Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
01 Jan 1973-Vol. 3, Iss: 1, pp 28-44
TL;DR: By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Abstract: The approach described in this paper represents a substantive departure from the conventional quantitative techniques of system analysis. It has three main distinguishing features: 1) use of so-called ``linguistic'' variables in place of or in addition to numerical variables; 2) characterization of simple relations between variables by fuzzy conditional statements; and 3) characterization of complex relations by fuzzy algorithms. A linguistic variable is defined as a variable whose values are sentences in a natural or artificial language. Thus, if tall, not tall, very tall, very very tall, etc. are values of height, then height is a linguistic variable. Fuzzy conditional statements are expressions of the form IF A THEN B, where A and B have fuzzy meaning, e.g., IF x is small THEN y is large, where small and large are viewed as labels of fuzzy sets. A fuzzy algorithm is an ordered sequence of instructions which may contain fuzzy assignment and conditional statements, e.g., x = very small, IF x is small THEN Y is large. The execution of such instructions is governed by the compositional rule of inference and the rule of the preponderant alternative. By relying on the use of linguistic variables and fuzzy algorithms, the approach provides an approximate and yet effective means of describing the behavior of systems which are too complex or too ill-defined to admit of precise mathematical analysis.
Citations
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01 Dec 1974
TL;DR: In this article, the authors describe a scheme in which a fuzzy algorithm is used to control plant, in this case, a laboratory-built steam engine, implemented as an interpreter of a set of rules expressed as fuzzy conditional statements.
Abstract: The paper describes a scheme in which a fuzzy algorithm is used to control plant, in this case, a laboratory-built steam engine. The algorithm is implemented as an interpreter of a set of rules expressed as fuzzy conditional statements. This implementation on a digital computer is used online, to control the plant. The merit of such a controller is discussed in the light of the results obtained.
3,916 citations
01 Jan 2000
TL;DR: This article briefly reviews the basic concepts about cognitive radio CR, and the need for software-defined radios is underlined and the most important notions used for such.
Abstract: An Integrated Agent Architecture for Software Defined Radio. Rapid-prototype cognitive radio, CR1, was developed to apply these.The modern software defined radio has been called the heart of a cognitive radio. Cognitive radio: an integrated agent architecture for software defined radio. Http:bwrc.eecs.berkeley.eduResearchMCMACR White paper final1.pdf. The cognitive radio, built on a software-defined radio, assumes. Radio: An Integrated Agent Architecture for Software Defined Radio, Ph.D. The need for software-defined radios is underlined and the most important notions used for such. Mitola III, Cognitive radio: an integrated agent architecture for software defined radio, Ph.D. This results in the set-theoretic ontology of radio knowledge defined in the. Cognitive Radio An Integrated Agent Architecture for Software.This article first briefly reviews the basic concepts about cognitive radio CR. Cognitive Radio-An Integrated Agent Architecture for Software Defined Radio. Cognitive Radio RHMZ 2007. Software-defined radio SDR idea 1. Cognitive radio: An integrated agent architecture for software.Cognitive Radio SOFTWARE DEFINED RADIO, AND ADAPTIVE WIRELESS SYSTEMS2 Cognitive Networks. 3 Joseph Mitola III, Cognitive Radio: An Integrated Agent Architecture for Software Defined Radio Stockholm.
3,814 citations
TL;DR: The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa and, as an approximation, fuzzy logic may be equated to CW.
Abstract: As its name suggests, computing with words (CW) is a methodology in which words are used in place of numbers for computing and reasoning. The point of this note is that fuzzy logic plays a pivotal role in CW and vice-versa. Thus, as an approximation, fuzzy logic may be equated to CW. There are two major imperatives for computing with words. First, computing with words is a necessity when the available information is too imprecise to justify the use of numbers, and second, when there is a tolerance for imprecision which can be exploited to achieve tractability, robustness, low solution cost, and better rapport with reality. Exploitation of the tolerance for imprecision is an issue of central importance in CW. In CW, a word is viewed as a label of a granule; that is, a fuzzy set of points drawn together by similarity, with the fuzzy set playing the role of a fuzzy constraint on a variable. The premises are assumed to be expressed as propositions in a natural language. In coming years, computing with words is likely to evolve into a basic methodology in its own right with wide-ranging ramifications on both basic and applied levels.
3,093 citations
TL;DR: M Modes of information granulation (IG) in which the granules are crisp (c-granular) play important roles in a wide variety of methods, approaches and techniques, but this does not reflect the fact that in almost all of human reasoning and concept formation thegranules are fuzzy (f- Granular).
2,624 citations
TL;DR: A general approach to quali- tative modeling based on fuzzy logic is discussed, which proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model.
