Showing papers on "Fuzzy number published in 1990"
01 Apr 1990
TL;DR: The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined and several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated.
Abstract: For pt.I see ibid., vol.20, no.2, p.404-18, 1990. The basic aspects of the FLC (fuzzy logic controller) decision-making logic are examined. Several issues, including the definitions of a fuzzy implication, compositional operators, the interpretations of the sentence connectives 'and' and 'also', and fuzzy inference mechanisms, are investigated. Defuzzification strategies, are discussed. Some of the representative applications of the FLC, from laboratory level to industrial process control, are briefly reported. Some unsolved problems are described, and further challenges in this field are discussed. >
5,502 citations
TL;DR: It is argued that both notions of a rough set and a fuzzy set aim to different purposes, and it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems.
Abstract: The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribut...
2,452 citations
TL;DR: A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy productionrule describes the fuzzy relation between two propositions and an efficient algorithm is proposed to perform fuzzy reasoning automatically.
Abstract: A fuzzy Petri net model (FPN) is presented to represent the fuzzy production rule of a rule-based system in which a fuzzy production rule describes the fuzzy relation between two propositions. Based on the fuzzy Petri net model, an efficient algorithm is proposed to perform fuzzy reasoning automatically. It can determine whether an antecedent-consequence relationship exists from proposition d/sub s/ to proposition d/sub j/, where d/sub s/ not=d/sub j/. If the degree of truth of proposition d/sub s/ is given, then the degrees of truth of proposition d/sub j/ can be evaluated. The formal description of the model and the fuzzy reasoning algorithm are shown in detail. The upper bound of the time complexity of the fuzzy reasoning algorithm is O(nm), where n is the number of places and m is the number of transitions. Its execution time is proportional to the number of nodes in a sprouting tree generated by the algorithm only generates necessary reasoning paths from a starting place to a goal place, it can be executed very efficiently. >
534 citations
TL;DR: It is proved theoretically that such a fuzzy controller, the smallest possible, with two inputs and a nonlinear defuzzification algorithm is equivalent to a nonfuzzy nonlinear proportional-integral (PI) controller with proportional-gain and integral-gain changing with error and rate change of error about a setpoint.
476 citations
TL;DR: A new geometric proof of the Subsethood Theorem is given, a corollary of which is that the apparently probabilistic relative frequency nA /N turns out to be the deterministic subsethood S(X, A), the degree to which the sample space X is contained in its subset A.
Abstract: Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets-as-points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hypercube and a nonfuzzy set with a vertex of the cube. Paradoxes of two-valued logic and set theory, such as Russell's paradox, correspond to the midpoint of the fuzzy cube. The fundamental questions of fuzzy theory—How fuzzy is a fuzzy set? How much is one fuzzy set a subset of another?—are answered geometrically with the Fuzzy Entropy Theorem, the Fuzzy Subsethood Theorem, and the Entropy-Subsethood Theorem. A new geometric proof of the Subsethood Theorem is given, a corollary of which is that the apparently probabilistic relative frequency nA /N turns out to be the deterministic subsethood S(X, A), the degree to which the sample space X is contained in its subset A. So the frequency of successful trials is viewed as the degree to which all trials are successful. Recent Bayesian polemics against fuzzy ...
413 citations
TL;DR: Using standard approximations for the membership functions, n-ary possibilistic and , or and neg operators are derived allowing a straightforward evaluation of the frequencies of hazard events in complex systems, simultaneously with their tolerances.
383 citations
TL;DR: A state-of-the-art of methodology and algorithms of fuzzy sets in the field of pattern recognition and clustering techniques are discussed and a problem of cluster validity expressed in terms of clustering indices is addressed.
354 citations
01 Nov 1990
TL;DR: This book discusses fuzzy logic with linguistic quantifiers in multiobjective decision making and optimization, a step towards more human-consistent models, and Stochastic Versus Fuzzy Approaches and Related Issues.
