Fuzzy logic approach for sustainable land use planning
|Novaline Jacob and Krishnan R
|The task of rating land suitability is to classify areas into land use classes according to their land characteristics. By representing areas as vectors in a feature space, one can use the distance between feature vector corresponding to an area and a land use class as a measure of their similarity. The similarity indicates the extent to which the area belongs to the land use class. To measure the similarity, we define a representative vector for each land use class and view the distance between an area vector and the representative vector as the distance between the vector and the class.
Highest Suitability (S1) – Lowest Suitability (S5)
Ci = Representative Pattern Vector of
i = land use class
Ci = (Ci1, Ci2, Ci3,…..Cin) n = No.
of physiographical characteristics /
A = Area Vector
A generalized family of distance metrics, dependent on the exponent p, for
estimating the distance between Area Vector & Class pattern vector can be expressed as (Zeleny 1982, pp. 317) :
Where βj is the weight assigned to the parameter j and p ranges from 1 to α.
Varying p affects the relative contribution of individual deviations from the representative pattern vector, a greater emphasis being given to larger deviations as p tends towards a (Jose & Lucien, This distance metric as usually applied includes a sensitivity analysis for the three strategic values: p = 1,2 and a nominal a (i.e p > 10). When p = 1 (a ‘city block’ distance metric), total compensation between criteria is assumed, meaning that a decrease of one unit of one criterion can be totally compensated by an equivalent gain on any other criterion. For p = 2 (a straight line, Euclidean or the shortest distance metric) there is only partial compensation and p = a represents a totally non-compensatory situation (Zeleny 1982, pp.322-325). In the present implementation a value of 4 has been assigned to p after doing the sensitivity analysis for values between 1 and 10 for p. The smaller the distance, the more similar or suitable is the area to the land use class in terms of the land qualities.
In Conventional Classification, A e Ci, if dE(A,Ci) < distance to all other land use classes / Objectives.
This decision rule defines sharp decision surfaces between classes such that a vector can be classified into a single class and the classification implies a full membership in that class. Such a method is referred to as a hard partition of feature space.
The method developed in this research is characterized by a fuzzy partition of feature space. The fuzzy classification method enables one to rate an area’s suitability by comprehensively taking into consideration all its characteristics and all the land cover classes. An area can be classified into the most similar land cover class. However, the classical set theory-based decisionmaking leads to serious information loss. This can be explained by taking two areas as examples. In determining their suitability for a given crop, the distances from the vector of the first area to the four classes are 0.50, 0.40, 0.10 and 0.00 respectively. The distances from the vector of the second area to the classes are 0.90, 0.10, 0.00 and 0.00. According to conventional classification, both areas should be classified into class 1. But, clearly the first area is much less suitable for the crop than the second area. The information contained in the distances is discarded when the area’s memberships are determined. To make fuller use of the information, a fuzzy partition of feature space can be used. This method helps to suggest first best crop/land use, second best crop/ land use and so on for the same area.
In a fuzzy partition, the classes are defined as fuzzy sets. An area can be associated with partial membership and belong to different classes to different extents. A fuzzy set is characterized by its membership function. We define membership function fc for land use class c as, In Fuzzy Classification,
fci(A) – Membership function fc for land
use class Ci
m – no. of classes
Σ dE(A,Ci) serves as a normalizing
For a given area, membership functions are defined for each land use class. By calculating the functions, each area will have membership grades to all the land use classes, indicating the extent to which this area belongs to each of the land use class.
In case, the physiographical characteristics of an area are equal to those of the representative vector of suitability class C, that is
dE(A,Ci) = 0,
the membership grade of the area in class C is defined as 1 and the grades in other classes as 0s. This implies that this area can be exactly categorized into class C. Steps Involved:
Step 1: Normalize the Area values and Pattern Vector values for each class
Step 2: Compute the distance between Pattern Vector and Area Vector
Step 3: Convert the distances into Partial Membership functions.