fsr (version 1.0.0)

fsr_geometric_operations: Fuzzy geometric set operations

Description

Fuzzy geometric set operations are given as a family of functions that implements spatial plateau set operations. These functions produces a spatial plateau object from a specific combination of other two spatial plateau objects, such as the intersection of two plateau region objects.

Usage

spa_intersection(pgo1, pgo2, itype = "min")
spa_union(pgo1, pgo2, utype = "max")
spa_difference(pgo1, pgo2, dtype = "f_diff")
spa_common_points(pline1, pline2, itype = "min")

Arguments

pgo1

A pgeometry object of any type.

pgo2

A pgeometry object of the same type of pgo1.

itype

A character value that indicates the name of a function implementing a t-norm. The default value is "min", which is the standard operator of the intersection.

utype

A character value that refers to a t-conorm. The default value is "max", which is the standard operator of the union.

dtype

A character value that indicates the name of a difference operator. The default value is "f_diff", which implements the standard fuzzy difference.

pline1

A pgeometry object of the type PLATEAULINE.

pline2

A pgeometry object of the type PLATEAULINE.

Value

A pgeometry object that is the result of the geometric manipulation between two spatial plateau objects.

Details

These functions implement geometric operations of the spatial plateau algebra. They receive two pgeometry objects of the same type together with an operation as inputs and yield another pgeometry object as output. The output object has the same type of the inputs. The family of fuzzy geometric set operations consists of the following functions:

• spa_intersection computes the geometric intersection of two spatial plateau objects. The membership degree of common points are calculated by using a t-norm operator given by the parameter itype. Currently, it can assume "min" (default) or "prod".

• spa_union computes the geometric union of two spatial plateau objects. The membership degree of common points are calculated by using a t-conorm operator given by the parameter utype. Currently, it can assume "max" (default).

• spa_difference computes the geometric difference of two spatial plateau objects. The membership degree of common points are calculated by using a diff operator given by the parameter dtype. Currently, it can assume "f_diff" (default fuzzy difference), "f_bound_diff" (fuzzy bounded difference), "f_symm_diff" (fuzzy symmetric difference), and "f_abs_diff" (fuzzy absolute difference).

Another related geometric function is:

• spa_common_points which gets the common points of two plateau line objects by using a t-norm to compute their membership degrees. It is different from the other functions since it gets two plateau line objects as input and yields a plateau point object as output.

Other t-norms, t-conorms, and diff operators can be implemented and given as values for the "itype", "utype", and "dtype", respectively. For this, the following steps should be performed:

1 - implement your function that accepts two numeric values as inputs and yields another numeric value as output. All values should be between 0 and 1. Recall that t-norms and t-conorms must have some specific properties according to the fuzzy set theory. 2 - use the name of your function as the character value of the corresponding "itype", "utype", or "dtype".

An example of operator is the source code of f_bound_diff:

f_bound_diff <- function(x, y) { max(0, (x - y)) }

References

Carniel, A. C.; Schneider, M. Spatial Plateau Algebra: An Executable Type System for Fuzzy Spatial Data Types. In Proceedings of the 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2018), pp. 1-8, 2018.

Examples

# NOT RUN {
library(sf)

pts1 <- rbind(c(1, 2), c(3, 2))
pts2 <- rbind(c(1, 1), c(2, 3), c(2, 1))
pts3 <- rbind(c(2, 2), c(3, 3))

cp1 <- component_from_sfg(st_multipoint(pts1), 0.3)
cp2 <- component_from_sfg(st_multipoint(pts2), 0.6)
cp3 <- component_from_sfg(st_multipoint(pts3), 1)

pp1 <- create_pgeometry(list(cp1, cp2, cp3), "PLATEAUPOINT")

pts4 <- rbind(c(0, 0), c(1, 1))
pts5 <- rbind(c(2, 3), c(1.2, 1.9), c(2, 1))
pts6 <- rbind(c(3, 1), c(1.5, 0.5))

cp4 <- component_from_sfg(st_multipoint(pts4), 0.4)
cp5 <- component_from_sfg(st_multipoint(pts5), 1)
cp6 <- component_from_sfg(st_multipoint(pts6), 0.7)

pp2 <- create_pgeometry(list(cp4, cp5, cp6), "PLATEAUPOINT")

pp1
pp2

spa_intersection(pp1, pp2)
spa_intersection(pp1, pp2, itype = "prod") #changing the t-norm
spa_union(pp1, pp2)
spa_difference(pp1, pp2)

# }