Showing papers on "Fuzzy number published in 1989"
TL;DR: Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied to introduce new results on intuitionism fuzzy sets.
1,238 citations
TL;DR: In this paper, the nonadditivity of Sugeno's fuzzy measures is interpreted in terms of addition and the rationality of the Choquet integral is discussed, and it is pointed out that a fuzzy measure on a set X expresses the interaction between the subsets of X and can be represented by an additive measure.
596 citations
Book•
01 Jan 1989
TL;DR: A survey of fundamental notions fuzzy set theory the model of natural language semantics and linguistic variables fuzzy logic decision and control fuzzy systems fuzzy algorithms and programming languages other applications general problems of fuzzy set theorists are surveyed.
Abstract: Survey of fundamental notions fuzzy set theory the model of natural language semantics and linguistic variables fuzzy logic decision and control fuzzy systems fuzzy algorithms and programming languages other applications general problems of fuzzy set theory.
491 citations
TL;DR: Fuzzy set theory, which is a generalization of Boolean algebra to situations where data are modelled by entities whose attributes have zones of gradual transition, rather than sharp boundaries, offers a useful alternative to existing methodology.
Abstract: SUMMARY
The rigid-data model consisting of discrete, sharply bounded internally uniform entities that is used in hierarchical and relational databases of soil profiles, choropleth soil maps and land evaluation classifications ignores important aspects of reality caused by internal inhomogeneity, short-range spatial variation, measurement error, complexity and imprecision. Considerable loss of information can occur when data that have been classified according to this model are retrieved or combined using the methods of simple Boolean algebra available in most soil and geographical information systems. Fuzzy set theory, which is a generalization of Boolean algebra to situations where data are modelled by entities whose attributes have zones of gradual transition, rather than sharp boundaries, offers a useful alternative to existing methodology. The basic principles of fuzzy sets, operations on fuzzy sets and the derivation of membership functions according to the Semantic Import Model are explained and illustrated with data from case studies in Venezuela and Kenya.
484 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: Some properties of the index are studied, as well as its behaviour on several particular cases, which are related to the relative importance of the different level sets.
335 citations
01 Jul 1989
TL;DR: L.A. Zadeh's (1975) possibility theory is used as a general framework for modeling temporal knowledge pervaded with imprecision or uncertainty, and Deductive patterns of reasoning involving fuzzy and/or uncertain temporal knowledge are established.
Abstract: L.A. Zadeh's (1975) possibility theory is used as a general framework for modeling temporal knowledge pervaded with imprecision or uncertainty. Ill-known dates, time intervals with fuzzy boundaries, fuzzy durations, and uncertain precedence relations between events can be dealt with in this approach. An explicit representation (in terms of possibility distributions) of the available information, which may be neither precise nor certain, is maintained. Deductive patterns of reasoning involving fuzzy and/or uncertain temporal knowledge are established, and the combination of fuzzy partial pieces of information is considered. A scheduled example with fuzzy temporal windows is discussed. >
304 citations
TL;DR: In this paper, the spaces of convergent and bounded sequences of fuzzy numbers have been discussed, and the convergence and bounded spaces of fuzzy sequences have been studied in the context of fuzzy counting.
299 citations
TL;DR: The aim of this paper is to describe the more important problems in fuzzylinear programming and to give a general model of fuzzy linear programming problems involving all of the above ones, and a resolution method for that general model is proposed.
297 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.
TL;DR: It is shown that arithmetic of fuzzy complex numbers may be performed in terms of α-cuts and closure under the basic arithmetic operations is shown.
TL;DR: These works shed new light on various interpretations of fuzzy sets and clarify their links with probability theory; conversely Zadeh's logical point of view on fuzzy sets suggests a set-theoretic perspective on uncertainty measures, that brings together numerical quantification and logic.
TL;DR: The fuzzy real line and its subspaces are illustrated, as well as certain categorical aspects of it, which make up the role and significance of fuzzy topology.
Abstract: CONTENTS Introduction ??0. Preliminaries: fuzzy sets ??1. Fuzzy topological spaces: the basic categories of fuzzy topology ??2. Fundamental interrelations between the category Top of topological spaces and the categories of fuzzy topology ??3. Local structure of fuzzy topological spaces ??4. Convergence structures in fuzzy spaces ??5. Separation in fuzzy spaces ??6. Normality and complete regularity type properties in fuzzy topology ??7. Compactness in fuzzy topology ??8. Connectedness in fuzzy spaces ??9. Fuzzy metric spaces and metrization of fuzzy spaces ??10. The fuzzy real line and its subspaces ??11. Fuzzy modification of a linearly ordered space ??12. Fuzzy probabilistic modification of a topological space ??13. The interval fuzzy real line ??14. On hyperspaces of fuzzy sets ??15. Another view of the subject of fuzzy topology and certain categorical aspects of it Conclusion: some reflections on the role and significance of fuzzy topology References
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.
