Showing papers on "Fuzzy associative matrix published in 1989"
TL;DR: The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation and describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference.
Abstract: The author presents a summary of the basic concepts and techniques underlying the application of fuzzy logic to knowledge representation. He then describes a number of examples relating to its use as a computational system for dealing with uncertainty and imprecision in the context of knowledge, meaning, and inference. It is noted that one of the basic aims of fuzzy logic is to provide a computational framework for knowledge representation and inference in an environment of uncertainty and imprecision. In such environments, fuzzy logic is effective when the solutions need not be precise and/or it is acceptable for a conclusion to have a dispositional rather than categorical validity. The importance of fuzzy logic derives from the fact that there are many real-world applications which fit these conditions, especially in the realm of knowledge-based systems for decision-making and control. >
532 citations
TL;DR: Three formulations of possibilistic linear regression analysis are proposed here to deal with fuzzy data to be able to obtain easily fuzzy parameters in possibillistic linear models and to add other constraint conditions which might be obtained from expert knowledge of fuzzy parameters.
348 citations
TL;DR: In this article, the authors considered linear programming problems with fuzzy constraints and fuzzy coefficients in both matrix and right hand side of the constraint set are considered, and the diversity of such methods provides a lot of different models from which fuzzy solutions to the former problem can be obtained.
240 citations
TL;DR: A zero-sum two-person game with imprecise values in its matrix of payoffs is considered and a method for its solution based on the establishment of a Fuzzy Linear Programming problem for each player is proposed.
220 citations
TL;DR: It is shown that every fuzzy group can be imbedded in a fuzzy group of the group of automorphisms of some fuzzy graph.
141 citations
01 Jul 1989
TL;DR: An approach is presented for analyzing the global behavior of a fuzzy dynamical system that applies the concept and method of cell-to-cell mapping to obtain the evolving trend of the states of a fuzzier system.
Abstract: An approach is presented for analyzing the global behavior of a fuzzy dynamical system that applies the concept and method of cell-to-cell mapping to obtain the evolving trend of the states of a fuzzy dynamical system. The behavior of the fuzzy system is characterized by equilibria, periodic motions, and their domain of attractions. Min-max operation accumulates the fuzziness of a fuzzy system in every step of iterations and makes the state evolution obscure. The proposed method transforms a given fuzzy mapping to at Z-to-Z mapping and does not accumulate fuzziness. Both the real and fuzzy initial state response analyses are discussed. An inverted pendulum controlled by a fuzzy controller is analyzed to illustrate the validity of the method. >
105 citations
TL;DR: The linear fuzzy controller is precisely equivalent to a linear non-fuzzy PI controller if mixed fuzzy logic is used to evaluate the control rules, when the fuzzy logics used are selected with due regard to prior associations implied by the control rule operands themselves.
103 citations
01 Sep 1989
TL;DR: A truth table for a J-K flip-flop is fuzzified, extending binary NOT, AND, and OR operations to fuzzy negation, t-norm and s-norm, respectively, and two types of fundamental characteristic equations of the fuzzy flip-Flop are introduced: the reset- and the set-type equations.
Abstract: The authors propose and define a fuzzy flip-flop that is an extended form of an ordinary binary flip-flop, specifically, a J-K flip-flop. A truth table for a J-K flip-flop is fuzzified, extending binary NOT, AND, and OR operations to fuzzy negation, t-norm and s-norm, respectively. Two types of fundamental characteristic equations of the fuzzy flip-flop are introduced: the reset- and the set-type equations, both of which are fuzzy extensions of a characteristic equation of a J-K flip-flop. Their characteristics are demonstrated graphically, especially in the case in which fuzzy negation, t-norm and s-norm relate to complementation, min, and max operations, respectively. Other fundamental fuzzy operations are examined, and their characteristics are demonstrated graphically. Both of the above types are unified in the case of complementation, min, and max operations, and a fundamental characteristic equation for a min-max-type fuzzy flip-flop negation, t-norm and s-norm gates is proposed. A circuit is presented and tested. >
82 citations
TL;DR: This paper introduces fuzziness into the resolution principle and unification and cause fuzzy logical inference to be significant in Fuzzy Prolog when the values of all variables are taken in the closed interval.
