Fuzzy Cognitive Mapping

Description

This package provides several functions to create and manipulate fuzzy cognitive maps.It is based on FCMapper for Excel, distributed at http://www.fcmappers.net/joomla/, developed by Michael Bachhofer and Martin Wildenberg.

Maps are inputted as adjacency matrices. Attributes of the maps and the equilibrium values of the concepts (including with user-defined contrained values) can be calculated. The maps can be graphed with a function that calls "igraph". Multiple maps with shared concepts can be aggregated.

Details

Functions:

-changes.scenario: Finds equilibrium values of concepts with no fixes values.

-check.matrix: Checks that fuzzy cognitive map is square and values are between -1 and 1.

-combine.maps: Aggregates multiple fuzzy cognitive maps into one.

-comp.scenarios: Compares the equilibrium values of two scenarios.

-comp.maps: Calculates similarity indices (S2 and Jaccard) of two coginitive maps.

-concept.indices: Calculated concept-level indices.

-graph.fcm: Plots fuzzy cognitive map by calling igraph package

-matrix.indices: Calculates matrix-level indices.

-nochanges.scenario: Finds equilibrium values of concepts with user-defined fixed values.

Author(s)

Shaun Turney and Michael Bachhofer

Maintainer: Shaun Turney <shaun.turney@mail.mcgill.ca>

References

http://www.fcmappers.net/

Kosko, B. (1986). Fuzzy cognitive maps. International journal of man-machine studies, 24(1), 65-75.

Glykas, M. (2010). Fuzzy Cognitive Maps. Advances in Theory, Methodologies, Tools and Applications, Series: Studies in Fuzziness and Soft Computing.

Ozesmi, U., & Ozesmi, S. L. (2004). Ecological models based on people's knowledge: a multi-step fuzzy cognitive mapping approach. Ecological Modelling, 176(1), 43-64.

Scenario with fixed values

Description

The equilibrium values of the concepts in a fuzzy cognitive map are calculated. One or more concept values can be fixed by the user to be within 0 or 1. At each iteration (time step) the fixed concepts are set back to their chosen values. A plot of the concept values over the iterations is given.

Usage

changes.scenario(matrix, concept.names, iter, set.concepts, set.values)

Arguments

Details

The fuzzy cognitive map should be in the form of quantitative adjacency matrices. The concept.names input is the names of the concepts in thefuzzy cognitive map. set.concepts is a character vector of the concepts the user wishes to fix, while set.values gives the desired values in the same order.

Value

A dataframe containing the equilibrium values of the concepts. If equilibrium has not been reached a warning will be printed. A plot of the concept values over the iterations is given.

Author(s)

Shaun Turney

See Also

nochanges.scenario

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

changes.scenario(matrix,concept.names,iter=25,set.concepts=c("B","G"),set.values=c(0.5,0))

Matrix validation

Description

The fuzzy cognitive map is checked to confirm that it is square and all values are within -1 and 1.

Usage

check.matrix(matrix)

Arguments

Details

The fuzzy cognitive map should be in the form of a quantitative adjacency matrix.

Value

If the matrix is not square then a warning will be printed. If the matrix contains values not between -1 and 1 then a warning will be printed along with the identify of the offending values. If the matrix is square or has no values outside of -1 and 1 then a confirmation is printed. The function checks the diagonal to determine whether there are self-loops and gives a warning if there are.

Author(s)

Shaun Turney

Examples

#Is not square and contains values outside of -1 and 1: 
matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,2,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(-5,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)

#Check
check.matrix(matrix)

#Matrix without issues:
matrix2 = matrix(nrow=7,ncol=7)
matrix2[1,] = c(0,-0.5,0,0,1,0,1)
matrix2[2,] = c(1,0,1,0.2,0,0,0.6)
matrix2[3,] = c(0,1,0,0,0,0,0)
matrix2[4,] = c(0.6,0,0,1,0,0,0.1)
matrix2[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix2[6,] = c(0,0,-1,0,0,0,0)
matrix2[7,] = c(0,0,0,-0.5,0,0,1)

#Check
check.matrix(matrix2)

Map aggregator

Description

Aggregates two fuzzy cognitive maps into one.

Usage

combine.maps(matrix1, matrix2, concept.names1, concept.names2)

Arguments

Details

The fuzzy cognitive maps should be in the form of quantitative adjacency matrices. The concept.names inputs are the names of the concepts in the first and second fuzzy cognitive maps, respectively.

Value

An aggregated fuzzy cognitive map in adjacency matrix format. It contains the edges and concepts of the two inputted fuzzy cognitive maps. Edges which are shared between the two fuzzy cognitive maps are averaged in the aggregated map.

Author(s)

Shaun Turney

Examples

#Matrix 1
matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

#Matrix 2
matrix2 = matrix(nrow=6,ncol=6)
matrix2[1,] = c(0,1,0,1,0,0)
matrix2[2,] = c(-1,1,0,-1,0,1)
matrix2[3,] = c(0,0,1,0,0,1)
matrix2[4,] = c(-1,0,0,0,0,0)
matrix2[5,] = c(0,0.5,0,0,1,0) 
matrix2[6,] = c(1,0,0,-1,0,0)
concept.names2 = c("E","F","G","H","I","J")

#Aggregate
combine.maps(matrix1=matrix,matrix2=matrix2,concept.names1=
concept.names,concept.names2=concept.names2)

Map comparison

Description

Calculates similarity indices (S2 and Jaccard) of two coginitive maps.

