FUZZY COGNITIVE MAPS FOR APPLIED SCIENCES AND ENGINEERING

Elpiniki I. PapageorgiouLecturer

Informatics & Computer Technology Department, Technological Educational Institute of Lamia,

3rd km Old National Road Lamia-Arthens, 35100 Lamia, Greece

epapageorgiou@teilam.gr

Overview of Fuzzy Cognitive MapsProposed by Kosko (1986) as an expansion of Cognitive Maps (used for representation of social knowledge).Soft Computing technique (Combination of Fuzzy Logic and Neural Networks)Have emerged as alternative tools for representing the behaviour of systems and peopleMainly designed by experts through an interactive procedure of knowledge acquisition.Consist of concepts and weighted arcs (expressing causality among interconnected Concepts)Two significant characteristics: (1) Causal relationships between nodes are fuzzified (Fuzzy degree of relationship)(2) The system is dynamic involving feedback, where the effect of change in a concept node affects other nodes, which in turn can affect the node initiating the change.

Fuzzy Cognitive Maps

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relation, no expresses ,0causality, negative expresses ,0causality, positive expresses ,0

ij

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ij

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Weighted arcs = causal relations among the nodesAi lie in [0,1], while Wij lie in [-1,1]

Concepts are the key factors of the system (stand for states, variables, inputs, outputs, trends and other characteristics of the system).

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• the new value of C i Concept at time step k

• the value of C i Concept at time step k-1

• the value of C j Concept at time step k-1

• the weight between concept C j and Ci

• f a threshold function : , λ determines grade (usually λ=1).

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FCM simulates till the convergence of concepts’ values to a steady state

Calculation Algorithm for FCMs

FCM simulation processBeginStep 1: Read the input vector A0

Step 2: Give the connection weight matrix - WStep 3: Calculate the concept vector at step k

Step 4: Apply threshold to output vector

Step 5: IF ( or ) STOPElse GO TO Step 1

End

(k ) (k 1) (k 1)

j iA A A W− −

≠

= + ∑

( )(k) (k)A f A=

(k 1) (k 1)A A+ −=(k 1) (k 1)A A 0.001+ −− <

Fuzzy Cognitive MapsAccording to Codara (1998) [4], FCMs can be used for several

purposes, including four functions:

Explanatory. It is focus on reconstructing the premises behind the behavior of a given agent, understanding the reasons for their decisions and for the actions they take, highlighting any distortions and limits in their representation of the situation.Prediction. This function is based on predicting the future decisionsand actions, or the reasons that a given agent will use to justify any new occurrences.Reflective. This function helps decision-makers to ponder over their representation of a given situation in order to ascertain its adequacy and possibly prompt the introduction of any necessary changes.Strategic. The last function is based on generating a more accurate description of a complex situation.

Development of FCMsTwo approaches are used: expert-based and computational-basedExpert-based: rely entirely on human expertise and domain knowledge (single expert or group of experts).

The main challenge in expert-based development of FCMs is to accurately estimate the strength of the relationships.

Computational-based: utilize historical data available for a given system to establish FCM model.

Semi-automated methods require a relatively limited human interventionAutomated approaches are able to compute the FCM model solely based on the historical data.This is the case of learning algorithms for FCM development.

Expert-based construction of FCMs

Step ΙChoose the number N and kind of concepts Ci of FCM

Step IIDetermine the direction of relationship, which concept influences another one.

Step ΙΙΙUse an inference rule to describe the relation between two concepts and infer a linguistic fuzzy set (weight) for the interconnection between the concepts.

Step ΙVLinguistic weights for every interconnection are combined, defuzzified and transformed in numerical weights.

Computational-based:Learning Algorithms for FCMs

Algorithms which modify the cause-effect relationships (connection or weight matrix) between the conceptsAlgorithms which are concentrated on learning the connection matrix, based either on expert intervention and/or on the available historical data.

