Showing papers on "Fuzzy number published in 1987"
Book•
01 Jan 1987
TL;DR: This book discusses the Logic of Decisions, Behavioral Decision Theory, and Decision Technology, as well as an Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.
Abstract: 1 Introduction.- The Logic of Decisions, Behavioral Decision Theory, and Decision Technology.- Optimization, Outranking, Evaluation.- Basics of Fuzzy Set Theory.- 2 Individual Decision Making in Fuzzy Environments.- Symmetrical Models.- Nonsymmetrical Models.- Fuzzy Utilities.- 3 Multi-Person Decision Making in Fuzzy Environments.- Basic Models.- Fuzzy Games.- Fuzzy Team Theory.- Fuzzy Group Decision Making.- 4 Fuzzy Mathematical Programming.- Fuzzy Linear and Nonlinear Programming.- Fuzzy Multi-Stage Programming.- 5 Multi-Criteria Decision Making in Ill-Structured Situations.- Fuzzy Multi-Criteria Programming.- Multi-Attribute Decision Making (MADM).- Fuzzy Outranking.- 6 Operators and Membership Functions in Decision Models.- Axiomatic, Pragmatic, and Empirical Justification.- The Measurement of Membership Functions.- Selecting Appropriate Operators in Decision Models.- 7 Decision Support Systems.- Knowledge-Based vs. Data-Based Systems.- Linguistic Variables, Fuzzy Logic, Approximate Reasoning.- An Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.- Expert Systems and Fuzzy Sets.
1,209 citations
TL;DR: This method allows a formal, fuzzy representation to be built for verbal decision algorithms and can have an effective computer representation.
990 citations
TL;DR: Generalizations to fuzzy integral equations and fuzzy functional differential equations are indicated and the extension principle and the use of extremal solutions of deterministic initial value problems are applied.
812 citations
TL;DR: Some light is shed on the debate between probability and possibility theory, and the problem of how to carry measure-theoretic notions into the field of possibility theory.
717 citations
TL;DR: The vertex method can avoid abnormality due to the discretization technique on the variables domain and the widening of the resulting function value set due to multi-occurrence of variables in the functional expression by conventional interval analysis methods.
550 citations
Book•
01 Jan 1987
TL;DR: This book discusses the role of Fuzzy Logic in the Management of Uncertainty in Expert Systems, and the concept of a Linguistic Variable and its application to Approximate Reasoning.
Abstract: Coping with the Imprecision of the Real World: An Interview with L.A Zadeh Fuzzy Sets Probability Measures of Fuzzy Events Decision Making in a Fuzzy Environment Similarity Relations and Fuzzy Orderings Outline of a New Approach to the Analysis of Complex Systems and Decision Processes A Fuzzy-Algorithmic Approach to the Definition of Complex or Imprecise Comcepts Fuzzy Sets as a Basis for a Theory of Possibility The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 1) The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 2) The Concept of a Linguistic Variable and Its Application to Approximate Reasoning (Part 3) A Theory of Approximate Reasoning The Role of Fuzzy Logic in the Management of Uncertainty in Expert Systems Syllogistic Reasoning in Fuzzy Logic and its Application to Usuality and Reasoning with Dispositions A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges PRUF-A Meaning Representation Language for Natural Languages A Computational Approach to Fuzzy Quantifiers in Natural Language A Theory of Commonsense Knowledge Test-Score Semantics as a Basis for a Computational Approach to the Representation of Meaning.
543 citations
TL;DR: A computational algorithm based on the α-cut representation of fuzzy sets and interval analysis is described which provides a discrete but exact solution to extended algebraic operations in a very efficient and simple manner.
540 citations
TL;DR: An additive model to solve Fuzzy Goal Programming (FGP) is formulated that uses arithmetic addition to aggregate the fuzzy goals to construct the relevant decision function.
484 citations
TL;DR: Since fuzzy data can be regarded as distribution of possibility, fuzzy data analysis by possibilistic linear models is proposed in this paper and can be considered as fuzzy interval analysis.
