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A Treatise on ManyValued Logics
 Studies in Logic and Computation
, 2001
"... The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with som ..."
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Cited by 52 (3 self)
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The paper considers the fundamental notions of many valued logic together with some of the main trends of the recent development of infinite valued systems, often called mathematical fuzzy logics. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon actual theoretical considerations about infinite valued logics. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1 Basic ideas 1.1 From classical to manyvalued logic Logical systems in general are based on some formalized language which includes a notion of well formed formula, and then are determined either semantically or syntactically. That a logical system is semantically determined means that one has a notion of interpretation or model 1 in the sense that w.r.t. each such interpretation every well formed formula has some (truth) value or represents a function into
Soft Computing: the Convergence of Emerging Reasoning Technologies
 Soft Computing
, 1997
"... The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to so ..."
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Cited by 50 (8 self)
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The term Soft Computing (SC) represents the combination of emerging problemsolving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, realworld problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagationtype algorithms.
What nonlinearity to choose? Mathematical foundations of fuzzy control
 Proceedings of the 1992 International Conference on Fuzzy Systems and Intelligent Control
, 1992
"... Abstract. Fuzzy control is a very successful way to transform the expert’s knowledge of the type “if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible ” into an actual control. To apply this transformation one must: 1) choose fuzzy varia ..."
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Cited by 25 (18 self)
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Abstract. Fuzzy control is a very successful way to transform the expert’s knowledge of the type “if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible ” into an actual control. To apply this transformation one must: 1) choose fuzzy variables corresponding to words like “small”, “big”; 2) choose operations corresponding to “and ” and “or”; 3) choose a method that transforms the resulting fuzzy variable for a into a single value ā. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From mathematical viewpoint these choice problems correspond to nonlinear optimization and are therefore extremely difficult. We develop a new mathematical formalism (based on group theory) that allows us to solve the problem of optimal choice and thus: 1) explain why the existing choices are really the best (in some situations); 2) explain a rather mysterious fact that the fuzzy control based on the experts’ knowledge is often better than the control by these same experts; 3) give choice recommendations for the cases when traditional choices do not work. Perspectives of space applications will be also discussed.
Measurement Of Membership Functions: Theoretical And Empirical Work
, 1995
"... This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear u ..."
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Cited by 21 (1 self)
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This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear using techniques from measurement theory.
Mathematical fuzzy logic as a tool for the treatment of vague information
 Information Sciences
, 2005
"... The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by ..."
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Cited by 10 (1 self)
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The paper considers some of the main trends of the recent development of mathematical fuzzy logic as an important tool in the toolbox of approximate reasoning techniques. Particularly the focus is on fuzzy logics as systems of formal logic constituted by a formalized language, by a semantics, and by a calculus for the derivation of formulas. Besides this logical approach also a more algebraic approach is discussed. And the paper ends with some hints toward applications which are based upon these theoretical considerations. Key words: mathematical fuzzy logic, algebraic semantics, continuous tnorms, leftcontinuous tnorms, Pavelkastyle fuzzy logic, fuzzy set theory, nonmonotonic fuzzy reasoning 1
Giles’s Game and the Proof Theory of ̷Lukasiewicz Logic
"... Abstract. In the 1970s, Robin Giles introduced a game combining Lorenzenstyle dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in ̷Lukasiewicz logic. In this pa ..."
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Cited by 3 (2 self)
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Abstract. In the 1970s, Robin Giles introduced a game combining Lorenzenstyle dialogue rules with a simple scheme for betting on the truth of atomic statements, and showed that the existence of winning strategies for the game corresponds to the validity of formulas in ̷Lukasiewicz logic. In this paper, it is shown that ‘disjunctive strategies’ for Giles’s game, combining ordinary strategies for all instances of the game played on the same formula, may be interpreted as derivations in a corresponding proof system. In particular, such strategies mirror derivations in a hypersequent calculus developed in recent work on the proof theory of ̷Lukasiewicz logic.
Multivalued logics and fuzzy reasoning
 BCS AISB Summer School
, 1975
"... These notes are concerned with recent developments in multivalued logic, particularly in fuzzy logic and its status as a model for human linguistic reasoning. This first section discusses the status of formal logic and the need for logics of approximate reasoning with vague data. The following secti ..."
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Cited by 3 (2 self)
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These notes are concerned with recent developments in multivalued logic, particularly in fuzzy logic and its status as a model for human linguistic reasoning. This first section discusses the status of formal logic and the need for logics of approximate reasoning with vague data. The following sections present a hasic account of fuzzy sets theory; fuzzy logics; Zadeh's model of linguistic hedges and fuzzy reasoning and finally a bibliography of all Zadeh's papers and other selected references. Models of the human reasoning process are clearly very relevant to artificial intelligence (AI) studies. Broadly there are two types: psychological models of what people actually do; and formal models of what logicians and philosophers feel a rational individual WOUld, or should, do. The main problem with the former is that it is extremely difficult to monitor thought processes the behaviorist approach is perhaps reasonable with rats but a ridiculously inadequate source of data on man the introspectionist approach is far more successful (e.g. in analysing human chess
Fuzzy Interpretation of Quantum Mechanics Made More Convincing: Every Statement with Real Numbers Can Be Reformulated in Logical Terms
, 1995
"... this paper, we will show that for every rational number a = m=n, such a formula exists ..."
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Cited by 2 (2 self)
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this paper, we will show that for every rational number a = m=n, such a formula exists
F.: Propositional fuzzy logics: Decidable for some (algebraic) operators; undecidable for more complicated ones
 Inter. Jour. Intel. Systems
, 1999
"... If we view fuzzy logic as a logic, i.e., as a particular case of a multivalued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these ..."
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Cited by 2 (1 self)
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If we view fuzzy logic as a logic, i.e., as a particular case of a multivalued logic, then one of the most natural questions to ask is whether the corresponding propositional logic is decidable, i.e., does there exist an algorithm that, given two propositional formulas F and G, decides whether these two formulas always have the same truth value. It is known that the simplest fuzzy logic, in which & = min and ∨ = max, is decidable. In this paper, we prove a more general result: that all propositional fuzzy logics with algebraic operations are decidable, We also show that this result cannot be generalized further: e.g., no deciding algorithm is possible for logics in which operations are algebraic with constructive (nonalgebraic) coefficients.
InfiniteValued Logic Based on TwoValued Logic and Probability  Part 1.4. The TEE Model for Grades of Membership
 THE INT. J. OF MANMACHINE STUDIES
, 1990
"... This paper precisates the meaning of numerical membership values and shows that there is no contradiction between a probabilistic interpretation of grades of membership on the one hand, and membership functions of the attribute universe whose ordinates add up to more than 1 on the other. The mem ..."
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Cited by 2 (0 self)
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This paper precisates the meaning of numerical membership values and shows that there is no contradiction between a probabilistic interpretation of grades of membership on the one hand, and membership functions of the attribute universe whose ordinates add up to more than 1 on the other. The membership value in a class , e.g., =tall, assigned by a subject to an object of a given attribute value u ex (e.g., u ex =exact height value) is interpreted as the subject's estimate of P (ju ex ) , the probability that this object would be assigned (by herself or another subject) the label in the presence of fuzziness #1, 2 or 3 (in an experimental or natural language LB (labeling) or YN (yesno) situation in which the subject uses a nonfuzzy threshold criterion in the universe U of estimated attribute values). = l is assumed to be an element of a label set , such as = fsmall, medium, tallg . The probabilistic `summing up to 1 requirement' applies to the sum of P ( l ju ...