1,867 research outputs found
Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology
Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted.
The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing
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
The VEX-93 environment as a hybrid tool for developing knowledge systems with different problem solving techniques
The paper describes VEX-93 as a hybrid environment for developing
knowledge-based and problem solver systems. It integrates methods and
techniques from artificial intelligence, image and signal processing and
data analysis, which can be mixed. Two hierarchical levels of reasoning
contains an intelligent toolbox with one upper strategic inference engine
and four lower ones containing specific reasoning models: truth-functional
(rule-based), probabilistic (causal networks), fuzzy (rule-based) and
case-based (frames). There are image/signal processing-analysis capabilities
in the form of programming languages with more than one hundred primitive
functions.
User-made programs are embeddable within knowledge basis, allowing the
combination of perception and reasoning. The data analyzer toolbox contains
a collection of numerical classification, pattern recognition and ordination
methods, with neural network tools and a data base query language at
inference engines's disposal.
VEX-93 is an open system able to communicate with external computer programs
relevant to a particular application. Metaknowledge can be used for
elaborate conclusions, and man-machine interaction includes, besides windows
and graphical interfaces, acceptance of voice commands and production of
speech output.
The system was conceived for real-world applications in general domains, but
an example of a concrete medical diagnostic support system at present under
completion as a cuban-spanish project is mentioned.
Present version of VEX-93 is a huge system composed by about one and half
millions of lines of C code and runs in microcomputers under Windows 3.1.Postprint (published version
A Fuzzy Logic Programming Environment for Managing Similarity and Truth Degrees
FASILL (acronym of "Fuzzy Aggregators and Similarity Into a Logic Language")
is a fuzzy logic programming language with implicit/explicit truth degree
annotations, a great variety of connectives and unification by similarity.
FASILL integrates and extends features coming from MALP (Multi-Adjoint Logic
Programming, a fuzzy logic language with explicitly annotated rules) and
Bousi~Prolog (which uses a weak unification algorithm and is well suited for
flexible query answering). Hence, it properly manages similarity and truth
degrees in a single framework combining the expressive benefits of both
languages. This paper presents the main features and implementations details of
FASILL. Along the paper we describe its syntax and operational semantics and we
give clues of the implementation of the lattice module and the similarity
module, two of the main building blocks of the new programming environment
which enriches the FLOPER system developed in our research group.Comment: In Proceedings PROLE 2014, arXiv:1501.0169
Ambiguity in multicriteria quality decisions.
Quality is becoming an issue of increasing strategic importance in business. The aim of this paper is to analyze quality from a decision-making perspective. Quality decisions are characterized by their ambiguity while their evaluation uses a multicriteria viewpoint. Fuzzy decision theory provides a conceptual framework to model decisions with these features. It enables the decision maker to add his/her own experience and any other type of information to that obtained from hard figures. This theory is applied to a set of quality decision alternatives which are evaluated using different criteria such as their impact on fixed costs, cost of quality, leadtime and flexibility. The approach provided in this paper can be extended to other quality decisions.Quality decision-making; Quality dimensions; Fuzzy multicriteria decision making;
Fredkin Gates for Finite-valued Reversible and Conservative Logics
The basic principles and results of Conservative Logic introduced by Fredkin
and Toffoli on the basis of a seminal paper of Landauer are extended to
d-valued logics, with a special attention to three-valued logics. Different
approaches to d-valued logics are examined in order to determine some possible
universal sets of logic primitives. In particular, we consider the typical
connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As
a result, some possible three-valued and d-valued universal gates are described
which realize a functionally complete set of fundamental connectives.Comment: 57 pages, 10 figures, 16 tables, 2 diagram
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Thinking intuitively: the rich (and at times illogical) world of concepts
Intuitive knowledge of the world involves knowing what kinds of things have which properties. We express it in generalities such as “ducks lay eggs”. It contrasts with extensional knowledge about actual individuals in the world, which we express in quantified statements such as “All US Presidents are male”. Reasoning based on this intuitive knowledge, while highly fluent and plausible may in fact lead us into logical fallacy. Several lines of research point to our conceptual memory as the source of this logical failure. We represent concepts with prototypical properties, judging likelihood and argument strength on the basis of similarity between ideas. Evidence that our minds represent the world in this intuitive way can be seen in a range of phenomena, including how people interpret logical connectives applied to everyday concepts, studies of creativity and emergence in conceptual combination, and demonstrations of the logically inconsistent beliefs that people express in their everyday language
Constraint-wish and satisfied-dissatisfied: an overview of two approaches for dealing with bipolar querying
In recent years, there has been an increasing interest in dealing with user preferences in flexible database querying, expressing both positive and negative information in a heterogeneous way. This is what is usually referred to as bipolar database querying. Different frameworks have been introduced to deal with such bipolarity. In this chapter, an overview of two approaches is given. The first approach is based on mandatory and desired requirements. Hereby the complement of a mandatory requirement can be considered as a specification of what is not desired at all. So, mandatory requirements indirectly contribute to negative information (expressing what the user does not want to retrieve), whereas desired requirements can be seen as positive information (expressing what the user prefers to retrieve). The second approach is directly based on positive requirements (expressing what the user wants to retrieve), and negative requirements (expressing what the user does not want to retrieve). Both approaches use pairs of satisfaction degrees as the underlying framework but have different semantics, and thus also different operators for criteria evaluation, ranking, aggregation, etc
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