fcm.infer: Fuzzy Cognitive Maps (FCMs) Inference

Description Usage Arguments Value Author(s) References Examples

Description

Estimates the Inference of a Fuzzy Cognitive Map. FCM is proven to be capable of causal inference and is applicable to complex decision problems where numerous interlinked dependent variables influence one another.

Usage

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fcm.infer(activation_vec, weight_mat, iter = 20, infer = "k",
  transform = "s", lambda = 1, e = 0.001)

Arguments

activation_vec

1 x m dataframe which contains the initial concept values. A concept is turned on or activated by making its vector element 1 or 0 or in [0, 1].

weight_mat

m x m dataframe which stores the weights assigned to the pairs of concepts. The weights are usually normalized to the interval [0, 1] or [-1, +1].

iter

The required number of iterations in order to reach the FCM convergence. Defaults to 20.

infer

Select an Inference Rule ('k' Kosko, 'mk' modified Kosko, 'r' Rescale,'kc' Kosko-clamped, 'mkc' modified Kosko-clamped or 'rc' Rescale-clamped). Default value is set to 'k'

transform

Contains the Transformation functions ('b' Bivalent, 'tr' Trivalent, 's' Sigmoid or 't' Hyperbolic tangent). The transformation function is used to reduce unbounded weighted sum to a certain range, which hinders quantitative analysis, but allows for qualitative comparisons between concepts. Default value is set equal to 's'.

lambda

A parameter that determines the steepness of the sigmoid and hyperbolic tangent function at values around 0. Different lambda value may perform more appropriate for different problems.

e

Epsilon (e) is a residual, describing the minimum error difference among the subsequent concepts. Its value depends on the application type. Defaults to to 0.001.

Value

Returns iter x m dataframe which contains the concepts' values of each iteration after the the transformation function.

Author(s)

Zoumpolia Dikopoulou <[email protected]>, <[email protected]>

Elpiniki Papageorgiou <[email protected]>, <[email protected]>

References

B. Kosko, "Fuzzy cognitive maps", International Journal of Man-Machine Studies 24, p.p. 65-75, 1986.

Groumpos, P.P, Stylios, C.D.; "Modelling supervisory control systems using fuzzy cognitive maps", Chaos, Solitons & Fractals, Volume 11, Issues 1–3, p.p. 329–336, 2000.

Papageorgiou E.I., "Fuzzy Cognitive Maps for Applied Sciences and Engineering From Fundamentals to Extensions and Learning Algorithms", Intelligent Systems Reference Library, Volume 54, 2014.

Papageorgiou E.I., Stylios C.D., GroumposP.P. , "Unsupervised learning techniques for finetuning fuzzy cognitive map causal links.", Int. J. Human Comput. Stud. Vol. 64, pp. 727–743, 2006.

Examples

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## Not run: 
# Example for the FCM inference


### Input data

act.vec <- data.frame(1, 1, 1, 0, 0, 0)    # Create the activation vector
colnames(act.vec) <- c("C1", "C2", "C3", "C4", "C5", "C6")  # Change the column names

C1 = c(0.0, 0.0, 0.6, 0.9, 0.0, 0.0)
C2 = c(0.1, 0.0, 0.0, 0.0, 0.0, 0.0)
C3 = c(0.0, 0.7, 0.0, 0.0, 0.9, 0.0)
C4 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.9)
C5 = c(0.0, 0.0, 0.0, 0.0, 0.0, -0.9)
C6 = c(-0.3, 0.0, 0.0, 0.0, 0.0, 0.0)
C7 = c(0.0, 0.0, 0.0, 0.0, 0.0, 0.8)

# Create the weight matrix
w.mat <- matrix(c(C1, C2, C3, C4, C5, C6), nrow = 6, ncol = 6, byrow = TRUE)
colnames(w.mat) <- c("C1", "C2", "C3", "C4", "C5", "C6")
w.mat <- as.data.frame(w.mat)



### Select the arguments for the fcm.infer function

output <- fcm.infer(act.vec, w.mat, 25, "r", "s")
View(output$values)          # View the concept values for each iteration


### Visualize the concepts' values for each state

library (reshape2)
library (ggplot2)
iterations <- as.numeric(rownames(output$values))  # create a numeric vector named "iterations"
df <- data.frame(iterations, output$values)   # add "iterations" in the "output$values" dataframe
df2 <- melt(df, id="iterations")   #transform df into long formats
ggplot(data=df2,
       aes(x=iterations, y=value, group=variable, colour=variable)) +
       theme_bw() + geom_line(size=0.7) + geom_point(size = 3)


## End(Not run)

LiaDD/Fuzzy-Cognitive-Maps-FCMs documentation built on May 5, 2019, 3:48 p.m.