Showing papers on "Membership function published in 1988"

Fuzzy Sets, Uncertainty and Information

Abstract: (1990). Fuzzy Sets, Uncertainty, and Information. Journal of the Operational Research Society: Vol. 41, No. 9, pp. 884-886.

Comparison of fuzzy numbers based on the probability measure of fuzzy events

Abstract: Most approaches for ranking fuzzy numbers proposed in the literature are based on fuzzy sets theory only, and suffer from lack of discrimination and occasionally conflict with intuition. It is true that fuzzy numbers are frequently partial order and cannot be compared. However,this does not alleviate the need for comparison in practical applications. In this paper the order of fuzzy numbers are determined based on the concept of probability measure of fuzzy events due to Zadeh. It considers both the mean and dispersion of alternatives and gives two groups of indices based on the uniform and the proportional probability distributions. The approach is also extended to the comparison of random fuzzy numbers by means of a mean fuzzy number. It is shown that several comparison indices in the literature can be obtained based on the probability present measure approach. Finally some typical examples are used to compare the various different approaches. The different interpretations of the dispersion index under different physical situations are emphasized.

Fuzzy Petri nets for rule-based decisionmaking

Abstract: The technique of fuzzy reasoning by transformations of fuzzy truth state vectors by fuzzy matrices is extended to Petri nets. The result is a novel type of neural network in which the transition bars serve as the neutrons, and the nodes are conditions. Conditions may be conjuncted and disjuncted in a natural way to allow the firing of the neurons. The neuron fires to feed the implication truths into one or more consequent conditions when the MIN of the truth values of the antecedent conditions is greater than the neuron threshold. Disjunctions are also modeled in a natural way. Modifications are made to the usual Petri model to allow fuzzy rule-based reasoning by propositional logic. First, fuzzy values are allowed for rules and truths of conditions that appear in rules. Next, multiple copies, rather than the original, of the fuzzy truth tokens are passed along all arrows that depart a node or transition bar where the truth resides. An algorithm is presented for reasoning using these networks, as well as a simple example for exercising the algorithm. Abduction may be done analogously be reversing all arrows and propagating truth tokens backwards. >

A new approach to handling fuzzy decision-making problems

Abstract: New techniques for handling fuzzy decision-making problems are introduced. Fuzzy production rules and fuzzy set theory are used for knowledge representation. In a classical production rule, the rule is executed if the pattern of its antecedent portion D/sub i/ perfectly matches the pattern of a set M of manifestations. However, in a fuzzy production rule, the rule is executed if the degree of matching is not less than a certain matching threshold value. By using a vector representation method, the antecedent portion of the fuzzy production rule and the set of manifestations can be represented by vectors of values and features, respectively. Then, a matching function can be used to measure the degree of similarity between the vectors, and the strength of confirmation calculation method can be used on the consequence d/sub i/ caused by M. An efficient algorithm to generate the maximum fuzzy cover of M to help the decision-maker make his decisions is proposed. >

Neighborhood systems and relational databases

Abstract: Queries in database can be classified roughly into two types: specific targets and fuzzy targets. Many queries are in effect fuzzy targets, however, because of lacking the supports, the user has been emulating them with specific targets by retiring a query repeatedly with minor changes. In this paper, we augment the relational database, with neighborhood systems, so the database can answer a fuzzy query. There have been many works to combine relational databases and fuzzy theory. Bucklles and Petry replaced attributes values by sets of values. Zemankova-Leech, Kandel, and Zviell used fuzzy logic. The formalism of present work is quite general, it allows numerical or nonnumerical measurements of fuzziness in relational databases. The fuzzy theory present here is quite different from the usual theory. Our basic assumption here is that: the data are not fuzzy, the queries are.Motro [Motr86] introduced the notion of distance into the relational databases. From that he can, then, define the notion of “close-ness” and develop goal queries. Though “distance” is a useful concept, yet very often the quantification of it is meaningless or extremely difficult. For example, “very close”, “very far” are meaningful concept of distance, yet there is no practical way to quantity them for all occasions. Our approach here is more direct, we define directly the meaning of “very close neighborhood”. Using the concept of neighborhoods is not very original, in fact, in the theory of topological spaces [Dugu66], mathematician has been using the “neighborhood system” to study the phenomena of “close-ness”. In the territory of fuzzy queries, the notion of “neighborhood” captures the essence of the qualitative information of “close-ness” better than the brute-force-quantified information (distance). A “fuzzy” neighborhood is a qualitative measure of fuzziness.On the surface, it seems a very complicated procedure to define a neighborhood for each value in the attribute. In fact, if we use the characteristic function (membership function) to define a subset, then the defining procedure is merely another type of distance function (non-measure distance or symbolic distance). Now, to define the neighborhood system one can simply re-entered the third column of the relation with linguistic values: “very close”, “close”, “far”. Note that there is a “greater than” relation among these linguistic values. In mathematical terms, they forms a lattice [Jaco60]. For technical reason, we require the values in third column be elements of a lattice. Note that real number is a lattice, so we get Motro's results back.