Abstract: I. The General Framework.- 1. Multiobjective programming under uncertainty : scope and goals of the book.- 2. Multiobjective programming : basic concepts and approaches.- 3. Stochastic programming : numerical solution techniques by semi-stochastic approximation methods.- 4. Fuzzy programming : a survey of recent developments.- II. The Stochastic Approach.- 1. Overview of different approaches for solving stochastic programming problems with multiple objective functions.- 2. "STRANGE" : an interactive method for multiobjective stochastic linear programming, and "STRANGE-MOMIX" : its extension to integer variables.- 3. Application of STRANGE to energy studies.- 4. Multiobjective stochastic linear programming with incomplete information : a general methodology.- 5. Computation of efficient solutions of stochastic optimization problems with applications to regression and scenario analysis.- III. The Fuzzy Approach.- 1. Interactive decision-making for multiobjective programming problems with fuzzy parameters.- 2. A possibilistic approach for multiobjective programming problems. Efficiency of solutions.- 3. "FLIP" : an interactive method for multiobjective linear programming with fuzzy coefficients.- 4. Application of "FLIP" method to farm structure optimization under uncertainty.- 5. "FULPAL" : an interactive method for solving (multiobjective) fuzzy linear programming problems.- 6. Multiple objective linear programming problems in the presence of fuzzy coefficients.- 7. Inequality constraints between fuzzy numbers and their use in mathematical programming.- 8. Using fuzzy logic with linguistic quantifiers in multiobjective decision making and optimization: A step towards more human-consistent models.- IV. Stochastic Versus Fuzzy Approaches and Related Issues.- 1. Stochastic versus possibilistic multiobjective programming.- 2. A comparison study of "STRANGE" and "FLIP".- 3. Multiobjective mathematical programming with inexact data.
291 citations
TL;DR: A new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0, 1] reflecting the decision maker's risk taking attitude is suggested.
262 citations
01 Jan 1990
TL;DR: This book discusses decision Making under Fuzziness, Fuzzy Games, and an approach to Customized End-User Views in Multi-User Information Retrieval Systems.
Abstract: 1. Introductory Sections.- Multiperson Decision Making: a Selective Review.- Fuzzy Set Theory as a Theory of Vagueness.- Vague Notions in the Theory of Voting.- 2. General Issues Related to Decision Making under Fuzziness.- Aggregation of Possibility Measures.- Modelling Valued Preference Relations.- Revealed Fuzzy Preferences.- Categories of Fuzzy Relations in Decision Making.- Determination and Interpretation of the Fuzzy Utility of an Act in an Uncertain Environment.- Extending Aggregation Operators for Multicriteria Decision Making.- Ranking Alternatives by Weak Transitivity Relations.- Calculating the Mean Knowledge Representation from Multiple Experts.- An Approach to Customized End-User Views in Multi-User Information Retrieval Systems.- 3. Group Decision Making under Fuzziness.- Means and Social Welfare Functions in Fuzzy Binary Relation Spaces.- Aggregation of Fuzzy Preferences.- Single - Peakedness in Weighted Aggregation of Fuzzy Opinions in a Fuzzy Group.- On Group Decision Making under Fuzzy Preferences.- Group Decision Making with Fuzzy and Non-Fuzzy Evaluations.- On Construction of the Fuzzy Multiattribute Risk Function for Group Decision Making.- Consensus Measures for Qualitative Order Relations.- On a Consensus Measure in a Group MCDM Problem.- Voting Procedures with a priori Incomplete Individual Profiles.- 4. Team Decision Making under Fuzziness.- A Team Decision Making Model for Distributed Problem Solving.- Evidential Teams.- 5. Fuzzy Games.- Fuzzy Goals and Sets of Choices in Two-Person Games.- Playing Matrix Games Defined by Linguistic Labels.- Fuzzy Convexity and Peripherial Core of an Exchange Economy Represented as a Fuzzy Game.- Fuzzy Sequencing Games.
TL;DR: In this paper, necessary and sufficient conditions for some linear and quadratic equations to have a solution when the parameters are either real or complex fuzzy numbers are presented, and applications in chemistry, economics, finance and physics are presented for these types of equations.
TL;DR: In this article, the extension principle is used to find Y = f( X 1,…, X n ) when we subtitute fuzzy numbers X i for the xi, 1⩽i ⩽n.
05 Dec 1990
TL;DR: It is shown that the direct method of Lyapunov can be used to determine sufficient conditions for global stability of a broad class of fuzzy control schemes and a measure of robustness is proposed that can be use to evaluate and possibly redesign a given fuzzy control system so as to enhance the range of its stable operation.
Abstract: A new approach to the stability analysis of fuzzy linguistic control (FLC) systems is presented. Specifically, it is shown that the direct method of Lyapunov can be used to determine sufficient conditions for global stability of a broad class of fuzzy control schemes. Moreover, a measure of robustness is proposed that can be used to evaluate and possibly redesign a given fuzzy control system so as to enhance the range of its stable operation. Finally, the application of the proposed methodology is shown and its implications in terms of control design are demonstrated by means of numeric examples. >
TL;DR: It is showed that the problem of fuzzy regression can be formulated as a mathematical programming problem and the special case of linear regression yields a linear programming problem.
TL;DR: The present paper is intended to emphasize and explore the possibility of the use of such a theory to develop a methodology which is computationally simple and easy to use in the quantitative assessment of failure probability of catastrophic events in PSA, particularly, in level-I studies.
