journal of forest science

Membership value
Membership value
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Fig. 4. Membership functions for fuzzy sets used in fuzzy reasoning mechanism
THEN y = 0.3x – 20x + 0.5x + 6x (Big)
3 1 2 3 4
I x is ‘Small or Medium’ and x is ‘Medium or
1 2
Small’ and x is ‘Big or Medium’ and x is ‘Small’
3 4
THEN y = 0.2x – 30x + 0.3x + 4x (Medium)
4 1 2 3 4
I x is ‘Small or Medium’ and x is ‘Medium or
1 2
Small’ and x is ‘Small’ and x is ‘Big or Medium’
3 4
THEN y = 0.1x – 40x + 0.1x + 2x (Small)
5 1 2 3 4
I x is ‘Small or Medium’ and x is ‘Medium or
1 2
Small’ and x is ‘Small’ and x is ‘Small’
3 4
THEN y = –5x – 50x – 0.5x – 20x (Very Small)
6 1 2 3 4
where x , x , x and x are the factors such as the distance be-
1 2 3 4
tween passing points, gradient between passing points, horizontal
distance toward the point on the road end and the vertical
distance toward the point on the road end. These factors are
described in detail in YOSHIMURA (1997).
The membership functions shown in ig. 4 are applied
to the actual values for four factors to determine the degree
of truth for the premise of each rule.
The method for selecting passing points and laying out
gradelines differs from the method described by
YOSHIMURA (1997) in two ways:
1. The cells where the estimated skidding distance does
not exceed the technological length of a cableway system
route or effective tractor skidding distance are selected
as possible passing points.
2. The passing points are interconnected by applying
a directional path distance model (GAO et al. 1996)
implemented in the Arc/Info GRID module PATHDIS-
TANCE. The path distance model automatically lays
out the gradeline between passing points using an additional
factor in the distance measure (surface, gradi-
ent and horizontal direction factor). This model enables
the expression of criteria which influence the
location of the road called “friction”. The friction indicates
the absolute/relative cost or degree of risk assessment
of moving through each cell. Minimizing the
friction between two passing points is controlled by
a gradient factor which takes into consideration the
effect of the value gradient from a cell to its neighbours.
The formula used to calculate the lowest total cost to
each of the neighbours and control gradeline projection
is:
CostDistance = SurfaceDistance × Verticalactor
Vertical factor
(y-axis)
Fig. 5. The binary vertical factor graph used in the PATH-
DISTANCE function
310 J. FOR. SCI., 47, 2001 (7): 307–313
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