68 citations
25 May 1989
TL;DR: Novel fuzzy microprocessors are described, which achieve fuzzy inference with deterministic input and output signals, and will rapidly permeate the industry.
Abstract: /uatnad Novel fuzzy microprocessors are described, which achieve fuzzy inference with deterministic input and output signals. These two kinds of fuzzy microprocessors are useful for constructing sophisticated fuzzy logic controller. One is a rule chip and the other is a defuzzifier chip. The former is in the monolithic form and the latter is in hybrid structure. These fuzzy microprocessors will rapidly permeate the industry.
43 citations
TL;DR: The problem of stability (with respect to changes of centres of fuzzy parameters) of the solution in Fuzzy Linear Programming problems with symmetrical triangular fuzzy numbers and extended operations and inequalities is focused on.
TL;DR: The pattern fuzzy logic described by a fuzzy logic function in disjunctive or conjunctive normal form can be easily realized in a two-stage optica system by programming the lens-arrays and the thresholding devices.
TL;DR: It has been demonstrated that the introduction of fuzzy concepts into expert systesms is not feasible but highly desirable and the additional power and advantages over traditional expert systems are illustrated.
Abstract: Much of the information resident in the knowledge base of a typical expert system is imprecise, incomplete or not totally reliable. The special features of a novel expert system shell based on fuzzy logic and numbers are presented. This rule-based system can deal with exact, inexact (fuzzy) and combined reasoning as well as uncertainty represented by fuzzy numbers. Natural language interface is built in naturally using fuzzy logic representation. Several application areas, namely, classification, risk analysis and information retrieval, are discussed with four appropriate sample expert systems actually built using this shell. Through these expert systems, the additional power and advantages over traditional expert systems are illustrated. It has been demonstrated that the introduction of fuzzy concepts into expert systesms is not feasible but highly desirable.
TL;DR: This paper generalizes Leontief's celebrated input-output analysis to incorporate fuzzy numbers and develops a fuzzier version of LaSalle's inequality model.
TL;DR: Some weaker forms of fuzzy continuous and fuzzy open maps between fuzzy topological spaces are studied, along with the introduction and investigations of a new class of non-fuzzy continuous maps.
01 Dec 1989
TL;DR: A fuzzy expert database system which is an integration of a fuzzy expert system building tool called SYSTEM Z-II and a database management system called Rdb/VMS, able to extract fuzzy data and terms stored in a database and used in the fuzzy reasoning in an expert system.
Abstract: Fuzzy concepts always exist in much of human reasoning as well as decision making. This paper presents a fuzzy expert database system which is an integration of a fuzzy expert system building tool called SYSTEM Z-II and a database management system called Rdb/VMS. This system is able to extract fuzzy data and terms stored in a database and used in the fuzzy reasoning in an expert system. It can also retrieve information by fuzzy database-queries which are generated by the expert system automatically. Many expert systems in different domain areas such as decision making can be constructed. Sample applications are described to demonstrate the flexibility and power of this system. The fuzzy query language defined and used in the system can also be used independently as a fuzzy enquiry tool in database applications.
01 Jan 1989
TL;DR: Two approaches for the formulation of information through fuzzy associations are presented and a fuzzy association is introduced as a fuzzy relation defined on a set of indices to a database.
Abstract: Two approaches for the formulation of information through fuzzy associations are presented. A fuzzy association is introduced as a fuzzy relation defined on a set of indices to a database. One approach is the extension of fuzzy indices to a database using fuzzy associations. A fuzzy association is a generalization of the concept of fuzzy thesauri. An algorithm for fuzzy information retrieval based on this approach is developed. The other approach represents the retrieval process as a block diagram. Maximum and minimum operations are used instead of the ordinary sum and product operations on the diagram. Studies of advanced indexing, such as the clustering of articles, are represented as feedback on the diagram. Properties of fuzzy information retrieval, such as level fuzzy sets and set operations on responses of the retrieval system, are discussed using the diagram representation. >
TL;DR: The behaviour of Warren's fuzzy boundary in semi-induced fuzzy topological spaces (fts's for short) is explained and the two axioms of semi-induction and structure C hold trivially for crisp fuzzy topologies.
