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"Set theory"
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What comes in sets?
Teaches set theory by looking at sets of objects, including eggs, markers, and sneakers.
Book
Souslin quasi-orders and bi-embeddability of uncountable structures
We provide analogues of the results from Friedman and Motto Ros (2011) and Camerlo, Marcone, and Motto Ros (2013) (which correspond
to the case
eBook
Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume
The simplicial volume is a homotopy invariant of manifolds introduced by Gromov in his pioneering paper
The first aim of this paper is to lay the foundation of the theory of
multicomplexes. After setting the main definitions, we construct the singular multicomplex
In the second part of this work we apply the theory of multicomplexes to the study of the bounded
cohomology of topological spaces. Our constructions and arguments culminate in the complete proofs of Gromov’s Mapping Theorem (which
implies in particular that the bounded cohomology of a space only depends on its fundamental group) and of Gromov’s Vanishing Theorem,
which ensures the vanishing of the simplicial volume of closed manifolds admitting an amenable cover of small multiplicity.
The
third and last part of the paper is devoted to the study of locally finite chains on non-compact spaces, hence to the simplicial volume
of open manifolds. We expand some ideas of Gromov to provide detailed proofs of a criterion for the vanishing and a criterion for the
finiteness of the simplicial volume of open manifolds. As a by-product of these results, we prove a criterion for the
eBook
How Firm Are the Foundations of Mind-Set Theory? The Claims Appear Stronger Than the Evidence
Mind-set refers to people’s beliefs about whether attributes are malleable (growth mind-set) or unchangeable (fixed mind-set). Proponents of mind-set theory have made bold claims about mind-set’s importance. For example, one’s mind-set is described as having profound effects on one’s motivation and achievements, creating different psychological worlds for people, and forming the core of people’s meaning systems. We examined the evidentiary strength of six key premises of mind-set theory in 438 participants; we reasoned that strongly worded claims should be supported by equally strong evidence. However, no support was found for most premises. All associations (rs) were significantly weaker than .20. Other achievement-motivation constructs, such as self-efficacy and need for achievement, have been found to correlate much more strongly with presumed associates of mind-set. The strongest association with mind-set (r = –.12) was opposite from the predicted direction. The results suggest that the foundations of mind-set theory are not firm and that bold claims about mind-set appear to be overstated.
Journal Article
A survey of decision making methods based on certain hybrid soft set models
Fuzzy set theory, rough set theory and soft set theory are all generic mathematical tools for dealing with uncertainties. There has been some progress concerning practical applications of these theories, especially, the use of these theories in decision making problems. In the present article, we review some decision making methods based on (fuzzy) soft sets, rough soft sets and soft rough sets. In particular, we provide several novel algorithms in decision making problems by combining these kinds of hybrid models. It may be served as a foundation for developing more complicated soft set models in decision making.
Journal Article
Hybrid genetic algorithm and a fuzzy logic classifier for heart disease diagnosis
For the past two decades, most of the people from developing countries are suffering from heart disease. Diagnosing these diseases at earlier stages helps patients reduce the risk of death and also in reducing the cost of treatment. The objective of adaptive genetic algorithm with fuzzy logic (AGAFL) model is to predict heart disease which will help medical practitioners in diagnosing heart disease at early stages. The model consists of the rough sets based heart disease feature selection module and the fuzzy rule based classification module. The generated rules from fuzzy classifiers are optimized by applying the adaptive genetic algorithm. First, important features which effect heart disease are selected by rough set theory. The second step predicts the heart disease using the hybrid AGAFL classifier. The experimentation is performed on the publicly available UCI heart disease datasets. Thorough experimental analysis shows that our approach has outperformed current existing methods.
Journal Article