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FUZZY SETS: HISTORY AND BASIC NOTIONS
"... This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's ..."
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This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.
Ten Questions and One Problem on Fuzzy Logic.
, 1998
"... Ten questions on fuzzy logic as a formal logic of consequence under vagueness are discussed; a problem of definability of truth is formulated. Recently I had a very interesting friendly email discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning t ..."
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Ten questions on fuzzy logic as a formal logic of consequence under vagueness are discussed; a problem of definability of truth is formulated. Recently I had a very interesting friendly email discussion with Professor Parikh on vagueness and fuzzy logic. Parikh published several papers concerning the notion of vagueness. They contain critical remarks on fuzzy logic and its ability to formalize reasoning under vagueness [10,11]. On the other hand, for some years I have tried to advocate fuzzy logic (in the narrow sense, as Zadeh says, i.e. as formal logical systems formalizing reasoning under vagueness) and in particular to show that such systems (of manyvalued logic of a certain kind) offer a fully fledged and extremely interesting logic [4,5]. But this leaves open the question of intuitive adequacy of manyvalued logic as a logic of vagueness. Below I shall try to isolate eight questions Parikh asks, add two more and to comment on all of them. Finally I formulate a problem on truth ...
REVISITING GILES’S GAME Reconciling Fuzzy Logic and Supervaluation ∗
"... We explain Giles’s characterization of ̷Lukasiewicz logic via a dialogue game combined with bets on results of experiments that may show dispersion. The game is generalized to other fuzzy logics and linked to recent results in proof theory. We argue that these results allow one to place tnorm based ..."
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We explain Giles’s characterization of ̷Lukasiewicz logic via a dialogue game combined with bets on results of experiments that may show dispersion. The game is generalized to other fuzzy logics and linked to recent results in proof theory. We argue that these results allow one to place tnorm based fuzzy logics in a common framework with supervaluation as a theory of vagueness.
Fuzzy Logic as a Theory of Vagueness: 15 Conceptual Questions
"... In spite of its successes as a tool in the field of engineering, fuzzy set theory has yet to achieve the universal footing that probability theory has across the various fields of mathematics, technology, philosophy and psychology. This paper sets out points of critique brought up regarding the fuzz ..."
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In spite of its successes as a tool in the field of engineering, fuzzy set theory has yet to achieve the universal footing that probability theory has across the various fields of mathematics, technology, philosophy and psychology. This paper sets out points of critique brought up regarding the fuzzy approach and seeks to analyze them, focusing on the question of whether anything that can be done about these matters. Do these criticisms have any practical relevance or any relevance with respect to the intended fields of usage. Do they or do they not diminish fuzzy logic’s suitability as a theory of vagueness? Keywords: Fuzzy Logic, Theory of Vagueness. 1
Bridges Between Contextual Linguistic Models of Vagueness and Tnorm Based Fuzzy Logic
, 2009
"... Linguistic models of vagueness usually record contexts of possible precisifications. A link between such models and fuzzy logic is established by extracting fuzzy sets from context based word meanings and analyzing standard logical connectives in this setting. In a further step Lawry’s voting semant ..."
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Linguistic models of vagueness usually record contexts of possible precisifications. A link between such models and fuzzy logic is established by extracting fuzzy sets from context based word meanings and analyzing standard logical connectives in this setting. In a further step Lawry’s voting semantics for fuzzy logics is used to reinterpret standard tnorm based truth functions from the point of view of context update semantics. 1
Exploring Dialogue Games as Foundation of Fuzzy Logic
"... A dialogue game based approach to the problem of providing a deeper semantic foundation for tnorm based fuzzy logics is explored. In particular, various versions, extensions and alternatives to Robin Giles’s dialogue and betting game for ̷Lukasiewicz logic are revisited and put in the context of o ..."
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A dialogue game based approach to the problem of providing a deeper semantic foundation for tnorm based fuzzy logics is explored. In particular, various versions, extensions and alternatives to Robin Giles’s dialogue and betting game for ̷Lukasiewicz logic are revisited and put in the context of other foundational research in logic. It emerges that dialogue games cover a wide range of topics relevant to approximate reasoning.