Showing papers on "Fuzzy logic published in 1984"
TL;DR: F fuzzy preference orderings are defined as fuzzy binary relations satisfying reciprocity and max-min transitivity and those orderings might be useful for proceeding the group decision making process smoothly, in the same manner as the extended contributive rule method.
1,074 citations
TL;DR: This approach, which enables a very general treatment of relational databases with fuzzy attribute values, makes an extensive use of dual possibility and necessity measures.
566 citations
TL;DR: An algorithm for constructing models on the basis of fuzzy and nonfuzzy data with the aid of fuzzy discretization and clustering techniques is proposed.
524 citations
TL;DR: Past work on fuzzy geometric concepts, which include connectedness, adjacency and surroundedness, starshapedness and convexity, area and perimeter, extent and diameter are summarized and some new results are included.
361 citations
TL;DR: From a logical standpoint, each logic has its corresponding set theory in which each logical operation is translated into a basic operation for set theory; namely, the relation ⊆ and = on sets are translation of the logical operations → and ↔.
Abstract: In 1965 Zadeh introduced the concept of fuzzy sets. The characteristic of fuzzy sets is that the range of truth value of the membership relation is the closed interval [0, 1] of real numbers. The logical operations ⊃, ∼ on [0, 1] which are used for Zadeh's fuzzy sets seem to be Łukasiewciz's logic, where p ⊃ q = min(1, 1 − p + q), ∼ p = 1 − p. L. S. Hay extended in [4] Łukasiewicz's logic to a predicate logic and proved its weak completeness theorem: if P is valid then P + Pn is provable for each positive integer n. She also showed that one can without losing consistency obtain completeness of the system by use of additional infinitary rule.Now, from a logical standpoint, each logic has its corresponding set theory in which each logical operation is translated into a basic operation for set theory; namely, the relation ⊆ and = on sets are translation of the logical operations → and ↔. For Łukasiewicz's logic, P Λ (P ⊃ Q). ⊃ Q is not valid. Translating it to the set version, it follows that the axiom of extensionality does not hold. Thus this very basic principle of set theory is not valid in the corresponding set theory.
265 citations
TL;DR: Fuzzy sets and fuzzy logic are qualitatively described, and the way in which they operate is illustrated by an example of a fuzzy controller.
Abstract: Fuzzy sets and fuzzy logic are qualitatively described, and the way in which they operate is illustrated by an example of a fuzzy controller. The application of fuzzy concepts to expert systems and computer vision is also discussed.
247 citations
TL;DR: The technique of parametric programming is used to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.
235 citations
TL;DR: General schemes for solving fuzzy relation equations with finite sets are derived and the relationship between these results and those of previous publications regarding this subject is discussed.
215 citations
TL;DR: The Fuzzy Linear Mathematical Programming problem is easily solved because of the concept of fuzzy objective based on the Fuzzification Principle and the relationship of duality among fuzzy constraints and fuzzy objectives is given.
177 citations
TL;DR: A partial solution to the problem of constructing a fuzzy map is presented, an algorithm that assimilates a fact first by imposing constraints on the fuzzy coordinates of the objects involved, then by rearranging or growing the tree of frames of reference.
171 citations
01 Jul 1984
TL;DR: The theory of approximate reasoning developed by L.A. Zadeh provides a natural format for representing the knowledge and performing the inferences in the rule-based expert systems by providing a new structure for including the rules that only require the satisfaction to some subset of the requirements in its antecedent.
Abstract: The concept of a rule-based expert system that includes data and production rules is discussed. It is shown how the theory of approximate reasoning developed by L.A. Zadeh (New York, Wiley, 1979) provides a natural format for representing the knowledge and performing the inferences in the rule-based expert systems. The representation ability of the systems is extended by providing a new structure for including the rules that only require the satisfaction to some subset of the requirements in its antecedent. This is accomplished by use of fuzzy quantifiers. A methodology is also provided for the inclusion of a form of uncertainty in the expert system associated with the belief attributed to the data and production rules.
TL;DR: It is proved that for a group G, a fuzzy subgroup is fuzzy normal if and only if it is constant on the conjugate classes of G .
01 Dec 1984
TL;DR: This paper describes a model of an autopilot controller based on fuzzy algorithms that maneuvers an aircraft from level flight into a final-approach flight path and maintains the aircraft along the glide path until just before touchdown.
Abstract: This paper describes a model of an autopilot controller based on fuzzy algorithms. The controller maneuvers an aircraft from level flight into a final-approach flight path and maintains the aircraft along the glide path until just before touchdown. To evaluate the performance and effectiveness of the model, the aircraft response to controller actions is simulated using flight simulation techniques. The effect of varying parameters and different defuzzification strategies on controller performance is analyzed.
TL;DR: This paper advocates that fuzzy sets theory provides a basis for solving this problem with sufficient consistency and rigorousness and shows that under reasonable restrictions, this solution is efficient (Pareto optimal) for the original problem.
Book•
01 Jan 1984
TL;DR: [B95] Boman, M.
Abstract: [B95] Boman, M.: " Rational Decisions and Multi-Agent Systems " in Proc.
TL;DR: A general query language, FRIL, which uses fuzzy base relations and rewrite rules is described and incorporates an automated fuzzy inference mechanism and should find applications in many areas of knowledge engineering such as expert systems, linguistic controllers, etc.
