## Spatial analysis and planning under imprecisionThe book deals with complexity, imprecision, human valuation, and uncertainty in spatial analysis and planning, providing a systematic exposure of a new philosophical and theoretical foundation for spatial analysis and planning under imprecision. Regional concepts and regionalization, spatial preference-utility-choice structures, spatial optimization with single and multiple objectives, dynamic spatial systems and their controls are analyzed in sequence. The analytical framework is based on fuzzy set theory. Basic concepts of fuzzy set theory are first discussed. Many numerical examples and empirical studies are provided to substantiate the theoretical arguments and empirical relevance of this approach. The book provides a more comprehensive perspective on uncertainty and a flexible framework for analysis in the real world, for problems such as commonly encountered spatial problems, urban and regional economic problems, and planning problems. Though the treatment is unconventional, it generally includes conventional analyses as special cases. |

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### Contents

INTRODUCTION | 1 |

BASIC CONCEPTS OF FUZZY SET THEORY | 14 |

REGIONAL CONCEPTS AND REGIONALIZATION | 66 |

Copyright | |

10 other sections not shown

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### Common terms and phrases

alternative analyzed approximately assignment Based behavior binary relation boundary characterized compromise solution concept convex defined Definition denoted discussed dynamic systems equilibrium problem example fh(x formulated framework fuzzy constraints fuzzy goal fuzzy ideal solution fuzzy linear programming fuzzy numbers fuzzy optimization problem fuzzy set theory fuzzy subset fuzzy utility grade of membership HA(x Hamming distance imprecise spatial interregional equilibrium Leung linear programming problem linguistic proposition mathematical matrix maximal membership function min-max min-operator models multiobjective objective function objectives and fuzzy obtained by solving operators optimal control optimal solution ordinary set output Ponsard possibility distribution precise constraints precise objectives probability theory randomness regions respectively satisfaction function similarity similarity matrix spatial analysis spatial choice spatial partial equilibrium spatial planning problems spatial systems spatial units state-transition sup sup tion tolerance interval transitive closure utility function xt+l