TL;DR: It is shown that restrictions of the induced fuzzy ordering on some special classes of fuzzy numbers are reflexive fuzzy orders.
Patent•
27 Sep 1989TL;DR: In this paper, a fuzzy data communication system includes a first fuzzy computer storing fuzzy functions and rules, a transmitter compiling the fuzzy function and rules stored in the first computer into a message to transmit the message, a receiver receiving the transmitted message to decompile fuzzy functions from the received message, and a second fuzzy computer implementing a fuzzy inference based on the decompiled fuzzy functions.
Abstract: A fuzzy data communication system includes a first fuzzy computer storing fuzzy functions and rules, a transmitter compiling the fuzzy functions and rules stored in the first computer into a message to transmit the message, a receiver receiving the transmitted message to decompile fuzzy functions and rules from the received message, and a second fuzzy computer implementing a fuzzy inference based on the decompiled fuzzy functions and rules.
TL;DR: This paper presents a comprehensive expert system shell which can deal with both exact and inexact reasoning, and a prototype of this proposed shell, code named as Z-IIe, has been implemented successfully.
Abstract: This paper presents a comprehensive expert system shell which can deal with both exact and inexact reasoning. A prototype of this proposed shell, code named as SYSTEM Z-IIe, has been implemented successfully. It is a rule-based system which employs fuzzy logic and numbers for its reasoning. Two basic inexact concepts, fuzziness and uncertainty, are both used and distinct from each other clearly in the system. Moreover, these two concepts have been built into two levels for inexact reasoning, i.e. the level of the rules and facts, and the level of the values of the objects of these rules and facts. Other features of Z-IIe include multiple fuzzy propositions in rules and dual fact input mechanisms. It also allows any combinations of fuzzy and normal terms and uncertainties. Fuzzy numeric comparison logic control is also available for the rules and facts. Its natural language interface which uses English with restricted syntax improves the efficiency of knowledge engineering. Z-IIe is also coupled to a Database Management System for supplying facts from existing databases if appropriate. All these features can be combined to build very powerful expert systems and are illustrated by an example.
TL;DR: A fuzzy logic software development shell is used that allows inclusion of both crisp and fuzzy rules in decision making and process control problems and results are given that compare this type of expert system to a human expert in some specific applications.
TL;DR: F fuzzy fields and fuzzy linear spaces which were initially defined by Nanda are redefined to be more suitable than the earlier.
TL;DR: The vertex method introduced previously for computer processing of fuzzy data is extended to include interactive fuzzy variables to solve three main groups of problems commonly encountered in fuzzy decision analysis.
TL;DR: It is argued that one should use the joint distribution, and not necessarily only the marginals in the extension principle, to perform operations to calculate M + N, M N, and evaluate M ⩽ N , M = N , etc.
14 Nov 1989
TL;DR: The method successfully constructs the rule base for a fuzzy controller, which is usually provided by human experts, and extracts qualitative control rules from the quantitative processes.
Abstract: A method of extracting the control rules for a fuzzy controller is proposed. The method successfully constructs the rule base for a fuzzy controller, which is usually provided by human experts. By using the concepts of cell state space and performance evaluation, an optimization algorithm is able to achieve the proper control of a process. The control rules can then be retrieved from the output of this algorithm. This method extracts qualitative control rules from the quantitative processes. >
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TL;DR: This work considers the problem of assigning to each left R-module the structure of a fuzzy module such that every R-homomorphism becomes a homomorphism of fuzzy modules.
TL;DR: It is shown that every fuzzy neighborhood structure N is given by some fuzzy quasi-uniformity and also N is induced bySome fuzzy uniformity if it is completely regular.
TL;DR: Fast computation formulas for the operation supx,ymin[h, z, ymin] are proved, in case the membership functions h, z of fuzzy numbers and non-fuzzy numbers are ‘triangular’, ‘rectangular‘ and the δ-function of Dirac.