Usage

  comp.maps(concept.names1,concept.names2)

Arguments

Value

The S2 and Jaccard similarity indices are calculated. S2 is the proportion of concepts that are shared between the two concept maps. Jaccard is calculated as a/(a+b+c) where "a is the number of concepts shared by the two maps, "b is the number of concepts present only in Map 1, and "c" is the number of concepts present only in Map 2.

Author(s)

Shaun Turney

See Also

changes.scenario nochanges.scenario

Examples

  concept.names1 = c("A","B","C","D","E","F","G")
  concept.names2 = c("C","D","E","F","G","H")
  
  comp.maps(concept.names1,concept.names2)

Scenario comparison

Description

The equilibrium values of two scenarios are compared.

Usage

comp.scenarios(scenario1, scenario2)

Arguments

Value

The difference between the equilibrium values of the two scenarios are given in a data frame along with the concept names, the scenario 1 values, the scenario 2 values, and the percent difference.

Note

The scenarios must be scenarios of fuzzy cognitive maps with the same concepts, though not neccesarily the same edges.

Author(s)

Shaun Turney

See Also

changes.scenario nochanges.scenario

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

scenario1 = nochanges.scenario(matrix,iter=25,concept.names)

scenario2 = changes.scenario(matrix,concept.names,iter=25,set.concepts=c("B"),set.values=c(0.5))

comp.scenarios(scenario1,scenario2)

Concept indices

Description

Concept-level indices are calculated, including the out-degree, in-degree, centrality, and whether it is a transmitter, reveiver, ordinary or unconnected concept.

Usage

concept.indices(matrix, concept.names)

Arguments

Details

The fuzzy cognitive map should be in the form of a quantitative adjacency matrix. The concept.names input is the names of the concepts in the fuzzy cognitive map.

Value

A dataframe containing the concept name, out-degree, in-degree, centrality, and whether it is a transmitter, reveiver, ordinary or unconnected concept.

Author(s)

Shaun Turney

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

concept.indices(matrix,concept.names)

Fuzzy cognitive map graph

Description

Creates a visual representation (circles and arrows) of the fuzzy cognitive map by calling igraph. The thickness of the arrows is determined by the magnitude of the edge value. Negative edges are red while positive edges are black.The size of the circles (concepts) is defined by the user.

Usage

graph.fcm(matrix, concept.sizes, concept.names)

Arguments

Details

The fuzzy cognitive maps should be in the form of quantitative adjacency matrices. The concept.names input is the names of the concepts in the fuzzy cognitive map. The concept.sizes is a vector of values between 0 and 1 and determines the size of the circles. The user may want to define concept.sizes as the equilibrium values of the concepts.

Value

An igraph plot with circles representing concepts and arrows representing edges.

Author(s)

Shaun Turney

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

results = nochanges.scenario(matrix,iter=25,concept.names)

graph.fcm(matrix,concept.sizes=results$Equilibrium_value,concept.names)

Matrix indices

Description

Matrix-level indices are calculated, including the number of connections, connection density, number of concepts, number of transmitters, number of receivers, number of no connections, number of ordinary, number of self-loops, connections per variable, complexity, and hierarchy.

Usage

matrix.indices(matrix)

Arguments

Details

The fuzzy cognitive maps should be in the form of a quantitative adjacency matrix.

Value

A dataframe containing the number of connections, connection density, number of concepts, number of transmitters, number of receivers, number of no connections, number of ordinary, number of self-loops, connections per variable, complexity, and hierarchy.

Author(s)

Shaun Turney

References

Ozesmi, U., & Ozesmi, S. L. (2004). Ecological models based on people's knowledge: a multi-step fuzzy cognitive mapping approach. Ecological Modelling, 176(1), 43-64.

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

matrix.indices(matrix)

Scenario with no fixed values

Description

The equilibrium values of the concepts in a fuzzy cognitive map are calculated. A plot of the concept values over the iterations is given. It activates the matrix with a vector of 1s and squeezes the resulting vector with a logic function. The function checks for convergence and gives a warning if convergence isn't reached. A plot of the concept values over the iterations is given.

Usage

nochanges.scenario(matrix, concept.names, iter)

Arguments

Details

The fuzzy cognitive map should be in the form of quantitative adjacency matrices. The concept.names input is the names of the concepts in thefuzzy cognitive map.

Value

A dataframe containing the equilibrium values of the concepts. If equilibrium has not been reached a warning will be printed. A plot of the concept values over the iterations is given.

Author(s)

Shaun Turney

See Also

nochanges.scenario

Examples

matrix = matrix(nrow=7,ncol=7)
matrix[1,] = c(0,-0.5,0,0,1,0,1)
matrix[2,] = c(1,0,1,0.2,0,0,0.6)
matrix[3,] = c(0,1,0,0,0,0,0)
matrix[4,] = c(0.6,0,0,1,0,0,0.1)
matrix[5,] = c(0,0.5,0,0,1,0,-0.6) 
matrix[6,] = c(0,0,-1,0,0,0,0)
matrix[7,] = c(0,0,0,-0.5,0,0,1)
concept.names = c("A","B","C","D","E","F","G")

nochanges.scenario(matrix,iter=25,concept.names)