Showing papers on "Fuzzy logic published in 1976"
01 Nov 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: It is proposed that adaptive techniques in linguistic controllers currently being studied may provide a useful possible approach to the use of fuzzy logic in the synthesis of controllers for dynamic plants.
Abstract: The purpose of this article is to survey the field of application of fuzzy logic in the synthesis of controllers for dynamic plants. A brief tutorial on the method of approach is also included here. Several groups of workers are currently studying various aspects of fuzzy controllers. For each such group a short account is given on the area of investigation undertaken. This along with the list of references provided here should give a broad picture of ongoing research on fuzzy controllers. Although most work is conducted using pilot scale or simulated plants, there are prospects also of an eventual application to a real plant. Some of the problems underlying actual application of fuzzy controllers are mentioned. These principally amount to the use of heuristics in plant controllers and the question of how to obtain an effective set of rules for a given plant. It is proposed that adaptive techniques in linguistic controllers currently being studied may provide a useful possible approach.
920 citations
01 Nov 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: The problem of borderline cases in set theory and the two classical approaches of precisifying them out, or admitting them as a third case, are discussed, leading to Zadeh's suggestion of continuous degrees of set membership.
Abstract: This paper gives an overview of the theory of fuzzy sets and fuzzy reasoning as proposed and developed by Lotfi Zadeh. In particular it reviews the philosophical and logical antecedents and foundations for this theory and its applications. The problem of borderline cases in set theory and the two classical approaches of precisifying them out, or admitting them as a third case, are discussed, leading to Zadeh's suggestion of continuous degrees of set membership. The extension of basic set operations to such fuzzy sets, and the relationship to other multivalued logics for set theory, are then outlined. The fuzzification of mathematical structures leads naturally to the concepts of fuzzy logics and inference, and consideration of implication suggests Łukasiewicz infinite-valued logic as a base logic for fuzzy reasoning. The paradoxes of the barber, and of sorites, are then analysed to illustrate fuzzy reasoning in action and lead naturally to Zadeh's theory of linguistic hedges and truth. Finally, the logical, modeltheoretic and psychological derivations of numeric values in fuzzy reasoning are discussed, and the rationale behind interest in fuzzy reasoning is summarized.
327 citations
302 citations
TL;DR: Fuzzy algorithms based on linguistic rules describing the operator's control strategy are applied toControl of a warm water plant using fuzzy set theory.
299 citations
TL;DR: The proposition that natural language concepts are represented as fuzzy sets of meaning components and that language operators—adverbs, negative markers, and adjectives— can be considered as operators on fuzzy sets was assessed empirically and was consistent with the hypothesis thatnatural language concepts and operators can be described more completely and more precisely using the framework of fuzzy set theory.
Abstract: SUMMARY Recent developments in semantic theory, such as the work of Labov (1973) and Lakoff (1973), have brought into question the assumption that meanings are precise. It has been proposed that the meanings of all terms are to a lesser or greater degree vague, such that, the boundary of the application of a term is never a point but a region where the term gradually moves from being applicable to nonapplicable. Developments in fuzzy set theory have made it possible to offer a formal treatment of vagueness of natural language concepts. In this article, the proposition that natural language concepts are represented as fuzzy sets of meaning components and that language operators—adverbs, negative markers, and adjectives— can be considered as operators on fuzzy sets was assessed empirically. In a series of experiments, we explored the application of fuzzy set theory to the meaning of phrases such as very small, sort of large, and so on. In Experiment 1, subjects judged the applicability of the set of phrases to a set of squares of varying size. The results indicated that the group interpretation of the phrases can be characterized within the framework of fuzzy set theory. Similar results were obtained in Experiment 2, where each subject's responses were analyzed individually. Although the responses of the subjects, in general, could be interpreted in terms of fuzzy logical operations, one subject responded in a more idiomatic style. Experiments 3 and 4 were attempts to influence the logical-idiomatic distinction in interpretatio n by (a) varying the presentation mode of the phrases and by (b) giving subjects only a single phrase to judge. Overall, the results were consistent with the hypothesis that natural language concepts and operators can be described more completely and more precisely using the framework of fuzzy set theory.
286 citations
01 May 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: In this article, a new form of logic is described, originally developed for the formalization of physical theories, the essential feature being a "fuzzification" of the concept of a proposition A proposition is not regarded as being necessarily true or false; it is defined not via truth conditions but in terms of a definite commitment that is assumed by the speaker.
