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Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: This paper provides an introduction to and an overview of type-2 fuzzy sets (T2 FS) and systems by answering the following questions: What is a T2 FS and how is it different from a T1 FS.
Abstract: This paper provides an introduction to and an overview of type-2 fuzzy sets (T2 FS) and systems. It does this by answering the following questions: What is a T2 FS and how is it different from a T1 FS? Is there new terminology for a T2 FS? Are there important representations of a T2 FS and, if so, why are they important? How and why are T2 FSs used in a rule-based system? What are the detailed computations for an interval T2 fuzzy logic system (IT2 FLS) and are they easy to understand? Is it possible to have an IT2 FLS without type reduction? How do we wrap this up and where can we go to learn more?
802 citations
01 Jan 2000
TL;DR: This chapter discusses the development of Fuzzy Set-Theoretic Operators and Quantifiers over time, and some of the techniques used to derive these operators and quantifiers were developed in the 1980s and 1990s.
Abstract: Foreword L.A. Zadeh. Preface. Series Foreword. Contributing Authors. General Introduction D. Dubois, H. Prade. Part I: Fuzzy Sets. 1. Fuzzy Sets: History and Basic Notions D. Dubois, et al. 2. Fuzzy Set-Theoretic Operators and Quantifiers J. Fodor, R.R. Yager. 3. Measurement of Membership Functions: Theoretical and Empirical Work T. Bilgic, I.B. Turksen. Part II: Fuzzy Relations. 4. An Introduction to Fuzzy Relations S. Ovchinnikov. 5. Fuzzy Equivalence Relations: Advanced Material D. Boixader, et al. 6. Analytical Solution Methods for Fuzzy Relational Equations B. De Baets. Part III: Uncertainty. 7. Possibility Theory, Probability and Fuzzy Sets: Misunderstandings, Bridges and Gaps D. Dubois, et al. 8. Measures of Uncertainty and Information G.J. Klir. 9. Quantifying Different Facets of Fuzzy Uncertainty N.R. Pal, J.C. Bezdek. Part IV: Fuzzy Sets on the Real Line. 10. Fuzzy Interval Analysis D. Dubois, et al. 11. Metric Topology of Fuzzy Numbers and Fuzzy Analysis P. Diamond, P. Kloeden. Index.
797 citations
TL;DR: Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems that relax the existing conditions reported in the previous literatures.
Abstract: This paper deals with the quadratic stability conditions of fuzzy control systems that relax the existing conditions reported in the previous literatures. Two new conditions are proposed and shown to be useful in analyzing and designing fuzzy control systems. The first one employs the S-procedure to utilize information regarding the premise parts of the fuzzy systems. The next one enlarges the class of fuzzy control systems, whose stability is ensured by representing the interactions among the fuzzy subsystems in a single matrix and solving it by linear matrix inequality. The relationships between the suggested stability conditions and the conventional well-known stability conditions reported in the previous literatures are also discussed, and it is shown in a rigorous manner that the second condition of this paper includes the conventional conditions. Finally, some examples and simulation results are presented to illustrate the effectiveness of the stability conditions.
783 citations
TL;DR: A fuzzy controller is designed which guarantees stability of the control system under a condition and the simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions.
Abstract: A robust stabilization problem for fuzzy systems is discussed in accordance with the definition of stability in the sense of Lyapunov. We consider two design problems: nonrobust controller design and robust controller design. The former is a design problem for fuzzy systems with no premise parameter uncertainty. The latter is a design problem for fuzzy systems with premise parameter uncertainty. To realize two design problems, we derive four stability conditions from a basic stability condition proposed by Tanaka and Sugeno: nonrobust condition, weak nonrobust condition, robust condition, and weak robust condition. We introduce concept of robust stability for fuzzy control systems with premise parameter uncertainty from the weak robust condition. To introduce robust stability, admissible region and variation region, which correspond to stability margin in the ordinary control theory, are defined. Furthermore, we develop a control system for backing up a computer simulated truck-trailer which is nonlinear and unstable. By approximating the truck-trailer by a fuzzy system with premise parameter uncertainty and by using concept of robust stability, we design a fuzzy controller which guarantees stability of the control system under a condition. The simulation results show that the designed fuzzy controller smoothly achieves backing up control of the truck-trailer from all initial positions. >
773 citations
TL;DR: A new method for ranking fuzzy numbers by distance method, based on calculating the centroid point, which can rank more than two fuzzy numbers simultaneously, and the fuzzy numbers need not be normal.
772 citations