Showing papers on "Fuzzy number published in 1984"
TL;DR: A FORTRAN-IV coding of the fuzzy c -means (FCM) clustering program is transmitted, which generates fuzzy partitions and prototypes for any set of numerical data.
5,287 citations
TL;DR: The distance between two points in a fuzzy metric space is a non-negative, upper semicontinuous, normal and convex fuzzy number.
738 citations
TL;DR: This fuzzy linear programming problem with fuzzy numbers can be regarded as a model of decision problems where human estimation is influential and a reasonable solution under consideration of the ambiguity of parameters is obtained.
440 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: 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
01 Mar 1984
TL;DR: The identification problem which plays a central role in further development of the theory of fuzzy systems and their applications is considered and Appropriate methods of determination of fuzzy relations are presented.
Abstract: The identification problem which plays a central role in further development of the theory of fuzzy systems and their applications is considered. The systems under consideration are of the type XRY or (X1X2 . . . Xn)RY, where X, X1, X2, . . ., X n, denote fuzzy sets of input and Y stands for fuzzy set of output, while R denotes a fuzzy relation expressing the relationships between input and output. Appropriate methods of determination of fuzzy relations are presented. The idea of probabilistic sets in the identification problem is discussed in detail.
215 citations
TL;DR: The methodology provided includes, as a special case, the resolution of fuzzy arithmetical operations, i.e. when ∗ stands for +, −, × or ÷, extended to fuzzy numbers (fuzzy subsets of the real line).
183 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: Some convergence theorems of sequence of fuzzy integrals are proved, especially, using the concept of autocontinuity, a necessary and sufficient condition for the convergence in measure theorem is given.
159 citations
01 Mar 1984
TL;DR: The concept of the sector bound nonlinearity has been considered for frequency domain stability analysis of linear single-input single- output (SISO) and decoupled multi-input multi-output (MIMO) systems associated with the fuzzy logic controller.
Abstract: The concept of the sector bound nonlinearity has been considered for frequency domain stability analysis of linear single-input single-output (SISO) and decoupled multi-input multi-output (MIMO) systems associated with the fuzzy logic controller. For analysis of the fuzzy logic controller, the system's model is considered to be available in transfer-function form, but for generation of the fuzzy logic controller no model description is necessary. A generalized Nyquist-type stability analysis is presented.
TL;DR: Methods of aggregating all the fuzzy sets into one fuzzy set μ, defined on the issues, so that μAϵL gives the final ranking for issue A, are discussed.
TL;DR: The properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets, on fuzzy numbers and on fuzzy probabilistic sets.
01 Mar 1984
TL;DR: Fuzzy linear programming problems are discussed in which both constraints and objective functions are assumed to be fuzzy inequalities and it is shown how to reduce this problem to the conventional linear programming problem so that it can be easily solved by the ordinary algorithms of linear programming.
Abstract: Fuzzy linear programming problems are discussed in which both constraints and objective functions are assumed to be fuzzy inequalities. The problem is to obtain a fuzzy solution such that the fuzzy inequalities hold. It is shown how to reduce this problem to the conventional linear programming problem so that it can be easily solved by the ordinary algorithms of linear programming.
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...
02 Jul 1984
TL;DR: In this paper, a notion of implicit fuzzy quantifiers which are approximations to all and always, e.g., almost all, almost always, most, frequently, etc.
Abstract: Informally, a disposition is a proposition which is preponderantly, but no necessarily always, true. For example, birds can fly is a disposition, as are the propositions Swedes are blond and Spaniards are dark.An idea which underlies the theory described in this paper is that a disposition may be viewed as a proposition with implicit fuzzy quantifiers which are approximations to all and always, e.g., almost all, almost always, most, frequently, etc. For example, birds can fly may be interpreted as the result of supressing the fuzzy quantifier most in the proposition most birds can fly. Similarly, young men like young women may be read as most young men like mostly young women. The process of transforming a disposition into a proposition is referred to as explicitation or restoration.Explicitation sets the stage for representing the meaning of a proposition through the use of test-score semantics (Zadeh, 1978, 1982). In this approach to semantics, the meaning of a proposition, p, is represented as a procedure which tests, scores and aggregates the elastic constraints which are induced by p.The paper closes with a description of an approach to reasoning with dispositions which is based on the concept of a fuzzy syllogism. Syllogistic reasoning with dispositions has an important bearing on commonsense reasoning as well as on the management of uncertainty in expert systems. As a simple application of the techniques described in this paper, we formulate a definition of typicality -- a concept which plays an important role in human cognition and is of relevance to default reasoning.
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.
TL;DR: This paper attempts to simplify the calculation process of the structure function and to newly define the state of the top event by the membership function, using fuzzy sets theory, and shows that the importance of each basic event can be evaluated through fuzzy operations.
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: 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: The theoretical results are shown to conform well to previously published experimental results on monochrome images.
Abstract: The following topics are discussed: (1) a measure for the information contained in fuzzy sets, (2) the relation between fuzzy information and Shannon's information], and (3) the relation between fuzzy information and physical entropy. Some related examples are presented. The theoretical results are shown to conform well to previously published experimental results on monochrome images.
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: This paper proposes a definition of perimeter for fuzzy subsets of the plane and shows that it reduces to the standard definition if the fuzzy subset is an ordinary subset.
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.
TL;DR: A limit of a sequence of fuzzy numbers is defined and its some properties are shown and a strong law of large numbers for fuzzy random variables is shown.
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.
01 Nov 1984
TL;DR: The concept of L2-stability and its graphical interpretation, i.e. the circle criterion, are used and the use of the classical Nyquist locus and the gain-phase chart are brought into the picture.
Abstract: A hybrid (fuzzy and nonfuzzy) design concept has been proposed for the linear single-input single-output (SISO) system associated with fuzzy logic controllers. In the present design techniques, the concept of L2-stability and its graphical interpretation, i.e. the circle criterion, are used. Thus the use of the classical Nyquist locus and the gain-phase chart are brought into the picture. The drawbacks of the L2-stability/circle criterion are indicated and overcome. In the present design technique, which is graphical in nature, the designer is given a feel for the system. Examples are provided to illustrate the application of hybrid controller's structure for the synthesis of the linear SISO system associated with the fuzzy logic controller.
TL;DR: This paper proposes definitions of intrinsic and extrinsic diameter for fuzzy subsets which reduce to the ordinary definitions when the subsets are crisp and height and width for a fuzzy subset are defined.
TL;DR: A “softening” of a basic formulation of multicriterion optimization and control (multistage decision making) is presented and a calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used.