Abstract: A new form of logic is described, originally developed for the formalization of physical theories, the essential feature being a “fuzzification” of the concept of a proposition A proposition is not regarded as being necessarily true or false; it is defined not via truth conditions but in terms of a definite commitment that is assumed by the speaker In the case of an atomic proposition the commitment amounts to a bet on the outcome of some agreed test; for a compound proposition it leads to a dialogue between the speaker and an opponent The resulting logic corresponds closely to the infinitevalued logic Ł α, of Łukasiewicz In fact, the approach provides a dialogue interpretation of Ł ∞ and leads to a convenient method for establishing logical identities Set theory is then developed, not by taking set as a primitive concept but by assuming each set A is determined by a property P characteristic of its members: A = {x:P(x)} When this is expressed formally the result can be read in two ways according to whether the underlying logic is classical logic or Ł ∞ (with the above interpretation) If the propositions P(x) are classical we get ordinary sets; if they are propositions in the new “fuzzy” sense we get fuzzy sets ( f -sets) The situation is illustrated by a number of definitions and theorems involving simple operations on f -sets Lastly, the notion of a convex f-set is defined, and a simple theorem is stated and proved using Ł ∞ and the dialogue method of proof All statements and proofs are expressed in terms of the new logic In particular, use of the quantitative notion of “grade of membership” in a fuzzy set is entirely avoided
220 citations
01 Nov 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: A new type of experiment is proposed to better understand the fuzzy behaviour of a human operator in a man-machine system and ought to provide a much better understanding of the operator's fuzzy algorithm for adapting his experience to the development of the fuzzy algorithms for the new task.
Abstract: A new type of experiment is'proposed to better understand the fuzzy behaviour of a human operator in a man-machine system. The published applications of fuzzy set theory to the control of a simple steam engine are used as a convenient example to illustrate how some of the current applications of fuzzy set theory may be modified to carry out this type of experiment. The rationale for this proposal is developed by reviewing studies of the classification of human height and applications of fuzzy set theory to handwritten character recognition and control system design. Based on this brief review, both the results to be expected from such an experiment and how they might be analyzed are discussed. A key result is that such experiments ought to provide a much better understanding of the operator's fuzzy algorithm for adapting his experience to the development of the fuzzy algorithm for the new task.
206 citations
TL;DR: The method basically consists of computing final ratings for each alternative and comparing the weighted final ratings, and considering each of these variables as fuzzy quantities, characterized by appropriate membership functions.
158 citations
25 May 1976
TL;DR: An avenue for further work in this area is described where the need is to go beyond a purely descriptive approach, and means for implementing a prescriptive or a self-organizing system are explored.
Abstract: This paper describes an application of fuzzy logic in designing controllers for industrial plants. A Fuzzy Logic is used to synthesise linguistic control protocol of a skilled operator. The method has been applied to pilot scale plants as well as in a practical industrial situation. The merits of this method in its usefulness to control engineering are discussed. This work also illustrates the potential for using fuzzy logic in modelling and decision making. An avenue for further work in this area is described where the need is to go beyond a purely descriptive approach and explore means by which a prescriptive system may be implemented.
130 citations
TL;DR: The modes (both useful and otherwise) in which optimization has been applied to public systems problems and the need for optimization models which somehow “fit” the decision-makers' methods and backgrounds will be discussed.
Abstract: Because public systems problems are frequently ill-defined and have fuzzy constraints and vague multiple objectives, their solution by means of formal optimization models is not widely accepted. This paper will explore the modes (both useful and otherwise) in which optimization has been applied to such problems. The need for optimization models which somehow “fit” the decision-makers' methods and backgrounds will be discussed. Several other aspects of public systems optimization will be considered, in a somewhat random fashion. This paper will raise more questions than answers.
TL;DR: To deal with the organization problems of data in this conceptual model, the conventional concept of a list is extended to a fuzzy list and the notion of an inverted file structure can be extended to the fuzzy data in the retrieval model.
Abstract: This paper is concerned with the organization and retrieval of records in document retrieval systems which admit of imprecision in the form of fuzziness in document characterization and retrieval rules. A mathematical model for such systems, based on the theory of fuzzy sets, is introduced. A document retrieval system, as defined in this paper, is a quadruple (X, D, Q, γ), where X is a collection of the document descriptions (also referred to as index records, or records); D is the descriptor set; Q is a query set; γ: QxX → [0, 1], (called the matching function) assigns to each pair (q, x) where q ϵ Q and x ϵ X, a number γ(q, x) in the interval [0, 1], called the matching index for the query q and the document description x. In our system model, each document description x is defined as a fuzzy set in the descriptor set D. As a fuzzy subset of D, each x is characterized by a membership function μx: D → [0, 1], where μx(d), representing the grade of membership of d in x, is referred to as the index weight of the descriptor d for the document representation x. The retrieval response of the system is defined in terms of the matching function γ. More specifically, given a query q, the index record retrieval response, f(q), is defined to be a fuzzy set in X whose membership function is given by μ ƒ(q) (x) = γ(q, x) . To deal with the organization problems of data in our conceptual model, the conventional concept of a list is extended to a fuzzy list. Specifically, L(d), the fuzzy list corresponding to a descriptor d, is defined as a fuzzy set in the document description set X whose membership function is given by μ l (d) (x) = μ x , (d) . In this way, the notion of an inverted file structure can be extended to the fuzzy data in our retrieval model.
