A fuzzy cognitive map (FCM) is a

cognitive map A cognitive map is a type of mental representation which serves an individual to acquire, code, store, recall, and decode information about the relative locations and attributes of phenomena in their everyday or metaphorical spatial environment. T ...

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. Fuzzy cognitive maps were introduced by

Bart Kosko Bart Andrew Kosko (born February 7, 1960) is a writer and professor of electrical engineering and law at the University of Southern California (USC). He is a researcher and popularizer of fuzzy logic, neural networks, and noise, and author of sev ...

Robert Axelrod Robert Marshall Axelrod (born May 27, 1943) is an American political scientist. He is Professor of Political Science and Public Policy at the University of Michigan where he has been since 1974. He is best known for his interdisciplinary work o ...

introduced cognitive maps as a formal way of representing social scientific knowledge and modeling decision making in social and political systems, then brought in the computation.

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Fuzzy cognitive maps are signed fuzzy digraphs. They are visually similar to, but distinct from, Hasse diagrams.

Spreadsheet A spreadsheet is a computer application for computation, organization, analysis and storage of data in tabular form. Spreadsheets were developed as computerized analogs of paper accounting worksheets. The program operates on data entered in c ...

s or tables are used to map FCMs into

matric Matriculation is the formal process of entering a university, or of becoming eligible to enter by fulfilling certain academic requirements such as a matriculation examination. Australia In Australia, the term "matriculation" is seldom used now ...

es for further computation. FCM is a technique used for causal knowledge acquisition and representation, it supports causal knowledge reasoning process and belong to the

neuro-fuzzy In the field of artificial intelligence, neuro-fuzzy refers to combinations of artificial neural networks and fuzzy logic. Overview Neuro-fuzzy hybridization results in a hybrid intelligent system that these two techniques by combining the human ...

system that aim at solving decision making problems, modeling and simulate complex systems. Learning algorithms have been proposed for training and updating FCMs weights mostly based on ideas coming from the field of

Artificial Neural Network Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains. An ANN is based on a collection of connected unit ...

s. Adaptation and learning methodologies used to adapt the FCM model and adjust its weights. Kosko and Dickerson (Dickerson & Kosko, 1994) suggested the Differential

Hebbian Learning Hebbian theory is a neuroscientific theory claiming that an increase in synaptic efficacy arises from a presynaptic cell's repeated and persistent stimulation of a postsynaptic cell. It is an attempt to explain synaptic plasticity, the adaptatio ...

(DHL) to train FCM. There have been proposed algorithms based on the initial Hebbian algorithm; others algorithms come from the field of

genetic algorithms In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...

, swarm intelligence and evolutionary computation. Learning algorithms are used to overcome the shortcomings that the traditional FCM present i.e. decreasing the human intervention by suggested automated FCM candidates; or by activating only the most relevant concepts every execution time; or by making models more transparent and dynamic. Fuzzy cognitive maps (FCMs) have gained considerable research interest due to their ability in representing structured knowledge and model complex systems in various fields. This growing interest led to the need for enhancement and making more reliable models that can better represent real situations. A first simple application of FCMs is described in a bookWilliam R. Taylor:
Lethal American Confusion
(How Bush and the Pacifists Each Failed in the War on Terrorism)'', 2006, (FCM application in chapter 14) of William R. Taylor, where the war in Afghanistan and Iraq is analyzed. In

's book ''Fuzzy Thinking'',Bart Kosko: ''Fuzzy Thinking'', 1993/1995, (Chapter 12: Adaptive Fuzzy Systems)'' several Hasse diagrams illustrate the use of FCMs. As an example, one FCM quoted from Rod TaberRod Taber: ''Knowledge Processing with Fuzzy Cognitive Maps'', Expert Systems with Applications, vol. 2, no. 1, 83-87, 1991 (

Hasse diagram In order theory, a Hasse diagram (; ) is a type of mathematical diagram used to represent a finite partially ordered set, in the form of a drawing of its transitive reduction. Concretely, for a partially ordered set ''(S, ≤)'' one represents ...

in German Wikipedia) describes 11 factors of the American cocaine market and the relations between these factors. For computations, Taylor uses pentavalent logic (scalar values out of ). That particular map of Taber uses trivalent logic (scalar values out of ). 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 and decision support. *In economics, FCMs support the use of game theory in more complex settings. * In education for modeling Critical Success Factors of

Learning Management Systems A learning management system (LMS) is a software application for the administration, documentation, tracking, reporting, automation, and delivery of educational courses, training programs, materials or learning and development programs. The learni ...

. * In medical applications to model systems, provide diagnosis, develop

decision support systems A decision support system (DSS) is an information system that supports business or organizational decision-making activities. DSSs serve the management, operations and planning levels of an organization (usually mid and higher management) and ...

and medical assessment. * In engineering for

modeling A model is an informative representation of an object, person or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin ''modulus'', a measure. Models c ...

and

control Control may refer to: Basic meanings Economics and business * Control (management), an element of management * Control, an element of management accounting * Comptroller (or controller), a senior financial officer in an organization * Controllin ...

mainly of complex systems and reliability engineering *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 systems 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, risk analysis and assessment, IT scenarios FCMappers is an international online community for the analysis and the visualization of fuzzy cognitive maps. FCMappers offer support for starting with FCM and also provide a

Microsoft Excel Microsoft Excel is a spreadsheet developed by Microsoft for Windows, macOS, Android and iOS. It features calculation or computation capabilities, graphing tools, pivot tables, and a macro programming language called Visual Basic for App ...

-based tool that is able to check and analyse FCMs. The output is saved as Pajek file and can be visualized within third party software like Pajek, Visone, etc. They also offer to adapt the software to specific research needs. Additional FCM software tools, such as Mental Modeler, have recently been developed as a decision-support tool for use in

social science Social science is one of the branches of science, devoted to the study of societies and the relationships among individuals within those societies. The term was formerly used to refer to the field of sociology, the original "science of so ...

research, collaborative decision-making, and natural resource planning.

References

{{Reflist, 30em Knowledge representation Fuzzy logic

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References