Figure with weight adaptation

Objectives of learned models:

To generate the same state vector sequence for the same initial state vector

To converge system in desired regions for output concepts values

To generate accepted decision concepts with less errors

Learning algorithmsThree categories:Hebbian-based learning (differential Hebbian, active hebbian, non-linear Hebbian, data-driven NHL): produce weight matrices on the basis of experts’ knowledge that lead the FCM to converge into a given decision state or converge into an acceptable region for the specific target problem.Population-based (genetic, real coded genetic algorithm (RCGA), evolutionary, particle swarms, memetic algorithms, evolution strategies, differential evolution): compute weight matrices on the basis of historical data that best fit the sequence of input state vectors or patterns. The expert is substituted by historical data.Hybrid (hebbian and evolutionary-based, ie. RCGA-NHL, NHL-DE, NHL-GA): compute weight matrices on the basis of experts’knowledge and historical data

Advantages/Usefulness of learning algorithms for FCMs

Improve FCM constructionProvide desired regions for output concepts Keep problem constraintsExploits experts knowledge but it is not heavily dependent on itUse historical data when they are availableReveal possible mistakes at the constraints posed by the expertsFast learning (no any computational load)Reliable decision making

FCM characteristicssimplicity, flexibility to model design, adaptability to different situations,easiness of use learning algorithms

Modeling complex situations

System Analysis

Decision support tasks

These capabilities make them essential for:

FCM application papers at last decade

(last access in Scopus at May 3, 2011)

FCM Application DomainsSocial and political sciences,Engineering, Information technology, Robotics, Virtual systems, Medicine, Education, Pattern recognition, BusinessSoftware systemsTelecommunicationsHealth informaticsEnvironment etc.

Paradigms of Typical problems solved by FCMs

ParadigmTypical problems solved by FCMs

Description

Control Prediction interpreting, monitoring

Business Planning, management, decision making, inference

Medicine Decision support, modeling, prediction, classification

Robotics Navigation, learning, prediction

Environment Knowledge representation, reasoning, stakeholders’ analysis, policy making

InformationTechnology Modeling, analysis

Example FCM applications at first two months of 2011

Research Works (at the first two months of 2011)-presented at scopus

FCM Area

Application Domain Problem Solving

Kannappan et al. [93] Medicine Classification, prediction

Jetter and Schweinfort [95] Solar energy Modeling, policy scenarios

Baykasoglu, et al. [88] Industial process control Learning, control

Beena, and Ganguli [87] Structural damage detection Learning

Song et al. [28] Business Classification and prediction

Hanafizadeh, and Aliehyaei [89] Information Technology Modeling, analysis

Lee et al. [90] Sales assessment Reasoning

Papageorgiou [12] Medicine Knowledge representation, decision making

Iakovidis and Papageorgiou [20] Medicine Decision making, reasoning

Chytas et al. [91] Business Planning, analysis

Salmeron and Lopez [94] Information Technology Knowledge representation, decision making

Acampora et al. [107] Ambient Intelligence Emotional service-oriented architecture

Vaščák and Hirota [108] Engineering Decision making, reasoning

Papageorgiou et al [109] Agriculture Classification, prediction

Conventional FCMSome assumptions/constraints

Rather subjective knowledge on the behavior of a complex system.Use simple monotonic and symmetric causal relations between concepts which are not correct in real world causal relations.Strongly dependence from experts’ beliefs and judgment. Most experts have different point of views and use different scales to evaluate the problems. Designers must select the activation function slope valueFCM does not handle the whole uncertainty inherent in complex domains by assessing the nodes and edges with discrete values. FCM would need measures about the associated uncertainty in weights and concepts.

FCM extensions

FCM extensions

Current extensions are usually designed to solve three FCM drawbacks:uncertainty modeling (FGCM, iFCM, BDD-FCM, RCM), dynamics issues (DCN, DRFCM, FCM, E-FCM, FTCM, TQFCM), rules-based knowledge representation (RBFCM, FRI-FCM).

