A fuzzy set approach to non-equilibrium thermodynamics
TL;DR: In this article, a fuzzy set formulation of the phenomenological equations and a realistic approach for studying the entropy production in physical systems, the time trajectories of chemical reactions, etc.
About: This article is published in Fuzzy Sets and Systems.The article was published on 1992-04-10. It has received 4 citations till now. The article focuses on the topics: Thermodynamic system & Non-equilibrium thermodynamics.
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24 May 2001
37 citations
01 Jan 1997
TL;DR: In this article, a major paradigm change that concerns the role of uncertainty in science is discussed, which is manifested by a transition from the traditional attitude toward uncertainty, where uncertainty is undesirable and the ideal is to eliminate it, to an alternative attitude, according to which uncertainty is fundamental and its avoidance is counterproductive.
Abstract: This chapter reviews a major paradigmatic change that concerns the role of uncertainty in science. This change is manifested by a transition from the traditional attitude toward uncertainty in science, according to which uncertainty is undesirable and the ideal is to eliminate it, to an alternative attitude, according to which uncertainty is fundamental and its avoidance is counterproductive. The chapter focuses on the mathematics pertaining to fuzzy set theory and its role in science. The classical mathematical theories by which certain types of uncertainty can be expressed are the classical set theory and the probability theory. In terms of the set theory, uncertainty is expressed by any given set of possible alternatives in situations where only one of the alternatives may actually happen. The probability theory expresses uncertainty in terms of a classical measure on the subsets of a given universal set of alternatives. The measure is a function that, according to the situation, assigns a number in the unit interval [0,1] to each subset of the universal set. Due to the additivity of classical measures, the probability of each subset is uniquely determined from the probabilities assigned to the smallest non-empty subsets of the universal set, each consisting of exactly one alternative. The fuzzy set theory is a generalization of the classical set theory, and the fuzzy measure theory is a generalization of the classical measure theory, and hence it is also a generalization of the probability theory.
9 citations
TL;DR: Fuzzy set formulation of the phenomenological equations of chemical kinetics is presented and demonstrated for some important types of chemical reactions.
Abstract: Fuzzy set formulation of the phenomenological equations of chemical kinetics is presented and demonstrated for some important types of chemical reactions. The algorithms obtained are used in a number of examples for calculating the fuzzy time trajectories.
4 citations
TL;DR: The possibility of generalising dimensional analysis methods by considering the physical quantities as fuzzy sets by formulating the basic principles of dimensional analysis in fuzzyfied form is shown.
1 citations
References
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01 Jan 1973
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.
8,547 citations
Book•
31 Jul 1985
TL;DR: The book updates the research agenda with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research.
Abstract: Fuzzy Set Theory - And Its Applications, Third Edition is a textbook for courses in fuzzy set theory. It can also be used as an introduction to the subject. The character of a textbook is balanced with the dynamic nature of the research in the field by including many useful references to develop a deeper understanding among interested readers. The book updates the research agenda (which has witnessed profound and startling advances since its inception some 30 years ago) with chapters on possibility theory, fuzzy logic and approximate reasoning, expert systems, fuzzy control, fuzzy data analysis, decision making and fuzzy set models in operations research. All chapters have been updated. Exercises are included.
7,877 citations
TL;DR: F fuzzy logic is suggested, which is the logic underlying approximate or, equivalently, fuzzy reasoning, which leads to various basic syllogisms which may be used as rules of combination of evidence in expert systems.
1,278 citations
Book•
01 Jan 1987
TL;DR: This book discusses the Logic of Decisions, Behavioral Decision Theory, and Decision Technology, as well as an Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.
Abstract: 1 Introduction.- The Logic of Decisions, Behavioral Decision Theory, and Decision Technology.- Optimization, Outranking, Evaluation.- Basics of Fuzzy Set Theory.- 2 Individual Decision Making in Fuzzy Environments.- Symmetrical Models.- Nonsymmetrical Models.- Fuzzy Utilities.- 3 Multi-Person Decision Making in Fuzzy Environments.- Basic Models.- Fuzzy Games.- Fuzzy Team Theory.- Fuzzy Group Decision Making.- 4 Fuzzy Mathematical Programming.- Fuzzy Linear and Nonlinear Programming.- Fuzzy Multi-Stage Programming.- 5 Multi-Criteria Decision Making in Ill-Structured Situations.- Fuzzy Multi-Criteria Programming.- Multi-Attribute Decision Making (MADM).- Fuzzy Outranking.- 6 Operators and Membership Functions in Decision Models.- Axiomatic, Pragmatic, and Empirical Justification.- The Measurement of Membership Functions.- Selecting Appropriate Operators in Decision Models.- 7 Decision Support Systems.- Knowledge-Based vs. Data-Based Systems.- Linguistic Variables, Fuzzy Logic, Approximate Reasoning.- An Interactive Decision Support System for Fuzzy and Semi-fuzzy Multi-Objective Problems.- Expert Systems and Fuzzy Sets.
1,209 citations