467 citations
01 Jul 1987
TL;DR: The required computer capacity and time for implementing the proposed algorithms and related resulting models are-significantly reduced by introducing the concept of the "referential fuzzy sets."
Abstract: The algorithms of fuzzy model identification and self-learning for multi-input/multi-output dynamic systems are proposed. The required computer capacity and time for implementing the proposed algorithms and related resulting models are-significantly reduced by introducing the concept of the "referential fuzzy sets." Two numerical examples are given to show that the proposed algorithms can provide the fuzzy models with satisfactory accuracy.
445 citations
Book•
01 Apr 1987TL;DR: It is shown that a fuzzy group can be associated with a fuzzy graph in a natural way and some properties of fuzzy graphs are considered and the notions of eccentricity and center are introduced.
TL;DR: This paper develops fuzzy analogues of the elementary compound interest problems in the mathematics of finance, and develops a method of comparing fuzzy net cash flows in order to rank fuzzy investment alternatives from best to worst.
TL;DR: These new concepts are illustrated and discussed in the context of an example from a terminal ballistics problem, where the least squares model fitting to the described fuzzy vector data deviates in important aspects from ordinary least squares.
01 Dec 1987
TL;DR: A unified approach for comparing the performance of fuzzy and nonfuzzy controller designs is presented and relationships are established between the gain parameters for the two classes of controller designs.
Abstract: A unified approach for comparing the performance of fuzzy and nonfuzzy controller designs is presented. Relationships are established between the gain parameters for the two classes of controller designs. The methods presented apply equally well to proportional-plus-integral, linear multiband, and multilevel relay controllers.
TL;DR: The notion of twofold fuzzy sets was introduced in this article, where the relevant information for determining the membership status is incomplete and the notion of fuzzy sets are used to represent sets where the membership of some elements may be ill-known rather than just a matter of degree.
TL;DR: F fuzzy extreme solutions are computed and are presented to the decision maker and each of the proposed compromise solutions are fuzzy-efficient.
TL;DR: It is shown that the generalized notion (probabilistic approximate classification) of rough sets can be conveniently described by the concept of fuzzy sets and argued that there does not exist a universal definition for the fuzzy intersection (union) operation.
TL;DR: A method of solving a fuzzy multi-objective structural optimization problem using ordinary single- objective programming techniques is presented.
Abstract: It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.
TL;DR: A new method for the fitting of differentiable fuzzy model functions to crisp data by restricting them to sets which depend on a fuzzy parameter vector and assuming that the vector has a conical membership function.
TL;DR: The main idea is to consider a fuzzy subset of an images as the nested family of its level-cuts, interpret this family as a body of evidence in the sense of Shafer, and any intrinsic parameter can be calculated as a mathematical expectation based on a probability density function.
TL;DR: The extensions of Gödel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete.
Abstract: This paper is an attempt to develop the many-valued first-order fuzzy logic. The set of its truth, values is supposed to be either a finite chain or the interval 〈0, 1〉 of reals. These are special cases of a residuated lattice 〈L, ∨, ∧, ⊗, →, 1, 0〉. It has been previously proved that the fuzzy propositional logic based on the same sets of truth values is semantically complete. In this paper the syntax and semantics of the first-order fuzzy logic is developed. Except for the basic connectives and quantifiers, its language may contain also additional n-ary connectives and quantifiers. Many propositions analogous to those in the classical logic are proved. The notion of the fuzzy theory in the first-order fuzzy logic is introduced and its canonical model is constructed. Finally, the extensions of Godel's completeness theorems are proved which confirm that the first-order fuzzy logic is also semantically complete.
TL;DR: For fuzzy sets A and B a new characterization is given for relations A ⊂B and A = B, and some results are obtained in the functions of the fuzzy topological spaces defined by Azad and those are defined here.
TL;DR: The Dedekind-MacNeille completion of a partially ordered L-valued set is established, and specializing this situation to the set of all crisp rational numbers the authors obtain in a unique way the fuzzy Dedeksind real numbers.