FCM extensionsRule-based FCMs (Carvalho and Tomé (2001) )Dynamic Cognitive Networks (Miao et al. 2001)Fuzzy Time Cognitive Maps (Wei et al. (2008) applies the FTCM proposed by Park and Kim (1995)). Time Automata FCM (Acampora et al. (2011))Fuzzy Grey Cognitive Maps (Salmeron, 2010)Intuitionistic FCMs (Papageorgiou & Iakovidis, 2009)Agent-based FCM (Stula et al. 2010)Evolutionary FCMs (Cai et al. (2010) )Genetically-evolved FCMs (Andreou et al. 2003)Rough Cognitive Maps (Chunying et al. (2011))Belief-Degree distributed FCMs (Ruan et al, (2011) Fuzzy Cognitive Networks (Kottas et al. (2007) )Dynamic Random FCMs (Aguilar (2003))Case-based FCMs (Georgopoulou and Stylios, 2003)

Rule-based FCMsProposed as an evolution of FCMs including relations other than monotonic causality.RBFCM are iterative fuzzy rule based systems with fuzzy mechanisms to deal with feedback, including timing and new methods with uncertainty propagation. They defined several kinds of concept relations (causal, inference, alternatives, probabilistic, opposition, conjunction, and so on) to deal with the complexity of the dynamic qualitative systems. Include a new fuzzy operation, Fuzzy Carry Accumulation, which is key to model the qualitative causal relations, Fuzzy Causal Relations, while maintaining the FCM’s versatility and simplicity. RB-FCMs exploit important concepts such as implicit time and time delays while they consider a novel important parameter called B-Time. B-Time represents the resolution of the simulation or, in other words, the highest level of temporal detail that a simulation can provide in the modeled system.

Fuzzy time cognitive mapTime lag is supported in the fuzzy time cognitive map. Expert defines time lag as a linguistic variable with accompanying fuzzy values. For example, time lag can be defined with the set {I, N, L}—“immediate,” “normal,” and “long” that has attached values {1, 2, 3}, where 1 is time lag of 1 time units (for example, around 1 month), 2 is time lag of 2 time units, etc.

Agent-based FCMsProposed for injecting the concept of Multi-Agent System (MAS) into the FCM and the different inference algorithms in each node enabled the simulation of systems with diverse behavior concepts. Rodin et al. (2009) use MAS to simulate biological processes. FCMs are integrated in cells to model Mitogen-activated protein kinases.FCM-based personalized recommendation agents called Fuzzy Cognitive Agents (Miao et al. 2007). They were designed to give personalized suggestions based on the user’s current preferences, other user’s common preferences, and expert’s domain knowledge.

Dynamic Cognitive NetworkDynamic causal relationships between the FCM concepts DCN can support a full set of time related features DCN relies on the Laplacian framework to describe the causal relationships. The transformation between fuzzy knowledge and Laplacian functions imposes more modeling efforts to system designers. It is not easy for domain experts to model their cognitive knowledge by this way.

DCN applied to PLANTATION INVESTMENT STRAGEGY

DCN illustrates the analysis on a decision-making example—plantation investment strategyplanting and logging both have continuous accumulative effect on the fund and can be represented by 1/s , which is of the 1st-order integral type. This cannot be represented by FCMs. The growth of saplings is represented by a two-year delay in the DCN..

Intuitionistic FCM (iFCM)Models knowledge using intuitionistic fuzzy setsHandles experts’ hesitancy for decision makingTakes into account a cue regarding the credibility of the rule expressed by the expert in the FCM construction processIntroduces expert’s hesitancy in the determination of the causal relations between the concepts of a domainConsiders hesitancy weights (membership and non-membership weights)New intuitionistic reasoning so that it captures the degree of hesitancy in the relationsModel formulation to be less sensitive in missing data

Intuitionistic fuzzy setsGiven a universe of discourse E an IFS is defined as

Where define the degree of membershipand non-membership, respectively, of the element x.

