal densities, given a finite sample X drawn from the mixture. The behavior of the algorithm is compared with that of the ordinary ISODATA clustering process and the maximum likelihood method, for a specific bivariate mixture.

Fuzzy Neural Networks

Abstract: In this paper, the McCulloch-Pitts model of a neuron is extended to a more general model which allows the activity of a neuron to be a “fuzzy” rather than an “all-or-none” process. The generalized model is called a fuzzy neuron. Some basic properties of fuzzy neural networks as well as their applications to the synthesis of fuzzy automata are investigated. It is shown that any n-state minimal fuzzy automatan can be realized by a network of m fuzzy neurons, where ⌈log2n⌉

Representation theorems for fuzzy concepts

Abstract: In this paper representation theorems are given for L‐sets. In a particular case, by choosing a suitable L, fuzzy sets and flou sets are obtained and the connection of these concepts with the continuous logic and n‐valued logics is shown. Representation theorems of the same type are given for L‐topological subspaces and L‐algebraic substructures. The possibility of generalizing these results is taken into consideration.

Prescriptive method for deriving control policy in a fuzzy-logic controller

Abstract: A method of controlling a plant by a fuzzy algorithm has been proposed earlier. This method requires the complete description of the control policy as linguistic rules. Here we give a prescriptive method for deriving the best policy during run time. Results suggest the method is useful when the plant is subject to time-varying parameter changes and unknown disturbances.

Fuzzy machines in a category

Abstract: “Fuzzy theories” and “distributive laws” are used to define “fuzzy systems” in an arbitrary category. The resulting minimal realization theory provides new insights even in classical cases (so that, for non-deterministic sequential machines, the minimal realization problem is reformulated in terms of the structure of join-irreducibles in finite lattices). The definition of “fuzzy theory” is of independent interest and meshes well with philosophical aspects of fuzzy set theory.

Conditional fuzzy measures and their applications

Abstract: Publisher Summary This chapter introduces a set function, that is, conditional fuzzy measure and a relation between a priori and a posteriori fuzzy measures. These are very useful for describing any kind of transition of fuzzy phenomena such as communication of rumors, the reprint of color photograph, and the development of human abilities by education. The common characteristics of these phenomena are that the measures describing their status are very vague and that their transitions are influenced greatly by the subjectivity of the people who are involved in such fuzzy phenomena. It is well known that the uncertainty of human behavior is sometimes conveniently expressed by the subjective probability (judgmental probability) in Bayesian statistics. But one cannot say that this is the best way of expressing the fuzziness unless the problem is directly related to decision making.

Stochastic and fuzzy logics

Abstract: It is shown that it is possible to regard stochastic and fuzzy logics as being derived from two different constraints on a probability logic: statistical independence (stochastic) and logical implication (fuzzy). To contrast the merits of the two logics, some published data on a fuzzy-logic controller is reanalysed using stochastic logic and it is shown that no significant difference results in the control policy.

Interpretation and execution of fuzzy programs

Abstract: In this paper, a fuzzy program is defined through a flowchart where each arc is associated with a fuzzy relation (called a fuzzy branching condition) and a fuzzy assignment. Input, program and output variables occurring in a fuzzy program represent fuzzy subsets. A fuzzy program is interpreted as implicitly defining a tree; and the execution of the fuzzy program is equivalent to searching a solution path in the tree, i.e., tree searching. Examples of fuzzy programs and their executions are given.

Contemporary research in philosophical logic and linguistic semantics : proceedings of a conference held at the University of Western Ontario, London, Canada

Abstract: Counterfactuals and Comparative Possibility.- Presuppositions.- Incomplete Assertion and Belnap Connectives.- Dimensions of Truth.- Speaking of Nothing.- The Structure of Efficacy.- Harris and Chomsky at the Syntax-Semantics Boundary.- Some Transformational Extensions of Montague Grammar.- Hedges: A Study in Meaning Criteria and the Logic of Fuzzy Concepts.- Comments: Lakoff's Fuzzy Propositional Logic.- On the Semantics of Negation.- Verbs of Bitching.

