Add an antecedent to an FSI model — fsi_add

fsi_add_fsa() adds a fuzzy spatial antecedent to a fuzzy spatial inference (FSI) model. A fuzzy spatial antecedent corresponds to a layer of fuzzy spatial objects (i.e., spatial plateau objects) that describe the different characteristics of the problem. The antecedent has a linguistic variable and its fuzzy spatial objects have linguistic values so that they are used in the IF part of fuzzy rules.

Usage

fsi_add_fsa(fsi, lvar, tbl)

Arguments

fsi: The FSI model instantiated with the fsi_create() function.
lvar: A character value that represents a linguistic variable of the antecedent.
tbl: A tibble with spatial plateau objects annotated with linguistic values of the linguistic variable specified by the above lvar parameter.

Value

An FSI model populated with a fuzzy spatial antecedent.

Details

The fsi_add_fsa() function adds a fuzzy spatial antecedent composed of a linguistic variable and its corresponding pgeometry objects annotated by linguistic values. The format of tbl is the same as the output of the function spa_creator(), allowing users to directly provide plateau region objects as input when designing FSI models.

References

Carniel, A. C.; Galdino, F.; Philippsen, J. S.; Schneider, M. Handling Fuzzy Spatial Data in R Using the fsr Package. In Proceedings of the 29th International Conference on Advances in Geographic Information Systems (AM SIGSPATIAL 2021), pp. 526-535, 2021.

Underlying concepts and formal definitions of FSI models are introduced in:

Carniel, A. C.; Schneider, M. Fuzzy inference on fuzzy spatial objects (FIFUS) for spatial decision support systems. In Proceedings of the 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2017), pp. 1-6, 2017.

Examples

library(tibble)

trap_mf <- function(a, b, c, d) {
  function(x) {
    pmax(pmin((x - a)/(b - a), 1, (d - x)/(d - c), na.rm = TRUE), 0)
  }
}

trim_mf <- function(a, b, c) {
  function(x) {
    pmax(pmin((x - a)/(b - a), (c - x)/(c - b), na.rm = TRUE), 0)
  }
}

# Creating spatial plateau objects for the linguistic variable "accommodation price"
lvals_accom_price <- c("cut-rate", "affordable", "expensive")
cut_rate_mf <- trap_mf(0, 0, 10, 48)
affordable_mf <- trap_mf(10, 48, 80, 115)
expensive_mf <- trap_mf(80, 115, 10000, 10000)

# Example of point dataset
accom_price <- tibble(longitude = c(-74.0, -74.0, -74.0), 
                      latitude = c(40.8, 40.75, 40.7),
                      price = c(150, 76, 60))
 
accom_price_layer <- spa_creator(accom_price, classes = lvals_accom_price, 
                         mfs = c(cut_rate_mf, affordable_mf, expensive_mf))
                         
# Creating the FSI model
fsi <- fsi_create("To visit or not to visit, that is the question", 
                  default_conseq = trim_mf(10, 30, 60))

# Adding the fuzzy spatial antecedent to the FSI model
fsi <- fsi_add_fsa(fsi, "accommodation price", accom_price_layer)