Fuzzy cognitive map
Encyclopedia
A Fuzzy cognitive map is a cognitive map
within which the relations between the elements (e.g. concepts, events, project resources) of a "mental landscape" can be used to compute the "strength of impact" of these elements. The theory behind that computation is fuzzy logic
.
Fuzzy cognitive maps are signed fuzzy digraphs. They may look at first blush like Hasse diagrams but they are not.
Spreadsheet
s or tables are used to map FCMs into Matric
es for further computation.
A collection of papers with applications in various disciplines is presented in the book "Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Applications and Tools edited by Michael Glykas and prefaced by Bart Kosko. A simple application of FCMs is described in a book of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko
's book Fuzzy Thinking, several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod Taber describes 11 factors of the American cocaine market and the relations between these factors. For computations, Taylor uses pentavalent logic (scalar values out of {-1,-0.5,0,+0.5,+1}). That particular map of Taber uses trivalent logic (scalar values out of {-1,0,+1}). Taber et al. also illustrate the dynamics of map fusion and give a theorem on the convergence of combination in a related article
While applications in social sciences introduced FCMs to the public, they are used in a much wider range of applications, which all have to deal with creating and using models of uncertainty and complex processes and systems. Examples:
FCMappers - an international online community for the analysis and the visualization of fuzzy cognitive maps offer support for starting with FCM and also provide a MS-Excel based tool that is able to check and analyse FCMs. The output is saved as Pajek file and can be visualized within 3rd party software like Pajek, Visone,... . They also offer to adapt the software to specific research needs. On their webpage you also will find a linklist for interesting scientific articles, related software, institutes, people and projects. The FCMappers have about one thousand registered members worldwide.
Cognitive map
Cognitive maps are a type of mental processing composed of a series of psychological transformations by which an individual can acquire, code, store, recall, and decode information about the relative locations and attributes of phenomena in their everyday or metaphorical spatial environment.The...
within which the relations between the elements (e.g. concepts, events, project resources) of a "mental landscape" can be used to compute the "strength of impact" of these elements. The theory behind that computation is fuzzy logic
Fuzzy logic
Fuzzy logic is a form of many-valued logic; it deals with reasoning that is approximate rather than fixed and exact. In contrast with traditional logic theory, where binary sets have two-valued logic: true or false, fuzzy logic variables may have a truth value that ranges in degree between 0 and 1...
.
Fuzzy cognitive maps are signed fuzzy digraphs. They may look at first blush like Hasse diagrams but they are not.
Spreadsheet
Spreadsheet
A spreadsheet is a computer application that simulates a paper accounting worksheet. It displays multiple cells usually in a two-dimensional matrix or grid consisting of rows and columns. Each cell contains alphanumeric text, numeric values or formulas...
s or tables are used to map FCMs into Matric
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
es for further computation.
A collection of papers with applications in various disciplines is presented in the book "Fuzzy Cognitive Maps: Advances in Theory, Methodologies, Applications and Tools edited by Michael Glykas and prefaced by Bart Kosko. A simple application of FCMs is described in a book of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. And in Bart Kosko
Bart Kosko
Bart Andrew Kosko is a writer and professor of electrical engineering and law at the University of Southern California...
's book Fuzzy Thinking, several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod Taber describes 11 factors of the American cocaine market and the relations between these factors. For computations, Taylor uses pentavalent logic (scalar values out of {-1,-0.5,0,+0.5,+1}). That particular map of Taber uses trivalent logic (scalar values out of {-1,0,+1}). Taber et al. also illustrate the dynamics of map fusion and give a theorem on the convergence of combination in a related article
While applications in social sciences introduced FCMs to the public, they are used in a much wider range of applications, which all have to deal with creating and using models of uncertainty and complex processes and systems. Examples:
- In business FCMs can be used for product planning.
- In economics, FCMs support the use of game theoryGame theoryGame theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
in more complex settings. - In project planning FCMs help to analyze the mutual dependencies between project resources.
- In robotics FCMs support machines to develop fuzzy models of their environments and to use these models to make crisp decisions.
- In computer assisted learning FCMs enable computers to check, whether students understand their lessons.
- In expert systemExpert systemIn artificial intelligence, an expert system is a computer system that emulates the decision-making ability of a human expert. Expert systems are designed to solve complex problems by reasoning about knowledge, like an expert, and not by following the procedure of a developer as is the case in...
s a few or many FCMs can be aggregated into one FCM in order to process estimates of knowledgeable persons. - In IT project management, a FCM-based methodology helps to success modelling .
FCMappers - an international online community for the analysis and the visualization of fuzzy cognitive maps offer support for starting with FCM and also provide a MS-Excel based tool that is able to check and analyse FCMs. The output is saved as Pajek file and can be visualized within 3rd party software like Pajek, Visone,... . They also offer to adapt the software to specific research needs. On their webpage you also will find a linklist for interesting scientific articles, related software, institutes, people and projects. The FCMappers have about one thousand registered members worldwide.