Patent•
05 Nov 1987TL;DR: In this article, a fuzzy membership function is represented by electric signals distributed on a plurality of lines, and a fuzzy inference engine for executing a predetermined fuzzy operation among fuzzy membership functions that have been generated.
Abstract: A fuzzy computer basically includes a plurality of fuzzy membership function generator circuits, and a fuzzy inference engine for executing a predetermined fuzzy operation among fuzzy membership functions that have been generated. A fuzzy membership function is represented by electric signals distributed on a plurality of lines.
01 Jan 1987
TL;DR: In applications data used for updating a-priori information are often fuzzy, therefore the resulting fuzzyness of a-posteriori distributions has to be modelled and an analogue of predictive distributions under fuzzyness must be developed.
Abstract: In applications data used for updating a-priori information are often fuzzy. These fuzzy data are usually not described by standard Bayesian inference. Statistical analysis has to take care of this fuzzyness which can be described by fuzzy numbers. Therefore the resulting fuzzyness of a-posteriori distributions has to be modelled and an analogue of predictive distributions under fuzzyness must be developed. Moreover for a fuzzy observation it is not always possible to decide if it is a member of a certain event. This kind of uncertainty states the following question: Is additivity for the measurement of uncertainty in general valid or a generalization of probability, postulating superadditivity, necessary.
TL;DR: This paper deals with “rationality” as a fuzzy property, by suggesting a definition of “fuzzy opinion” different from the classical fuzzy preference relation, and suggests the possibility of proving the existence of rules with non-complete irrationality.
Abstract: This paper deals with living systems at the individual and group levels. In particular, fuzzy set theory is applied to study Arrow's paradox in aggregation preference problems: such impossibility theorems are based on using the Aristotelian logic; thus Lukasievicz's censure to sciences founded on that logic is also fully applicable. In this paper we deal with “rationality” as a fuzzy property, by suggesting a definition of “fuzzy opinion” different from the classical fuzzy preference relation. Whenever this definition is applied, Arrow's theorems are deemed as results about the impossibility of complete rationality. Nevertheless, the possibility of proving the existence of rules with non-complete irrationality is revealed
TL;DR: In this paper, the authors proposed an interactive fuzzy satisficing method, which takes into consideration the fuzziness in problem formulation as well as that in the judgments of the decision maker (DM) as a human being.
Abstract: The fuzziness induced in the decision making in the actual system in general, comprises fuzziness in the formulation of the problem and that in the judgments of the decision maker (DM) as a human being. This paper proposes an interactive fuzzy satisficing method, which takes into consideration the fuzziness in problem formulation as well as that in the judgments of DM. The multiobjective nonlinear programming problem containing fuzzy parameters is transformed into the α -multiobjective nonlinear programming problem. After determining the fuzzy goal of DM for each objective function by eliciting the membership function, the following reference values are set: the fuzziness index α of DM for the fuzzy parameter; and the reference membership values, which are reference for the membership functions. For the specified α and the reference membership values, the corresponding augmented minimax problem is solved, and DM is supplied with the α-Pareto optimal, together with the trade-off ratios among membership functions and the trade-off ratios between α and the membership functions. Obtaining the result, the DM takes the information concerning current α-Pareto optimal solution and the trade-off ratios into consideration, and respond by updating the reference membership values and the value of α if necessary. In this way the satisficing solution finally is derived for DM, thereby ensuring the α-Pareto optimality. This is the proposed interactive fuzzy satisficing method. The interactive process is demonstrated for a numerical example by the interactive computer program.
TL;DR: The present note defines a projection operator that should be used along with the multiplicative conjunction in the process of fuzzy reasoning and shows that the perimeter, diameter, and height fit more comfortably with the notion of area.
TL;DR: It is shown that a sum or mean of independent fuzzy random variables converges in the limit to a fuzzy Gaussian random variable, thus providing a fuzzy analogue of the central limit theorem of classical probability theory.