TL;DR: It is argued here that, in many situations, a more appropriate tool for capturing the inherent imprecisions of human value judgements may be fuzzy orderings.
TL;DR: The mean and variance of the parameters involved in the problem under consideration are estimated here using a new method using fuzzy set and system theory, which is not sensitive to small variations in the membership values.
Abstract: Probabilistic methods are being used increasingly in construction engineering. However, when a parameter is expressed in linguistic rather than mathematical terms, classical probability theory fails to incorporate the information. The linguistic variables can be translated into mathematical measures using fuzzy set and system theory. A construction management problem, i.e., estimation of the duration of an activity, is solved using this theory. In order to implement the proposed technique, various membership functions need to be estimated using judgment or with the assistance of experts. The proposed technique is not sensitive to small variations in the membership values. This is a very desirable property. However, the method is sensitive to the choice of the fuzzy relations. The uncertainty in the fuzzy relations can be modeled along with other sources of uncertainty. The mean and variance of the parameters involved in the problem under consideration are estimated here using a new method. The method maxi...
TL;DR: In this paper, the authors proposed a new approach to formulating fuzzy priorities in a goal programming problem, which leads to a formulation in which tradeoffs between goals more closely reflect the decision maker's intentions than in other noninteractive approaches.
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01 Jan 1984
TL;DR: The Alternative Set Theory and its approach to Cantor's Set Theory as mentioned in this paper is a general framework for fuzzy set theory, and it is based on the notion of Fuzzy Probability Measures.
Abstract: Notes on Vagueness and Mathematics.- Fuzzy Set Theory: Some Aspects of the Early Development.- Plausibility Measures - A General Framework for Possibility and Fuzzy Probability Measures.- Controlled-Error Theories of Proximity and Dominance.- Impartial Truth.- A Geometry of Logic.- Representations of Transitive Fuzzy Relations.- Fuzziness and Fuzzy Equality.- Large Societies and Individual Strategy Selection: A Case Study of Ambiguity.- The Alternative Set Theory and its Approach to Cantor's Set Theory.- Aspects of Vagueness and Some Epistemological Problems Related to their Formalization.- An Inquiry into Indistinguishability Operators.- A Theory of Commonsense Knowledge.- Index of Names.- Index of Subjects.
01 Dec 1984
TL;DR: This paper discusses an application of fuzzy control to parking a car by modelling a man's parking actions using a model car equipped with sensing devices and a micro-processor.
Abstract: This paper discusses an application of fuzzy control to parking a car. Fuzzy control rules are derived by modelling a man's parking actions. Experiments are successfully performed using a model car equipped with sensing devices and a micro-processor.
TL;DR: The phase (offset) controller using fuzzy control statements that is useful when the traffic is rather heavy is proposed that is effective even for the control of successive traffic junctions.
01 Jan 1984
TL;DR: A survey of fuzzy-set -theoretic operations is proposed with emphasis on set-differences and inclusions, and general procedures for a systematic generation of such connectives are described.
Abstract: A survey of fuzzy-set -theoretic operations is proposed with emphasis on set-differences and inclusions. General procedures for a systematic generation of such connectives are described. Their importance for a proper statement and analysis of equations involving fuzzy numbers is stressed. The study of such equations leads to the definition of new types of fuzzy arithmetics where errors (or imprecision) compensate. Such "optimistic" fuzzy arithmetics are based on inclusion (i.e. im plication) connectives while the usual "pessimistic" fuzzy arithmetics are based on intersection connectives.
TL;DR: New approaches to unsupervised fuzzy classification of multidimensional data by using ‘semi-fuzzy’ or ‘soft’ clustering techniques to achieve this goal are discussed.
TL;DR: The fuzzy relational database model originated by the authors is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra.
01 Jan 1984
TL;DR: By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations.
Abstract: By substituting the classical lattice operator min of the unit real interval with a triangular norm of Schweizer and Sklar, the usual fuzzy relational equations theory of Sanchez can be generalized to wider theory of fuzzy equations. Considering a remarkable class of triangular norms, for such type of equations defined on finite sets, we characterize the upper an lower solutions.
We also characterize the solutions posessing a minimal fuzziness measure of Yager valued with respect to a triangular norm and conorm.
Moreover we discuss the problem of characterization of the approximate solutions of fuzzy equations.
Finally, the role of the equations considered here in creation of a formal framework for copying with fuzziness is illustrated by various examples in some well known schemes in applications of fuzzy set theory.
TL;DR: Various statistical techniques for the analysis of imprecise data and for inference based on imprecising data are developed and some possible applications to the assessment of credibility in expert systems are indicated.
01 Mar 1984
TL;DR: It is shown that the identification uncertainty is characterized in terms of the maximum solution and the infimum of all the minimal solutions, independent of the function used to define the uncertainty measure.
Abstract: The identification problem for systems with fuzzy relations is solved by applying a general method of solving finite fuzzy relation equations. It is shown that the identification uncertainty is characterized in terms of the maximum solution and the infimum of all the minimal solutions. The result is independent of the function used to define the uncertainty measure. A method for calculating the infimum of all the minimal solutions without calculating these minimal solutions is also derived and results in an efficient method for calculating the identification uncertainty.
TL;DR: The problem of the existence of fixed points for fuzzy maps is studied and uniform structures on sets of fuzzy subsets are defined and the ‘closed convergence’ and ‘myope convergence” structures which have properties close to the corresponding traditional ones are described.