01 Sep 1989
TL;DR: An algorithm designed to rank any number of fuzzy numbers is presented and it is concluded that the present algorithm is both accurate and efficient.
Abstract: In order to rank three or more fuzzy numbers it is necessary to consider not only the accuracy and effectiveness of the method but also its numerical efficiency. An algorithm designed to rank any number of fuzzy numbers is presented. The algorithm is verified by testing it on the set of 13 cases of paired examples, which are normal and convex fuzzy numbers, given in T.Y. Tseng and C.M. Klein (1988). The results are compared with those of W. Kolodziejczyk's R1 index (1986), and the performance of both algorithms is evaluated. It is concluded that the present algorithm is both accurate and efficient. >
TL;DR: In this article, a general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains, and analytical results for M/F/1 and FM/FM/1 systems are presented.
Abstract: A general approach for queuing systems in a fuzzy environment is proposed based on Zadeh's extension principle, the possibility concept and fuzzy Markov chains. To illustrate the approach, analytical results for M/F/1 and FM/FM/1 systems are presented. Fuzzy queues are much more realistic than the commonly used crisp queues in many practical situations. A simple numerical example is also presented.
TL;DR: The concept of an integral of a fuzzy mapping is introduced that generalises the integral introduced by Matloka and also extends Riemann-Stieltjes integral over a closed interval to fuzzy mappings.
TL;DR: Based on the proposed methods for multiobjective linear, linear fractional and nonlinear programming problems with fuzzy parameters, interactive computer programs are developed and an illustrative numerical example for nonlinear case is demonstrated.
TL;DR: An interactive fuzzy satisficing method for multiobjective nonlinear programming problems with fuzzy numbers that can be derived efficiently from among an M-α-Pareto optimal solution set is presented.
TL;DR: In this paper, two different approaches of fuzzy clustering, fuzzy classification and fuzzy equivalence, are introduced in the process of part-family formation and a dynamic part family assignment procedure is presented using the methodology of fuzzy pattern recognition to assign new parts to existing PFs.
Abstract: Group Technology (GT) is one of the key issues in a successful implementation of flexible manufacturing systems ( FMSs). The objective of GT is, through the use of a part-family (PF) formation scheme, to reduce unnecessary variation proliferation. A part family is a group of parts presenting similar geometry and/or requiring a similar production process. Traditional schemes such as classification and coding and production flow analysis do not consider uncertainty or impreciseness in PF formation. In order to incorporate the uncertainty which is inherent in the measurement of similarities between parts, fuzzy mathematics is employed in this research. Two different approaches of fuzzy cluster analysis, fuzzy classification and fuzzy equivalence, are introduced in the process of part-family formation. In addition, a dynamic part-family assignment procedure is presented using the methodology of fuzzy pattern recognition to assign new parts to existing PFs. A computer program is developed, and several rotation...
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. >
TL;DR: It is shown that there exists a correspondence between fuzzy equivalence relations and certain classes of fuzzy subsets and there are certain lattice theoretic properties of fuzzy equivalences relations on a set.
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.
TL;DR: The resemblance relation, which is defined to be a fuzzified version of a tolerance relation, is shown how the resemblance relation can be used to reduce redundancy in fuzzy relational database systems.
TL;DR: A very fast method of ranking alternatives using fuzzy numbers discussed in [1] and [2] is shown.
TL;DR: A fuzzy version of the Project Evaluation and Review Technique PERT is presented which is computationally easier to use than the original, probabilistic version and avoids several shortcomings of the probabilism version.
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. >
TL;DR: An interactive method for solving a (multi-criteria) linear program, where coefficients of the objective functions and/or of the constraints are known exactly but imprecisely and the original fuzzy problem is transformed into a crisp satisfactory model.
TL;DR: This paper formulates a computational model for obtaining all induced spatial constraints on a set of landmarks, given aSet of approximate quantitative and qualitative constraints on them, which may be incomplete, and perhaps even conflicting.
Abstract: Qualitative reasoning is useful as it facilitates reasoning with incomplete and weak information and aids the subsequent application of more detailed quantitative theories. Adoption of qualitative techniques for spatial reasoning can be very useful in situations where it is difficult to obtain precise informationand where there are real constraints of memory, time and hostile threats. This paper formulates a computational model for obtaining all induced spatial constraints on a set of landmarks, given a set of approximate quantitative and qualitative constraints on them, which may be incomplete, and perhaps even conflicting.