FUZZY MATHEMATICS

FUZZY MATHEMATICS

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CONNECTED SPACE

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  Connected space 29 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia For other uses, see  Connection (disambiguation) . Connected and disconnected subspaces of  R ² From top to bottom: red space  A , pink space  B , yellow space  C  and orange space  D  are all  connected spaces , whereas green space  E  (made of  subsets  E 1 , E 2 , E 3 , and E 4 ) is  disconnected . Furthermore,  A  and  B  are also  simply connected  ( genus  0), while  C  and  D  are not:  C  has genus 1 and  D  has genus 4. In  topology  and related branches of  mathematics , a  connected space  is a  topological space  that cannot be represented as the  union  of two or more  disjoint   non-empty   open subsets . Connectedness is one of the principal  topological pro...
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Probability

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  Probability 108 languages Article Talk Read Edit View history From Wikipedia, the free encyclopedia For the mathematical field of probability specifically, see  Probability theory . For other uses, see  Probability (disambiguation) . Probability Outline Catalog of articles Probabilists Glossary Notation Journals Category   Mathematics portal v t e Part of a series on  statistics Probability theory Probability   Axioms Determinism   System Indeterminism Randomness Probability space Sample space Event   Collectively exhaustive events Elementary event Mutual exclusivity Outcome Singleton Experiment   Bernoulli trial Probability distribution   Bernoulli distribution Binomial distribution Normal distribution Probability measure Random variable   Bernoulli process Continuous or discrete Expected value Markov chain Observed value Random walk Stochastic process Complementary event Joint probability Marginal probability Conditional probabi...
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Probability theory

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  Probability theory Like other  theories , the  theory of probability  is a representation of its concepts in formal terms—that is, in terms that can be considered separately from their meaning. These formal terms are manipulated by the rules of mathematics and logic, and any results are interpreted or translated back into the problem domain. There have been at least two successful attempts to formalize probability, namely the  Kolmogorov  formulation and the  Cox  formulation. In Kolmogorov's formulation (see also  probability space ),  sets  are interpreted as  events  and probability as a  measure  on a class of sets. In  Cox's theorem , probability is taken as a primitive (i.e., not further analyzed), and the emphasis is on constructing a consistent assignment of probability values to propositions. In both cases, the  laws of probability  are the same, except for technical details. There are o...
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