Spatial classification using fuzzy membership models

Abstract: In the usual statistical approach to spatial classification, it is assumed that each pixel belongs to precisely one of a small number of known groups. This framework is extended to include mixed-pixel data; then, only a proportion of each pixel belongs to each group. Two models based on multivariate Gaussian random fields are proposed to model this fuzzy membership process. The problems of predicting the group membership and estimating the parameters are discussed. Some simulations are presented to study the properties of this approach, and an example is given using Landsat remote-sensing data. >

Combining Fuzzy Imprecision With Probabilistic Uncertainty in Decision Making

Abstract: Essay on the history of the development of many-valued logics and some related topics.- 1. Introductory Sections.- Uncertainty aversion and separated effects in decision making under uncertainty.- Essentials of decision making under generalized uncertainty.- Decision evaluation methods under uncertainty and imprecision.- 2. Basic Theoretical Issues.- Fuzzy random variables.- Fuzzy P-measures and their application in decision making.- Theory and applications of fuzzy statistics.- Confidence intervals for the parameters of a linguistic random variable.- On combining uncertainty measures.- On the combination of vague evidence of the probabilistic origin.- Fuzzy evaluation of communicators.- Uncertain associational relations: compatibility and transition relations in reasoning.- 3. Fuzzy Sets Involving Random Aspects.- Stochastic fuzzy sets: a survey.- Probabilistic sets - a survey.- 4. Decision - Making - Related Models Involving Fuzziness and Randomness.- Decision making based on fuzzy stochastic and statistical dominance.- Decision making in a probabilistic fuzzy environment.- Randomness and fuzziness in a linear programming problem.- Comparison of methodologies for multicriteria feasibility -constrained fuzzy and multiple - objective stochastic linear programming.- Fuzzy dynamic programming with stochastic systems.- Probabilistic - possibilistic approach to some statistical problems with fuzzy experimental observations.- Estimation of life-time with fuzzy prior information: application in reliability.- Questionnaires with fuzzy and probabilistic elements.- From fuzzy data to a single action - a simulation approach.- 5. Applications.- Probabilistic sets in classification and pattern recognition.- Fuzzy optimization of radiation protection and nuclear safety.- Application of fuzzy statistical decision making in countermeasures against great earthquakes.- From an oriental market to the European monetary system: some fuzzy - sers - related ideas.

Imprecise (fuzzy) information in geostatistics

Abstract: A methodology based on fuzzy set theory for the utilization of imprecise data in geostatistics is presented. A common problem preventing a broader use of geostatistics has been the insufficient amount of accurate measurement data. In certain cases, additional but uncertain (soft) information is available and can be encoded as subjective probabilities, and then the soft kriging method can be applied (Journel, 1986). In other cases, a fuzzy encoding of soft information may be more realistic and simplify the numerical calculations. Imprecise (fuzzy) spatial information on the possible variogram is integrated into a single variogram which is used in a fuzzy kriging procedure. The overall uncertainty of prediction is represented by the estimation variance and the calculated membership function for each kriged point. The methodology is applied to the permeability prediction of a soil liner for hazardous waste containment. The available number of hard measurement data (20) was not enough for a classical geostatistical analysis. An additional 20 soft data made it possible to prepare kriged contour maps using the fuzzy geostatistical procedure.

Fuzzy sets in psychology

Abstract: Possibility Theory, Fuzzy Logic, and Psychological Explanation (M. Smithson). Quantifiers as Fuzzy Concepts (S.E. Newstead). A Common Framework for Colloquial Quantifiers and Probability Terms (A.C. Zimmer). An Empirical Study of the Integration of Linguistic Probabilities (R. Zwick, D.V. Budescu, T.S. Wallsten). A Fuzzy Propositional Account of Contextual Effects on Word Recognition (J. Rueckl). M-Fuzziness in Brain/Mind Modeling (G. Fuhrmann). The Weighted Fuzzy Expected Value as an Activation Function for the Parallel Distributed Processing Models (D. Kuncicky, A. Kandel). Fuzzy Logic with Linguistic Quantifiers: A Tool for Better Modeling of Human Evidence Aggregation processes? (J. Kacprzyk). Origins, Structure, and Function of Fuzzy Belief (G. Greco, A.F. Rocha). Acquisition of Membership Functions in Mental Workload Experiments (I.B. Turksen, N. Moray, E. Krushelnycky). A Fuzzy Set Model of Learning Disability: Identification from Clinical Data (J.M. Horvath). Towards a Fuzzy Theory of Behaviour Management (V.B. Cervin, J.C. Cervin). Practical Applications and Psychometric Evaluation of a Computerized Fuzzy Graphic Rating (B. Hesketh et al.). Indexes.

