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ClDo _ IIIIIIIoaIIIics bu _ die 'EI JDDi, *** sij'_ ...-..._. je _
...lIbupalaJllllllllll __ D'y_poa~: wbae it beIoap...die . . "...,.
. _ DOD to dlecluly __ * __ . ~ 1110 _ is dioapaI; -. . e _ may be
EricT. BeD IbIetodo--'_iL O. 1feaoriIide Mathematics is a tool for
dloogIrt. A bighly necessary tool in a world where both feedback
and noolineari- ties abound. Similarly, all kinds of parts of
IIIIIIhcmatiI:s serve as tools for odIcr parts and for ocher sci-
eoccs. Applying a simple rewriting rule to the quote on the right
above one finds suc:h stalements as: 'One ser- vice topology has
rcncIerM mathematical physics ...'; 'One service logic has rendered
computer science . * . '; 'One service category theory has rmdcn:d
mathematics ...'. All arguably true. And all statements obrainable
this way form part of the raison d'etm of this series. This series,
Mathmlatics tDIII Its Applications, saaned in 1977. Now that over
one hundred volumcs have appeared it seems opportune to reexamine
its scope. AI. the time I wrote "Growing spccialization and
divenification have brought a host of monographs and textbooks on
incJeasingly specialized topics. However, the 'tree' of knowledge
of JJJatbcmatics and reIatcd ficIds docs not grow only by putting
forth new bnDdIcs. It also happens, quite often in fact, that
brancbes which were thought to be comp1etcly disparate am suddenly
seen to be rdatcd.
Mathematical Principles of Fuzzy Logic provides a systematic study
of the formal theory of fuzzy logic. The book is based on logical
formalism demonstrating that fuzzy logic is a well-developed
logical theory. It includes the theory of functional systems in
fuzzy logic, providing an explanation of what can be represented,
and how, by formulas of fuzzy logic calculi. It also presents a
more general interpretation of fuzzy logic within the environment
of other proper categories of fuzzy sets stemming either from the
topos theory, or even generalizing the latter. This book presents
fuzzy logic as the mathematical theory of vagueness as well as the
theory of commonsense human reasoning, based on the use of natural
language, the distinguishing feature of which is the vagueness of
its semantics.
Mathematical Principles of Fuzzy Logic provides a systematic study
of the formal theory of fuzzy logic. The book is based on logical
formalism demonstrating that fuzzy logic is a well-developed
logical theory. It includes the theory of functional systems in
fuzzy logic, providing an explanation of what can be represented,
and how, by formulas of fuzzy logic calculi. It also presents a
more general interpretation of fuzzy logic within the environment
of other proper categories of fuzzy sets stemming either from the
topos theory, or even generalizing the latter. This book presents
fuzzy logic as the mathematical theory of vagueness as well as the
theory of commonsense human reasoning, based on the use of natural
language, the distinguishing feature of which is the vagueness of
its semantics.
ClDo _ IIIIIIIoaIIIics bu _ die 'EI JDDi, sij'_ . . . . -. . . _.
je _ . . . . . lIbupalaJllllllllll __ D'y_poa: wbae it beIoap. . .
. die . . ." . ., . . _ DOD to dlecluly __ __ . 1110 _ is dioapaI;
-. . e _ may be EricT. BeD IbIetodo--'_iL O. 1feaoriIide
Mathematics is a tool for dloogIrt. A bighly necessary tool in a
world where both feedback and noolineari ties abound. Similarly,
all kinds of parts of IIIIIIhcmatiI: s serve as tools for odIcr
parts and for ocher sci eoccs. Applying a simple rewriting rule to
the quote on the right above one finds suc: h stalements as: 'One
ser vice topology has rcncIerM mathematical physics . . . '; 'One
service logic has rendered computer science . . '; 'One service
category theory has rmdcn: d mathematics . . . '. All arguably
true. And all statements obrainable this way form part of the
raison d'etm of this series. This series, Mathmlatics tDIII Its
Applications, saaned in 1977. Now that over one hundred volumcs
have appeared it seems opportune to reexamine its scope. AI. the
time I wrote "Growing spccialization and divenification have
brought a host of monographs and textbooks on incJeasingly
specialized topics. However, the 'tree' of knowledge of
JJJatbcmatics and reIatcd ficIds docs not grow only by putting
forth new bnDdIcs. It also happens, quite often in fact, that
brancbes which were thought to be comp1etcly disparate am suddenly
seen to be rdatcd."
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