Fuzzy programs and their execution

Abstract: Publisher Summary This chapter discusses several methods that translate a given sequence of fuzzy instructions into another sequence of precise instructions called a machine program. A finite-state automaton is taken up as a fuzzy machine model that executes a fuzzy program. The chapter presents the formulation of an extended fuzzy machine based on a generalized automaton and a few procedures for execution of fuzzy programs. An L-fuzzy automaton with the weight space defined in the lattice ordered semigroup is considered as a general machine. Several machines are also derived from L-fuzzy automata as their specific examples. The chapter discusses a more general way of executing fuzzy programs by making use of the generalized fuzzy machine. The chapter presents a computer simulation of the process of human learning by making use of the concept of fuzzy program and learning algorithm.

On risk and decision making in a fuzzy environment

Abstract: A multistage decision process is a fuzzy mapping from X × UN → X where X and U are the state and policy spaces. Given the initial fuzzy set Si on X, the set of final fuzzy sets Sf on X has certain inclusive properties. Risk and optimum decisions are defined in terms of the inclusive properties.

On fuzzy robot planning

Abstract: Publisher Summary This chapter discusses a system for using fuzzy hints to get through a maze. It presents the notion of robustness and its importance. Robustness means the ability to respond without program modification to slightly perturbed or to somewhat inexactly specified situations. This ability seems to be very useful in various applications and is characteristic of the way people cope with their environment. The chapter discusses some problems with and approaches to natural language understanding. Natural language understanding seems to be a rather robust affair. It is like the navigation through a familiar but complex intersection : small changes in non-crucial features are easily tolerated.

Hierarchically intelligent control of a bionic arm

Abstract: A shoulder-disarticulation prosthesis with seven degrees of freedom is formulated as a decision process accepting fuzzy commands from the human nervous system. The problem is decomposed into a functional hierarchy of three levels associated with organization, coordination, and Self-Organizing control, respectively. The highest level transforms a complex command into a sequence of elementary motions. A fuzzy automaton in the middle level coordinates the action of the lowest level controllers which apply direct control inputs to the nonlinear plant.

Measurement in quantum mechanics as a stochastic process on spaces of fuzzy events

Abstract: The measurement of one or more observables can be considered to yield sample points which are in general fuzzy sets. Operationally these fuzzy sample points are the outcomes of calibration procedures undertaken to ensure the internal consistency of a scheme of measurement. By introducing generalized probability measures on σ-semifields of fuzzy events, one can view a quantum mechanical state as an ensemble of probability measures which specify the likelihood of occurrence of any specific fuzzy sample point at some instant. These sample points are the possible outcomes of any infinitely rapid succession of measurements at that instant of any sequence of observables of the system.

An approach to pattern recognition and associative memories using fuzzy logic

Abstract: The present paper discusses a classification algorithm of multicategory classifiers which is based on fuzzy logic and can be used even if statistical independency of pattern vectors is violated. The algorithm is comparatively simple and requires an unusually short time for learning. We also consider the memory systems that recall entities stored in an associative manner. Entities are stored in the form of fuzzy matrix and are recalled by fuzzy logic according to the conditional probability of each category. A computer simulation is made in English character reading and its results are presented.

Fuzzy Sets, L-Sets, Flou Sets

Abstract: This chapter is concerned mainly with concepts providing a rigorous framework within to study fuzziness. In doing so, we shall be forced to formulate definitions crisply and precisely. The features to be treated here are mostly of an algebraic nature. We will be interested first in the theory of fuzzy functions, the bread and butter of many applications. It provides an abstract formulation for many familiar concepts,. like similarity. Our intention is to define and describe the different types of fuzzy functions more commonly met with.

Experimental approach to fuzzy simulation of memorizing, forgetting and inference process

Abstract: Publisher Summary This chapter presents an approach of making fuzzy models of the memorizing-, forgetting- and inference processes that are essentially important in the human decision-making process. It illustrates a block diagram expression of a whole model of human decision making system, mapping expressions of experience process, memory process, and inference process based on memory. The chapter describes two types of fuzzy formulation of human decision-making. One is the decision-making based on memory only and the other is the one depending on both memory and inference based on memory. These processes are expressed by fuzzy relations. The chapter presents an experimental study to make a fuzzy model of memory process. It is found that the certainty degree of memory is a value of the membership function with its ambiguity and it varies with time either in the collapsing manner (forgetting) or in the emphasizing manner (sharpening). The certainty degree of memory and its ambiguity is a time function dependent on several subjective or objective factors governing the difficulty of memorizing.