TL;DR: A mathematical model of information retrieval system based on the concept of fuzzy thesaurus is presented, which makes it possible to retrieve documents with the highest degree of relevance to the information requests of the users of the information system.
Abstract: The object of this paper is to present a mathematical model of information retrieval system based on the concept of fuzzy thesaurus. For this purpose the mathematical methods of A. Zadeh's theory of fuzzy sets have been used. The application of the theory of fuzzy sets to the description of information retrieval system makes it possible (1) to take into account the fact that the degrȩe of importance of the particular terms in the search patterns of the particular documents and information requrets is of a continuous character, (2) to formalize the relations between terms describing documents and information requests (fuzzy thesaurus). The use of simple operations of the theory of fuzzy sets makes it possible to retrieve documents with the highest degree of relevance to the information requests of the users of the information system.
TL;DR: The use of fuzzy set theory to design controllers has been pursued as a combined project by the University of Manchester Institute of Science and Technology and the British Steel Corporation as mentioned in this paper, which has led to an on-plant trial at Cleveland Sinter Plant where anticipated improvements in plant performance were achieved.
01 Apr 1976
TL;DR: This letter describes the implementation of control systems designed using fuzzy algorithms and fuzzy logic and the resulting technique employs lookup tables, particularly when applied to short-word-length digital control systems.
Abstract: This letter describes the implementation of control systems designed using fuzzy algorithms and fuzzy logic. The resulting technique employs lookup tables. An assessment is made of the suitability of such tables, particularly when applied to short-word-length digital control systems. An interpreter program which can be used to generate the required lookup tables is also described.
TL;DR: The notion of fuzzy sample point is introduced, and generalized probability measures on fuzzy events are defined, and it is shown that such measures can be associated with quantum‐mechanical states when the fuzzy elementary events are represented by Gaussian distributions on phase space.
Abstract: The notion of fuzzy sample point is introduced, and generalized probability measures on fuzzy events are defined. This leads to the concept of spectral measure on fuzzy events. It is shown that such measures can be associated with quantum‐mechanical states when the fuzzy elementary events are represented by Gaussian distributions on phase space.
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TL;DR: To show how a fuzzy program is executed, a simulation system is exploited which controls a simple inchworm robot and fuzzy instructions are translated into machine instructions by the use of MAX-METHOD and backtracking.
Abstract: A fuzzy program is defined as an ordered sequence of fuzzy instructions. In the execution of a fuzzy program, fuzzy instructions are translated into machine instructions by the use of MAX-METHOD and backtracking. To show how a fuzzy program is executed, a simulation system is exploited which controls a simple inchworm robot. A few examples of computer simulations are presented which deal with the behavior of a stranger (or a robot) searching for his destination in a modeled town under simple fuzzy instructions.
01 Nov 1976-International Journal of Human-computer Studies \/ International Journal of Man-machine Studies
TL;DR: The IR systems are faced with a need to manage fuzziness and not merely to react to fuzziness, and fuzzy assignment is modelled as a system (X,Y,f:X→ℱ(Y)) where f(x)(y) is the link between the information item x and the descriptor y.
Abstract: The IR systems are faced with a need to manage fuzziness and not merely to react to fuzziness. The indexing process is viewed as representing the set X of information items by fuzzy subsets ℱ(Y) of the descriptor set Y. A fuzzy assignment is modelled as a system (X,Y,f:X→ℱ(Y)) where f(x)(y) is the link between the information item x and the descriptor y. The grade of importance of a subset of descriptors is expressed by a fuzzy measure μ:℘(Y)→[0,1]. In this way syntax estimation is made possible by using a fuzzy integral ff(x)(y)oμ. The information items are ranked according to a new application X→[0,1] induced by the global measure μ. Finally, a descriptor is viewed as a fuzzy set.
TL;DR: A method for the analysis of fuzzy systems using the concept of fuzzy sets is proposed, which enables us to represent quantitatively the sum (or product) of fuzzy variables like large and small, and the convolution of fuzzy sequences.
Abstract: The behaviour of the humanistic systems is too complex or too ill-defined to be analysed using definitive mathematics. In this paper we propose a method for the analysis of such systems using the concept of fuzzy sets. The methods for the manipulation of fuzzy variables are considered. These methods enable us to represent quantitatively the sum (or product) of fuzzy variables like large and small, and the convolution of fuzzy sequences. Since, while working with fuzzy variables, the data may become enormous, a technique for the data reduction is proposed. Using these techniques for the manipulation of fuzzy variables we are in a position to analyse fuzzy systems.