Abstract: This paper discusses a general approach to quali- tative modeling based on fuzzy logic. The method of qualitative modeling is divided into two parts: fuzzy modeling and linguistic approximation. It proposes to use a fuzzy clustering method (fuzzy c-means method) to identify the structure of a fuzzy model. To clarify the advantages of the proposed method, it also shows some examples of modeling, among them a model of a dynamical process and a model of a human operator's control action.
2,447 citations
References
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Book•
01 Jan 1970TL;DR: A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
Abstract: By decision-making in a fuzzy environment is meant a decision process in which the goals and/or the constraints, but not necessarily the system under control, are fuzzy in nature. This means that the goals and/or the constraints constitute classes of alternatives whose boundaries are not sharply defined.
An example of a fuzzy constraint is: “The cost of A should not be substantially higher than α,” where α is a specified constant. Similarly, an example of a fuzzy goal is: “x should be in the vicinity of x0,” where x0 is a constant. The italicized words are the sources of fuzziness in these examples.
Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in the space of alternatives. A fuzzy decision, then, may be viewed as an intersection of the given goals and constraints. A maximizing decision is defined as a point in the space of alternatives at which the membership function of a fuzzy decision attains its maximum value.
The use of these concepts is illustrated by examples involving multistage decision processes in which the system under control is either deterministic or stochastic. By using dynamic programming, the determination of a maximizing decision is reduced to the solution of a system of functional equations. A reverse-flow technique is described for the solution of a functional equation arising in connection with a decision process in which the termination time is defined implicitly by the condition that the process stops when the system under control enters a specified set of states in its state space.
6,919 citations
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
2,524 citations
"Outline of a New Approach to the An..." refers background in this paper
...IJB(y), for these compositions may be found in [2]....
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TL;DR: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets.
Abstract: A functional defined on the class of generalized characteristic functions (fuzzy sets), called “entropy≓, is introduced using no probabilistic concepts in order to obtain a global measure of the indefiniteness connected with the situations described by fuzzy sets. This “entropy≓ may be regarded as a measure of a quantity of information which is not necessarily related to random experiments. Some mathematical properties of this functional are analyzed and some considerations on its applicability to pattern analysis are made.
2,024 citations
TL;DR: Students of language, especially psychologists and linguistic philosophers, have long been attuned to the fact that natural language concepts have vague boundaries and fuzzy edges and that, consequently, natural language sentences will very often be neither true, nor false, nor nonsensical.
Abstract: Logicians have, by and large, engaged in the convenient fiction that sentences of natural languages (at least declarative sentences) are either true or false or, at worst, lack a truth value, or have a third value often interpreted as ‘nonsense’. And most contemporary linguists who have thought seriously about semantics, especially formal semantics, have largely shared this fiction, primarily for lack of a sensible alternative. Yet students of language, especially psychologists and linguistic philosophers, have long been attuned to the fact that natural language concepts have vague boundaries and fuzzy edges and that, consequently, natural language sentences will very often be neither true, nor false, nor nonsensical, but rather true to a certain extent and false to a certain extent, true in certain respects and false in other respects.
1,284 citations
Book•
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01 Aug 1996
TL;DR: A fuzzy algorithm is introduced which, though fuzzy rather than precise in nature, may eventually prove to be of use in a wide variety of problems relating to information processing, control, pattern recognition, system identification, artificial intelligence and, more generally, decision processes involving incomplete or uncertain data.
Abstract: Unlike most papers in Information and Control, our note contains no theorems and no proofs. Essentially, its purpose is to introduce a basic concept which, though fuzzy rather than precise in nature, may eventually prove to be of use in a wide variety of problems relating to information processing, control, pattern recognition, system identification, artificial intelligence and, more generally, decision processes involving incomplete or uncertain data. The concept in question will be called a fuzzy algorithm because it may be viewed as a generalization, through the process of fuzzification, of the conventional (nonfuzzy) conception of an algorithm. More specifically, unlike a nonfuzzy deterministic or nondeterministic algorithm (Floyd, 1967), a fuzzy algorithm may contain fuzzy statements, that is, statements containing names of fuzzy sets (Zadeh, 1965), by which we mean classes in which there may be grades of membership intermediate between full membership and nonmembership. To illustrate, fuzzy algorithms may contain fuzzy instructions such as:
971 citations
"Outline of a New Approach to the An..." refers background or methods in this paper
...A formal characterization of the concept of a fuzzy algorithm can be given in terms of the notion of a fuzzy Turing machine or a fuzzy Markoff algorithm [6], [7], [8]....
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...Essentially, a fuzzy algorithm [6] is an ordered sequence of instructions ( Jike a computer program) in which some of the instructions may contain labels of fuzzy sets....
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...what basis will such a number be chosen? As pointed out in [6], it is reasonable to assume that the result of execution will be that element of the fuzzy set which has the highest grade of membership in it....
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