## Fuzzy Logic and Probability Applications: Bridging the GapProbabilists and fuzzy enthusiasts tend to disagree about which philosophy is best and they rarely work together. As a result, textbooks usually suggest only one of these methods for problem solving, but not both. This book is an exception. The authors, investigators from both fields, have combined their talents to provide a practical guide showing that both fuzzy logic and probability have their place in the world of problem solving. They work together with mutual benefit for both disciplines, providing scientists and engineers with examples of and insight into the best tool for solving problems involving uncertainty. Fuzzy Logic and Probability Applications: Bridging the Gap makes an honest effort to show both the shortcomings and benefits of each technique, and even demonstrates useful combinations of the two. It provides clear descriptions of both fuzzy logic and probability, as well as the theoretical background, examples. |

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### Contents

Introduction | 3 |

Fuzzy Set Theory Fuzzy Logic and Fuzzy Systems | 29 |

Probability Theory | 55 |

distributions | 67 |

Bayesian Methods | 73 |

Considerations for Using Fuzzy Set Theory and Probability Theory | 87 |

Guidelines for Eliciting Expert Judgment as Probabilities or Fuzzy Logic | 105 |

Applications | 125 |

A Combined Fuzzy and Probability Approach | 193 |

Aircraft Integrity and Reliability | 219 |

Auto Reliability Project | 243 |

Control Charts for Statistical Process Control | 263 |

Fault Tree Logic Models | 325 |

Uncertainty Distributions Using Fuzzy Logic | 347 |

Signal Validation Using Bayesian Belief Networks and Fuzzy Logic | 365 |

393 | |

### Common terms and phrases

advisor analysis application approach assessment average basic events Bayes Bayesian Bayesian network beryllium exposure calculated Chapter combination component computed conditional probability control chart control limits damage defined defuzzification described detection determine developed disturbance rejection elicitation engineering equation error estimate Example 12 expert judgment expert system failure fault tree fuzzy control system fuzzy logic fuzzy relation fuzzy rules fuzzy set theory fuzzy system imprecision input Laviolette likelihood likelihood function linguistic Lukasiewicz mathematical matrix measure medium membership functions methodology methods mode nodes normal norms operation optimal output membership functions p-chart parameters performance degradation PID controller possible posterior prior probabilistic controller probability theory problem proposition random range reliability represents Ross sample sensor fault sensor reading setpoint setpoint tracking SFDIA shown in Figure shows simulation special-cause statistical structure Table tank temperature theorem uncertainty distributions updated variables wear Zadeh zero