{ }, ( ), ( )A AA x x x x Eμ γ= ∈

: [0,1]A Eμ → : [0,1]γ →A E

Satisfied conditions0 ( ) 1A xμ≤ ≤

0 ( ) 1γ≤ ≤A x

0 ( ) ( ) 1A Ax xμ γ≤ + ≤

( ) 1 ( ) ( )A A Ax x xπ μ γ= − −

Hesitancy

Hesitancy can be regarded as the indeterminacy degree of the membership of xin A, and it usually has a more intuitive interpretation than non-membership.

IFS Operations

{ }ExxxxxxxxBA BABABA ∈⋅⋅−+=⊕ )()(),()()()(, γγμμμμ

{ }ExxxxxxxxBA BABABA ∈⋅−+⋅=⊗ )()()()(),()(, γγγγμμ

{ }ExxxxA AA ∈=¬ )(),(,1 μγ Negation operation

Intuitionistic FCM modelExperts describe the cause-effect relations among two concepts, not only by their mutual influence, but also by the degree to which the expert hesitates to express that influence Hesitancy is represented through Intuitionistic Fuzzy Sets (IFS) improving knowledge elicitationiFCM-I first approach to introduce IFS and considers only the membership degree of weight and the hesitancy weightiFCM-II new general approach to iFCM-I which introduces intuitionistic concepts (having membership and non-membership values), intuitionistic weights and intuitionistic reasoningFor each concept, there is a hesitancy degree, which is used for the calculation of the non-membership value of the respective concept.

Trends-ConclusionsDevelopment of a hesitancy-aware cognitive model Efficient to model experts’ knowledge and support decisionsEffective with numeric, reproducible examples, on process control and decision support Directly applicable to the various domains where conventional FCMs have been previously applied for modelling of complex systems

FCM in EngineeringTo model and support a plant control system (Zhang et al. 1989)Construct a system for failure modes and effect analysis (Pelaez & Bowles, 1996)To fine tune fuzzy logic controllers (Gonzalez, L. T. Aguilar, and O. Castillo, 2009) To model supervisory control systems (Stylios & Groumpos, 2000)To model industrial process control problems for decision making (Papageorgiou et al. 2004,2005)To construct a maximum power point tracker (MPPT), which may operate in cooperation with a fuzzy MPPT controller (Kottas et al. 2008)To control unknown plants (Kottas et al. 2010)To structure mobile robot map-building (Beeson et al. 2010)To control method on district heating network (Lu et al. 2010)To decision making for robot soccer (Vaščák and Hirota, 2011)Identification and interpretation of sites that yield the highest potential of cryovolcanic activity in Titan (Furfaro et al., 2010)

FCM in MedicineTo support treatment planning process in radiotherapy (Papageorgiou et al. 2003)To model specific speech and language impairment (Georgopoulos & Stylios, 2003)To mine temporal medical data (Froelich et al. 2009)To characterize bladder and brain tumors (Papageorgiou et al. 2006, 2008)to model cell behavior in systems biology through the intracellular biochemical pathway (Rodin et al. 2009)To support urinary tract infections (Papageorgiou 2011)To support decision in Obstetrics (Stylios et al. 2008)To support decisions in pulmonary infections (Papageorgiou et al. 2009, Iakovidis & Papageorgiou, 2011).Autism classification (Kannappan et al. 2011)Pattern recognition (Papakostas et al. 2008)

FCM in Business and ManagementTo help in identification of market needs and technology potentials, detection and exploitation of idea sources (Jetter et al. 2006)To support the decision-making process in effect-based planning (Yaman & Polat, 2009)To model and evaluate trust dynamics in the virtual enterprises (Wei et al. 2008)To evaluate forward-backward analysis of RFID supply chain (Kim et al. 2008)To model and evaluates the performance of RFID-enabled reverse logistic operations (Trappey et al. 2010)To analyze collaborative planning, forecasting and replenishment (CPFR) supporting factors (Büyüközkan et al. 2009).To analyze the relationships between risk factors and risks (Lazzerini et al. 2010)

