Geoscience Reference
In-Depth Information
12 Fuzzy Modelling
Peter F. Fisher and Vincent B. Robinson
CONTENTS
Abstract .......................................................................................................................................... 283
12.1 Introduction .......................................................................................................................... 283
12.2 Sorites Paradox ..................................................................................................................... 285
12.3 Classical Sets and Boolean Logic ......................................................................................... 286
12.4 Fuzzy Set Theory .................................................................................................................. 288
12.5 Fuzzy Memberships .............................................................................................................. 289
12.5.1 Direct Assignment .................................................................................................... 290
12.5.2 Indirect Assignment.................................................................................................. 293
12.5.3 Assignment by Transformation................................................................................. 293
12.6 Fuzzy Logic .......................................................................................................................... 295
12.7 Fuzzy Regression .................................................................................................................. 299
12.8 Type-2 Fuzzy Sets .................................................................................................................300
12.9 Conclusions ...........................................................................................................................300
References ...................................................................................................................................... 301
ABSTRACT
Fuzzy sets are one of the ways in which modern GeoComputation (GC) can be enriched. Many
geographical phenomena can be considered to be vague or poorly defined. Vagueness has a long
history in the philosophical literature and is considered by some workers to be one of the major
problems for geography in general and geographical information in particular. The semantic
form of vagueness is directly addressed by fuzzy set theory; this chapter discusses how geo-
graphical objects and processes may be modelled by fuzzy sets and shows some novel products
from that modelling. Approaches using direct assignment, indirect assignment and assignment by
transformation are illustrated and discussed. The application of fuzzy logic and fuzzy modelling
is also identified.
12.1 INTRODUCTION
The modelling of fuzzy phenomena in GeoComputation (GC) addresses what has been called
one of the principal philosophical issues for geography: vagueness (Varzi, 2001a,b). Moreover,
exploitation of fuzzy concepts has produced a whole field of soft computing and soft set theo-
ries. The distinction between fuzzy sets and hard, crisp or classical sets, put simply, is one of
opposing qualities. Varzi (2001a) asks questions such as where exactly is the longest river, highest
mountain or largest city on earth, but he considers them to be profoundly unknowable, because
geographical expressions such as river, city and mountain are soft or vague concepts and more
importantly the positions of instances of proper nouns such as Amazon, Tokyo or Everest (if those
are indeed candidates for these geographical superlatives) cannot be unequivocally defined. As
Fisher et al. (2004) point out, the summit of a mountain (the highest point) can be precisely identi-
fied but it is trivial and the term mountain is not synonymous with the term summit . Indeed, the
283
 
Search WWH ::




Custom Search