Showing papers on "Fuzzy number published in 1982"
TL;DR: This paper deals successively with differentiation of ordinary functions at a fuzzy point and with differentiation at a nonfuzzy point, and with practical methods of computation are presented.
592 citations
TL;DR: This paper will give a characteristic of a field by a fuzzy ideal, as fuzzy invariant subgroups, fuzzy ideals, and to prove some fundamental properties of fuzzy algebra.
526 citations
TL;DR: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short) as discussed by the authors, which is actually set functions which are monotonic with respect to set inclusion.
Abstract: An axiomatic approach to a broad class of fuzzy measures in the sense of Sugeno is presented via the concept of triangular norm (t-norm for short). Fuzzy measures are actually set functions which are monotonic with respect to set inclusion. Triangular norms and conorms are semi-groups of the unit interval which have been thoroughly studied in the literature of functional equations. The proposed class encompasses probability measures, Zadeh's possibility measures and the dual notion of necessity measures. Any set function of the class can be expressed in terms of a density, and constructively defined out of this density. This feature makes the proposed framework attractive from a practical point of view for the representation and manipulation of subjective evidence. The link between t-norm and t-conorm based set functions and Shafer's belief functions is invesligaled.
304 citations
TL;DR: Using Zadeh's extension principle, the integral of fuzzy mappings over a crisp interval is defined, and provided a special analytical representation of the fuzzy mapping, the practical computation of such an integral is shown to be easy.
260 citations
253 citations
TL;DR: The family of all the solutions of a fuzzy relation equation on a finite set is considered, characterized by the set ofall the lower solutions, which can be obtained by a combinatorial algorithm.
181 citations
TL;DR: This paper introduces a subcategory of the category of fuzzy topological spaces and proves basic properties of this subcategory, the notion of fuzzy neighborhoods, which enables us to introduce a local theory of fuzzytopologies.
181 citations
TL;DR: Under the condition of Bayesian belief structure a whole family of possible definitions for the probability of fuzzy sets is obtained and a procedure for including belief qualification in pruf is suggested.
166 citations
TL;DR: Two existence theorems for fixed points of a fuzzy mapping are proved and an algorithm for computing approximations of such a fixed point is described, under the restrictive assumption that for any x in X, the membership function of Rχ has a ‘complementary function’.
145 citations
TL;DR: This paper tries to emphasize the relationships and the differences between the various points of view in the integration of mappings over fuzzy domains.
143 citations
TL;DR: It is shown that the strong law of large numbers holds also for fuzzy random variables and this result is used to give a consistent estimator for the expectation of a fuzzy random variable.
TL;DR: An axiomatic framework for formalizing the most general class of fuzzy complements is introduced and it is shown that the various measures of fuzziness described previously in the literature are special cases of this general class.
Abstract: An axiomatic framework for formalizing the most general class of fuzzy complements is introduced in this paper. It is then used for investigating a general class of measures of fuzziness based on the view that the degree of fuzziness of a fuzzy set should characterize the lack of distinction between the set and its complement. It is shown that the various measures of fuzziness described previously in the literature are special cases of this general class. A class of so-called distance-based measures of fuzziness is also introduced. These measures are described in terms of the notion of an aggregation function of differences between the membership grades characterizing a fuzzy set and those of its complement. It is shown that the class of distance-based measures is equal to the class of general measures of fuzziness. It is also shown that, given a particular fuzzy complement, aggregation functions which differ only in a multiplication constant represent the same measure of fuzziness.
TL;DR: A fuzzy dynamical system on an underlying complete, locally compact metric state space X is defined axiomatically in terms of a fuzzy attainability set mapping on X, and it is shown that the support of such a fuzzy dynamicals system on X is a crisp multivalued dynamical systems on X.
TL;DR: A binary operation ⊕ is constructed on the L-fuzzy real line R (L) which reduces to the usual addition on R if ⊆ is restricted to the embedded image of R in R ( L), which yields a partially ordered, abelian cancellation semigroup with identity, and which is jointly fuzzy continuous on R (l).
