5,169 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
The Combination of Paradoxical, Uncertain, and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference
The management and combination of uncertain, imprecise, fuzzy and even
paradoxical or high conflicting sources of information has always been, and
still remains today, of primal importance for the development of reliable
modern information systems involving artificial reasoning. In this chapter, we
present a survey of our recent theory of plausible and paradoxical reasoning,
known as Dezert-Smarandache Theory (DSmT) in the literature, developed for
dealing with imprecise, uncertain and paradoxical sources of information. We
focus our presentation here rather on the foundations of DSmT, and on the two
important new rules of combination, than on browsing specific applications of
DSmT available in literature. Several simple examples are given throughout the
presentation to show the efficiency and the generality of this new approach.
The last part of this chapter concerns the presentation of the neutrosophic
logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and
neutrosophic logic are useful tools in decision making after fusioning the
information using the DSm hybrid rule of combination of masses.Comment: 20 page
Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems
We propose a matrix model for two- and many-valued logic using families of
observables in Hilbert space, the eigenvalues give the truth values of logical
propositions where the atomic input proposition cases are represented by the
respective eigenvectors. For binary logic using the truth values {0,1} logical
observables are pairwise commuting projectors. For the truth values {+1,-1} the
operator system is formally equivalent to that of a composite spin 1/2 system,
the logical observables being isometries belonging to the Pauli group. Also in
this approach fuzzy logic arises naturally when considering non-eigenvectors.
The fuzzy membership function is obtained by the quantum mean value of the
logical projector observable and turns out to be a probability measure in
agreement with recent quantum cognition models. The analogy of many-valued
logic with quantum angular momentum is then established. Logical observables
for three-value logic are formulated as functions of the Lz observable of the
orbital angular momentum l=1. The representative 3-valued 2-argument logical
observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table
A temporal semantics for Nilpotent Minimum logic
In [Ban97] a connection among rough sets (in particular, pre-rough algebras)
and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we
present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95,
EG01]), in which the logic of every instant is given by {\L}3: a completeness
theorem will be shown. This is the prosecution of the work initiated in [AGM08]
and [ABM09], in which the authors construct a temporal semantics for the
many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table
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