TL;DR: Following some general-purpose theorems about operations on fuzzy quantities, conditions are provided for a consistent fuzzy extension of present and future value, both with one and several capitals.
TL;DR: The general ranking function approach is interpreted as a ranking process using a mean value and an interval relation, and a more general mean value for a fuzzy number is defined.
TL;DR: It is obtained that the lattice of fuzzy ideals is isomorphic to the lattices of fuzzy congruence on a generalized Boolean algebra and the products of fuzzy ideal are considered.
TL;DR: A formal approach to a differential inclusion with a fuzzy right-hand side is introduced, in accordance with the theory of fuzzy sets (FS), and a new formalism for differential systems with fuzzy unknown parameters is proposed.
TL;DR: It is found that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty in design, and that probability is best used to represent stochastic uncertainty.
Abstract: A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [25]. An analogous approach to representing and manipulatinguncertainty in choosing among alternatives (design imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. Examples using both approaches are presented, where the examples represent a progression from simple operations to more complex design equations. Results of the fuzzy sets and probability methods for the examples are shown graphically. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty in design, and that probability is best used to represent stochastic uncertainty.
TL;DR: In a new interactive fuzzy satisficing method for multiobjective linear programming problems with fuzzy parameters, the satisficing solution of the decision maker is derived efficiently from among M-α-Pareto optimal solutions.
TL;DR: Algorithms have been proposed which enable us to modify the original equation in a way leading to its genuine solution or at least an approximate one and distortion of the fuzzy set Y forms a cornerstone of the proposed procedures.
03 Dec 1990
TL;DR: Fuzzy set theory is applied to solve the problem of traffic assignment between two alternative routes on a highway network, where the driver's perceived travel time on each route is treated as a fuzzy number and his choice of route is based on an approximate reasoning model.
Abstract: Fuzzy set theory is applied to solve the problem of traffic assignment between two alternative routes on a highway network. The driver's perceived travel time on each route is treated as a fuzzy number, and his choice of route is based on an approximate reasoning model. The model consists of rules which indicate the degree of preference for each route given the approximate travel time of the two routes. Applying the model to each driver and then aggregating the individual preferences, a fuzzy network loading algorithm assigns traffic to each route. >
01 Feb 1990
TL;DR: High-performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of a spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics.
Abstract: The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. In this paper, high-performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of a spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.
TL;DR: A methodology for kriging with imprecise variogram parameters is developed and both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions.
Abstract: Imprecise variogram parameters are modeled with fuzzy set theory. The fit of a variogram model to experimental variograms is often subjective. The “accuracy” of the fit is modeled with imprecise variogram parameters. Measurement data often are insufficient to create “good” experimental variograms. In this case, prior knowledge and experience can contribute to determination of the variogram model parameters. A methodology for kriging with imprecise variogram parameters is developed. Both kriged values and estimation variances are calculated as fuzzy numbers and characterized by their membership functions. Besides estimation variance, the membership functions are used to create another uncertainty measure. This measure depends on both homogeneity and configuration of the data.
Journal Article•
TL;DR: This is the first part of the extensive paper which presents the syntax and semantics of first-order fuzzy logic, and introduces the structure of truth values and some main properties of its.
Abstract: This is the first part of the extensive paper which presents the syntax and semantics of first-order fuzzy logic. We introduce the structure of truth values and present some main properties of its. Then the language of first-order fuzzy logic and its syntax and semantics are defined, and proved many theorems demonstrating their good properties. The concept of a fuzzy theory is defined and the main properties of fuzzy theories are presented including the problem of their consistency and completeness
TL;DR: In this paper, triangular and trapezoidal fuzzy numbers are used to represent vague job processing times in job shop production systems, and the job sequencing algorithms of Johnson and Ignall and Schrage are modified to accept fuzzy job processing time.
Abstract: In practice, processing times can be more accurately represented as intervals with the most probable completion time somewhere near the middle of the interval. A fuzzy number which is essentially a generalized interval can represent this processing time interval exactly and naturally. In this work, triangular and trapezoidal fuzzy numbers are used to represent those vague job processing times in job shop production systems. The job sequencing algorithms of Johnson and Ignall and Schrage are modified to accept fuzzy job processing times. Fuzzy makespans and fuzzy mean flow times are then calculated for greater decision-making information. Numerous examples are used to illustrate the approach.
TL;DR: This paper evaluates the methd based on matrix of pairwise comparisons and eigenvalue theory by using a forward error analysis approach with the assumption that the true membership values in a fuzzy set are continuous in the interval (0, 1).
TL;DR: This result is used to extend Leontief's closed input-output analysis to fuzzy economies and obtain a fuzzy model of the world's economy.