TL;DR: FUZZY QMODEL utilizes the fuzzy c-means algorithm of Bezdek to provide an alternative initial mixing polyhedron and so can produce suitable solutions in the presence of noisy or “messy” data points.
Abstract: Many data sets can be viewed as a collection of samples representing mixtures of a relatively small number of end members. When end members are present in the sample set, the algorithm QMODEL by Klovan and Miesch can efficiently determine proportionate contributions. EXTENDED QMODEL by Full, Ehrlich, and Klovan was designed to deduce the composition of realistic end members when the end members are not represented by samples. However, in the presence of high levels of random variation or outliers not belonging to the system of interest, EXTENDED QMODEL may not be reliable inasmuch as it is largely dependent on extreme values for definition of an initial mixing polyhedron. FUZZY QMODEL utilizes the fuzzy c-means algorithm of Bezdek to provide an alternative initial mixing polyhedron. This algorithm utilizes the collective property of all the data rather than outliers and so can produce suitable solutions in the presence of noisy or “messy” data points.
TL;DR: An algorithm for solving transportation problems with fuzzy constraints is proposed and the relationship between the algebraic structure of the optimum solution of the deterministic problem and its fuzzy equivalent is investigated.
TL;DR: A dynamic programming functional equation for a multi-stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation, an extension of the Bellman-Zadeh model.
TL;DR: This paper will show that the mathematical requirements placed on the generalization in order that the lattice structures of the fuzzy subset theory be preserved are really quite minimal.
TL;DR: Axioms are proposed that could justify the natural definition of the probability of a fuzzy event initially given by Zadeh based on the postulate that the sum of the conditional probability and its complement given any fuzzy event adds to one or on soft independence for orthogonal sets with independent constitutive elements.
TL;DR: In this paper, the definition of the and operation in multivalued logic and decision making is investigated, and a set of basic properties for selecting an appropriate operator are given, as well as a general class of connectives.
Abstract: We investigate the definition of the “and” operation in multivalued logic and decision making. A set of basic properties are suggested. Rules for selecting an appropriate operator are given. A general class of connectives is also suggested.
TL;DR: The basic aspects such as mutual identification and control, stabilization control, control with constraints, generation of control rules of a fuzzy logic controller, important from the theoretical and applicational point of view are discussed and illustrated by means of numerical examples.
TL;DR: The main result is that element-dependent operations are not compatible with the preservation of the intersection and union under the inverse image of a function.
TL;DR: It is shown how such probabilities may be estimated from fuzzy data and a basic relation between joint, conditional and marginal fuzzy probabilities is established.
TL;DR: A general framework for a theory is presented that encompasses both statistical uncertainty and nonstatistical uncertainty, which relates to the concept of a fuzzy set and possibility theory, and the possibility of using this theory in Bayesian estimation with fuzzy prior information.
TL;DR: It is found that when ∗ is the operation Λ of the lattice, that the arithmetical mean of Λ-independent fuzzy numbers does not converge, and it is thought that this case could be a limit one.
TL;DR: The fuzzy control model is derived for which the input parameter is feed rate and the output parameter is workpiece surface finish which has to be controlled and can be applied to most industrial processes which are uncertain and do not conform to strict mathematical laws.
TL;DR: In spatial economic analysis, economic agents are assumed to make accurate economic calculations and optimise the objective functions under strict constraints of resource limitation, and these objective functions have clearly defined arguments and well-controlled parameters.
Abstract: It is implicitly accepted by spatial economic analysis that the economic behaviour of agents located in given spaces (market areas, regions, etc.) is precise, that is to say, their behaviour is such that a possible action (consumption, production) is, or is not, preferable to another. In otherwords, economic agents are assumed to make accurate economic calculations and optimise the objective functions under strict constraints of resource limitation. These objective functions have clearly defined arguments and well-controlled parameters.
TL;DR: It is shown that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations.