46,464 research outputs found
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear,
hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We
survey also results which show the tree different proof-theoretic frameworks
for many-valued logics, e.g. frameworks of the following deductive calculi:
Hilbert's style, sequent, and hypersequent. We present a general way that
allows to construct systematically analytic calculi for a large family of
non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and
p-adic valued logics characterized by a special format of semantics with an
appropriate rejection of Archimedes' axiom. These logics are built as different
extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's,
Product, and Post's logics). The informal sense of Archimedes' axiom is that
anything can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is infinite and it
is not well-founded and well-ordered. On the base of non-Archimedean valued
logics, we construct non-Archimedean valued interval neutrosophic logic INL by
which we can describe neutrality phenomena.Comment: 119 page
Fuzzy inequational logic
We present a logic for reasoning about graded inequalities which generalizes
the ordinary inequational logic used in universal algebra. The logic deals with
atomic predicate formulas of the form of inequalities between terms and
formalizes their semantic entailment and provability in graded setting which
allows to draw partially true conclusions from partially true assumptions. We
follow the Pavelka approach and define general degrees of semantic entailment
and provability using complete residuated lattices as structures of truth
degrees. We prove the logic is Pavelka-style complete. Furthermore, we present
a logic for reasoning about graded if-then rules which is obtained as
particular case of the general result
WARP: Weight Associative Rule Processor. A dedicated VLSI fuzzy logic megacell
During the last five years Fuzzy Logic has gained enormous popularity in the academic and industrial worlds. The success of this new methodology has led the microelectronics industry to create a new class of machines, called Fuzzy Machines, to overcome the limitations of traditional computing systems when utilized as Fuzzy Systems. This paper gives an overview of the methods by which Fuzzy Logic data structures are represented in the machines (each with its own advantages and inefficiencies). Next, the paper introduces WARP (Weight Associative Rule Processor) which is a dedicated VLSI megacell allowing the realization of a fuzzy controller suitable for a wide range of applications. WARP represents an innovative approach to VLSI Fuzzy controllers by utilizing different types of data structures for characterizing the membership functions during the various stages of the Fuzzy processing. WARP dedicated architecture has been designed in order to achieve high performance by exploiting the computational advantages offered by the different data representations
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