313 research outputs found
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
Tsallis entropy composition and the Heisenberg group
We present an embedding of the Tsallis entropy into the 3-dimensional
Heisenberg group, in order to understand the meaning of generalized
independence as encoded in the Tsallis entropy composition property. We infer
that the Tsallis entropy composition induces fractal properties on the
underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we
justify why the underlying configuration/phase space of systems described by
the Tsallis entropy has polynomial growth for both discrete and Riemannian
cases. We provide a geometric framework that elucidates Abe's formula for the
Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian
spaces.Comment: 26 pages, No figures, LaTeX2e. To be published in Int. J. Geom.
Methods Mod. Physic
Fuzzy Mathematics
This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value
Generalized Flux Vacua
We consider type II string theory compactified on a symmetric T^6/Z_2
orientifold. We study a general class of discrete deformations of the resulting
four-dimensional supergravity theory, including gaugings arising from geometric
and "nongeometric'' fluxes, as well as the usual R-R and NS-NS fluxes. Solving
the equations of motion associated with the resulting N = 1 superpotential, we
find parametrically controllable infinite families of supersymmetric vacua with
all moduli stabilized. We also describe some aspects of the distribution of
generic solutions to the SUSY equations of motion for this model, and note in
particular the existence of an apparently infinite number of solutions in a
finite range of the parameter space of the four-dimensional effective theory.Comment: 30 pages, 4 .eps figures; v2, reference adde
Renormalised singular stochastic PDEs
Extended decorations on naturally decorated trees were introduced in the work
of Bruned, Hairer and Zambotti on algebraic renormalization of regularity
structures to provide a convenient framework for the renormalization of systems
of singular stochastic PDEs within that setting. This non-dynamical feature of
the trees complicated the analysis of the dynamical counterpart of the
renormalization process. We provide a new proof of the renormalized system
by-passing the use of extended decorations and working for a large class of
renormalization maps, with the BPHZ renormalization as a special case. The
proof reveals important algebraic properties connected to preparation maps
A Novel Method of the Generalized Interval-Valued Fuzzy Rough Approximation Operators
Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are shown to be equivalent to the generalized interval fuzzy rough approximation operators introduced by Dubois, which are determined by any interval-valued fuzzy binary relation expressed in a generalized approximation space. Main properties of these operators are discussed under different interval-valued fuzzy binary relations, and the illustrative examples are given to demonstrate the main features of the proposed operators
Sequences of refinements of rough sets: logical and algebraic aspects
In this thesis, a generalization of the classical Rough set theory is developed considering the so-called sequences of orthopairs that we define as special sequences of rough sets.
Mainly, our aim is to introduce some operations between sequences of orthopairs, and to discover how to generate them starting from the operations concerning standard rough sets. Also, we prove several representation theorems representing the class of finite centered Kleene algebras with the interpolation property, and some classes of finite residuated lattices (more precisely, we consider Nelson algebras, Nelson lattices, IUML-algebras and Kleene lattice with implication) as sequences of orthopairs.
Moreover, as an application, we show that a sequence of orthopairs can be used to represent an examiner's opinion on a number of candidates applying for a job, and we show that opinions of two or more examiners can be combined using operations between sequences of orthopairs in order to get a final decision on each candidate.
Finally, we provide the original modal logic SOn with semantics based on sequences of orthopairs, and we employ it to describe the knowledge of an agent that increases over time, as new information is provided. Modal logic Son is characterized by the sequences (□1,…, □n) and (O1,…, On) of n modal operators corresponding to a sequence (t1,…, tn) of consecutive times. Furthermore, the operator □i of (□1,…, □n) represents the knowledge of an agent at time ti, and it coincides with the necessity modal operator of S5 logic. On the other hand, the main innovative aspect of modal logic SOn is the presence of the sequence (O1,…, On), since Oi establishes whether an agent is interested in knowing a given fact at time ti
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