An event based fuzzy temporal logic

Abstract: A temporal logic is developed to deal with events that are uncertain with regard to their occurrence in a given interval of time. Events are represented as fuzzy sets with the membership function giving the possibility of occurrence of the event in a given interval of time. An axiomatization of the fuzzy event calculus is presented, and several of its properties are proved. The logic is simple but powerful; it can determine effectively the various temporal relations between uncertain events or their combinations. >

A new approach to inference in approximate reasoning and its application to computer vision

Abstract: We introduce a new approach to inference in approximate reasoning based on truth value restriction. The degree to which the actual given value A of a variable X agrees with the antecedent value B in a production "If X is B then Y is C" is represented as a fuzzy subset of a truth space. We introduce a new form of implication based on the exponential operation. A new compatibility relation based on the input value A and the antecedent value B is defined. A fuzzy truth value true derived from the antecedent value B is also defined. It is shown that by mapping this compatibility relation into the truth space, a fuzzy truth value is generated which produces an exponential family of the fuzzy truth value true. We show that the inferred consequent can be generated from this truth value. Theoretical results showing the validity of this method to (1) chain rules consisting of several single fuzzy conditional propositions, and (2) conjunctive fuzzy conditional propositions, are also presented. Theoretical results demonstrate that our method is superior to the existing methods under several criteria including modus ponens and modus tollens. We also introduce several approaches based on the above methodology for evaluating the degree of match between the set of conditions occurring in the antecedents of a fuzzy production rule and the input data, and for combining evidence coming from different pieces of knowledge. A fuzzy rule-based production system employing the above methodology is developed and tested in temporal and multisensor target detection and recognition. The application involves the use of temporal sequences of forward looking infrared (FLIR) and TV images. The system consists of the three phases: (1) prescreening, (2) scene recognition, (3) contextual knowledge-based validation. In all cases, new methods for automatically generating the linguistic values from the image data are described.

Plasticity Theory Based on Fuzzy Sets

Abstract: This paper presents a general theory that describes the cyclic loading behavior of different materials. It is mathematically based on the theory of fuzzy sets. From the constitutive modeling point of view it is closely related to many previous cyclic plasticity models. Instead of utilizing two or more yield or bounding surfaces one more general surface is introduced in the space spanned by the stress and a membership function. This concept allows us to define many different models within the same mathematical framework. Several possibilities of the theory are examined with the aid of one-dimensional examples. The paper considers constitutive models with and without memory, as well as models with fading memory, with isotropic and kinematic hardening, as well as without hardening. The fuzzy-sets formulation describes different phenomena during cyclic loading such as hysteresis loops, cyclic stabilization effects, smooth elastic-plastic transition, and so on, which are illustrated with pertinent examples.

Speed change controller for automatic transmission

Abstract: PURPOSE:To carry out speed change conformable to the intension of a driver by making fuzzy reasoning based on signals indicating vehicle speed, acceleration, engine load, variation rates thereof and running resistance, then determining a gear position. CONSTITUTION:Operating condition signals of a vehicle detected through means for detecting vehicle speed, engine load, variation rate of engine load and running resistance are provided to a speed change ratio determining means. The speed change ratio determining means makes fuzzy reasoning based on a membership function of a fuzzy set preset by a membership function setting means and determines a specific speed change ratio. A speed change actuator is driven through a drive means based on the determined speed change ratio so as to carry out specific speed change. Consequently, the vehicle can be operated through fuzzy control with such speed change ratio as can be obtained through human judged operation.

Fuzzy sets and t -norms in the light of fuzzy logic

Abstract: The paper is a discussion of the many-valued fuzzy logic, which is syntactico-semantically complete and its impact on the fuzzy set theory, namely on the operations with fuzzy sets. Arguments that all the operations with membership grades must fulfil the so called fitting condition are given. It follows that general t -norms are not suitable to be basis of the operations with fuzzy sets. Some general classes of operations with membership grades are presented.

Controller for automatic transmission

Abstract: PURPOSE: To carry out the control similar to the operation of an expert driver by determining the speed change gear stage by carrying out the fuzzy estimation from the operation state detection values, estimation values including the change of the excessive driving power, and a set membership function. CONSTITUTION: A controller 60 for an automatic transmission detects the operation stages including the engine revolution speed, throttle opening degree and opening speed, car speed and accelerating speed, and the road tilt angle, and estimates the operation states including the change of the operation states and the excess driving power which is obtained from the traveling resistance due to the road surface tilt angle for all the gear stages permitting speed change from the stage at present. A membership function in a fuzzy collection is previously set for the change of the detected operation states and the estimated operation states, and the speed change gear stage is determined by carrying out the fuzzy estimation from the detection values and the estimated values, and the solenoids 36 and 38 of a shift valve are driven, and the speed change stage of a speed change mechanism is controlled. Therefore, the judgement operation similar to the speed change judgement and operation which an expert driver carries out can be realized during control. COPYRIGHT: (C)1990,JPO&Japio

Fuzzy Dynamic Programming with Stochastic Systems

Abstract: Multistage decision making in a fuzzy environment (fuzzy constraints, fuzzy goals and fuzzy decisions) is considered. As a tool for solving these problems, fuzzy dynamic programming for the case of a deterministic and fuzzy system under control is provided. Then, the case of a stochastic system under control is discussed in detail. Two formulations are shown: first, the classic one due to Bellman and Zadeh (1970) in which an optimal sequence of controls is sought to maximize the probability of attainment of a fuzzy goal subject to fuzzy constraints, and second, an alternative one due to Kacprzyk and Staniewski (1980) in which an optimal sequence of controls is sought to maximize the expected value of the fuzzy decision.