07 Jun 1976
TL;DR: A fairly exhaustive introduction to the theory and applications of fuzzy sets lists 238 papers dealing with a great variety of recent investigations.
Abstract: The notion of fuzzy sets---sets with imprecise boundaries---is a natural cornerstone upon which to build algorithms based on approximate reasoning. Since their inception in 1965 by Zadeh, fuzzy sets have led to first steps towards quantifying data analysis in many fields previously immune to mathematical examination. A fairly exhaustive introduction to the theory and applications of fuzzy sets lists 238 papers dealing with a great variety of recent investigations.
TL;DR: A procedural knowledge base system using fuzzy concepts for medical diagnosis is proposed and a classification of fuzzy concepts as being either primary or secondary is shown.
Abstract: A procedural knowledge base system using fuzzy concepts for medical diagnosis is proposed. A classification of fuzzy concepts as being either primary or secondary is shown.
TL;DR: In this paper, a general formulation of fuzzy programs or fuzzy algorithms is introduced and the relationship between this formulation and other existing formulations is studied.
TL;DR: Some applications of fuzzy set theory in the area of communications and information systems are examined, which have direct applications in fuzzy communication, fuzzy problem-solving, fuzzy information retrieval, and fuzzy teleconferencing.
Abstract: In this paper we shall examine some applications of fuzzy set theory in the area of communications and information systems. With the advent of computers, the telephone and the television, there are potentialities of all kinds of communication services into the home. Fuzzy problems are very likely to occur with user groups requesting methods to understand fuzzy needs. Thus problems in fuzzy communication, fuzzy problem-solving, fuzzy information retrieval, and fuzzy teleconferencing have direct applications of fuzzy set theory, which are considered.
TL;DR: It is shown in this paper that it is possible to develop fuzzy structuring methods based on a fuzzy reach ability matrix and fuzzy graphs, which are based onA reachability matrix of an inter connection matrix is developed to aid the solution process.
Abstract: It is natural to inquire if fuzzy set theoretic methods could enhance the structuring method. It is shown in this paper that it is possible to develop fuzzy structuring methods. These are based on a fuzzy reach ability matrix and fuzzy graphs. Panel members respond to a relational question “is siRsj ?”along a scale from 0% to 100% representing a set of polar concepts, such as “dense-sparse.” The characteristic logic equation has its fuzzy version in the matrix form. However, in the element form, the problem is more complicated. A reachability matrix of an inter connection matrix is developed to aid the solution process. Measures of incertitude (fuzzy entropy) guide the panel members in choosing appropriate entries. Incertitudes of the set S of issues and of the fuzzy graph ┌R are defined.
TL;DR: A new method for solving the problem of optimal assignment of employees to work places in a given organizational structure by using in a “direct” way of verbal descriptions determining the work results of particular employees and the whole structure as functions of some factors.
01 Apr 1976
TL;DR: Some methodologles based on fuzzy set theory are proposed for emitting and verifying lexical hypotheses in a Speech Understanding System.
Abstract: Some methodologles based on fuzzy set theory are proposed for emitting and verifying lexical hypotheses in a Speech Understanding System. Context-independent and context-dependent features are extracted from spectrogram patterns with a procedure that establishes a correspondence relation between a speech segment and its linguistic interpretation. The syllabic hypotheses are used for emitting lexical hypotheses by an algorithm that compensates for partial corruption of the syllabic information exploiting the lexical redundancy.
TL;DR: It is shown that the well-known quadratic performance criterion in deterministic optimal control is equivalent to the exponential membership function of a certain fuzzy decision (set) in a stochastic setting.
25 May 1976
TL;DR: In inference processes which are approximate rather than precise in nature, systems in which the dependence of the truth-values of the consequents on those of the premises admits of precise characterization are considered.
Abstract: Much of human reasoning is based on inference processes which are approximate rather than precise in nature. Generally, such processes fall outside the scope of existing logical systems — systems in which the dependence of the truth-values of the consequents on those of the premises admits of precise characterization.
TL;DR: An algorithm for obtaining simple disjunctive decompositions of fuzzy functions is described and special properties of the decomposed fuzzy structures are introduced and their relationships to two-valued logic are investigated.
Abstract: An algorithm for obtaining simple disjunctive decompositions of fuzzy functions is described. The insufficiency of Boolean methods for simplification of fuzzy functions is discussed. Special properties of the decomposed fuzzy structures are introduced and their relationships to two-valued logic are investigated. This new algorithm is the first one in a containing research in the area of multivalued and fuzzy decompositions of complex systems.