Displaying similar documents to “Introduction to Formal Preference Spaces”

Semantics of MML Query - Ordering

Grzegorz Bancerek (2013)

Formalized Mathematics

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Semantics of order directives of MML Query is presented. The formalization is done according to [1]

N-Dimensional Binary Vector Spaces

Kenichi Arai, Hiroyuki Okazaki (2013)

Formalized Mathematics

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The binary set {0, 1} together with modulo-2 addition and multiplication is called a binary field, which is denoted by F2. The binary field F2 is defined in [1]. A vector space over F2 is called a binary vector space. The set of all binary vectors of length n forms an n-dimensional vector space Vn over F2. Binary fields and n-dimensional binary vector spaces play an important role in practical computer science, for example, coding theory [15] and cryptology. In cryptology, binary fields...

Morphology for Image Processing. Part I

Hiroshi Yamazaki, Czesław Byliński, Katsumi Wasaki (2012)

Formalized Mathematics

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In this article we defined mathematical morphology image processing with set operations. First, we defined Minkowski set operations and proved their properties. Next, we defined basic image processing, dilation and erosion proving basic fact about them [5], [8].

Relational Formal Characterization of Rough Sets

Adam Grabowski (2013)

Formalized Mathematics

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The notion of a rough set, developed by Pawlak [10], is an important tool to describe situation of incomplete or partially unknown information. In this article, which is essentially the continuation of [6], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library). Here we drop the classical equivalence- and tolerance-based...

Free Interpretation, Quotient Interpretation and Substitution of a Letter with a Term for First Order Languages

Marco Caminati (2011)

Formalized Mathematics

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Fourth of a series of articles laying down the bases for classical first order model theory. This paper supplies a toolkit of constructions to work with languages and interpretations, and results relating them. The free interpretation of a language, having as a universe the set of terms of the language itself, is defined.The quotient of an interpreteation with respect to an equivalence relation is built, and shown to remain an interpretation when the relation respects it. Both the concepts...

Lexicographic combinations of preference relations in the context of Possibilistic Decision Theory.

Lluís Godo, Adriana Zapico (2006)

Mathware and Soft Computing

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In Possibilistic Decision Theory (PDT), decisions are ranked by a pressimistic or by an optimistic qualitative criteria. The preference relations induced by these criteria have been axiomatized by corresponding sets of rationality postulates, both à la von Neumann and Morgenstern and à la Savage. In this paper we first address a particular issue regarding the axiomatic systems of PDT à la von Neumann and Morgenstern. Namely, we show how to adapt the axiomatic systems for the pessimistic...

Preliminaries to Classical First Order Model Theory

Marco Caminati (2011)

Formalized Mathematics

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First of a series of articles laying down the bases for classical first order model theory. These articles introduce a framework for treating arbitrary languages with equality. This framework is kept as generic and modular as possible: both the language and the derivation rule are introduced as a type, rather than a fixed functor; definitions and results regarding syntax, semantics, interpretations and sequent derivation rules, respectively, are confined to separate articles, to mark...

Representation Theorem for Stacks

Grzegorz Bancerek (2011)

Formalized Mathematics

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In the paper the concept of stacks is formalized. As the main result the Theorem of Representation for Stacks is given. Formalization is done according to [13].

Measuring criteria weights by means of Dimension Theory.

Daniel Gómez, Javier Montero de Juan, Javier Yáñez Gestoso (2006)

Mathware and Soft Computing

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Measuring criteria weights in multicriteria decision making is a key issue in order to amalgamate information when reality is being described from several different points of view. In this paper we propose a method for evaluating those weights taking advantage of Dimension Theory, which allows the representation of the set of alternatives within a real space, provided that decision maker preferences satisfy certain consistency conditions. Such a representation allows a first information...