Environment and AgricultureTo model a generic shallow lake ecosystem (Isaak et al. 2008)To assess local knowledge use in agroforestry management To model a New Zealand dryland ecosystem to anticipate pest management outcomes (Ramsey et al. 2009)To analyze semi-quantitative scenarios (Kok, 2008)As a communication and learning tool for linking stakeholders and modelers in scenario studies (Vliet et al. 2010)To Stakeholders’ analysis (Ozesmi & Ozesmi, 2004, Giordano et al. 2010)To policy making in water use (Kafetzis et al. 2010)To support decisions in cotton yield prediction and management in precision agriculture (Papageorgiou et al. 2009)

FCM in MedicineTo support treatment planning process in radiotherapy (Papageorgiou et al. 2003)To model specific speech and language impairment (Georgopoulos & Stylios, 2003)To mine temporal medical data (Froelich et al. 2009)To characterize bladder and brain tumors (Papageorgiou et al. 2006, 2008)to model cell behavior in systems biology through the intracellular biochemical pathway (Rodin et al. 2009)To support urinary tract infections (Papageorgiou 2011)To support decision in Obstetrics (Stylios et al. 2008)To support decisions in pulmonary infections (Papageorgiou et al. 2009, Iakovidis & Papageorgiou, 2011).Autism classification (Kannappan et al. 2011)Pattern recognition (Papakostas et al. 2008)

FCM in Business and ManagementTo help in identification of market needs and technology potentials, detection and exploitation of idea sources (Jetter et al. 2006)To support the decision-making process in effect-based planning (Yaman & Polat, 2009)To model and evaluate trust dynamics in the virtual enterprises (Wei et al. 2008)To evaluate forward-backward analysis of RFID supply chain (Kim et al. 2008)To model and evaluates the performance of RFID-enabled reverse logistic operations (Trappey et al. 2010)To analyze collaborative planning, forecasting and replenishment (CPFR) supporting factors (Büyüközkan et al. 2009).To analyze the relationships between risk factors and risks (Lazzerini et al. 2010)

Environment and AgricultureTo model a generic shallow lake ecosystem ( )To assess local knowledge use in agroforestry management ()To model a New Zealand dryland ecosystem to anticipate pest management outcomes To analyze semi-quantitative scenarios (Kok, 2008)As a communication and learning tool for linking stakeholders and modelers in scenario studies (Vliet et al. 2010)To Stakeholders’ analysis (Ozesmi & Ozesmi, 2004, Giordano et al. 2010)To policy making in water use (Kafetzis et al. 2010)To support decisions in cotton yield prediction and management in precision agriculture (Papageorgiou et al. 2009)

Example FCMs from Environment

Other FCM ApplicationsInformation Technology and Systems

For mapping success, modeling Critical Success Factors (CSFs) perceptions and the relations between them (Rodriguez-Repiso et al. 2007)For modeling a Enterprise Resource Planning selection (Bueno & Salmeron, 2008)For modeling LMS Critical Success Factors (Salmeron, 2009)For analyzing software’s usability quality character system in order to find a software usability malfunction discovers and improve problems (Lai et al. 2009)

TelecommunicationsTo model and analyze distributed wireless peer-to-peer (P2P) networks (Li et al. 2009)To model a new project idea, the Mobile Payment System (MPS) project, related to the fast evolving world of mobile telecommunications (Rodriguez-Repiso et al. 2007)

Trends on FCM theory and applicationsTheory. A lot of works analyze FCM dynamics, but scarce research is done on FCM static analysis. Learning. Automatic learning in FCMs used to focus on weights adjustment. More research is needed on automatic construction and learning algorithms. It would do FCMs less expert dependent.Extensions. The current extensions are usually designed to solve three FCM drawbacks, uncertainty modeling (FGCM, iFCM, BDD-FCM, RCM), dynamics issues (DCN, DRFCM, FCM, E-FCM, FTCM, TQFCM), and rules-based knowledge representation (RBFCM, FRI-FCM). The extensions of conventional FCM seem to be a useful trend for overcoming FCM limitations.Application Domains. The main domains where FCM are applied are medicine, business, information technology, industrial processes and control, engineering, environment and agriculture

Thank you for the attention!

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