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arxiv: 1906.11247 · v2 · pith:5VSN5W4Onew · submitted 2019-06-26 · 💻 cs.AI · cs.LG· stat.ML

Beyond DAGs: Modeling Causal Feedback with Fuzzy Cognitive Maps

Osonde Osoba , Bart Kosko This is my paper

Pith reviewed 2026-05-25 15:16 UTC · model grok-4.3

classification 💻 cs.AI cs.LGstat.ML
keywords fuzzy cognitive mapscausal feedbackdirected acyclic graphsexpert fusionpolicy simulationinsurgencythucydides trapcausal transitivity
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The pith

Fuzzy cognitive maps model causal feedback with fuzzy signed directed graphs that allow cycles and expert matrix combination.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that fuzzy cognitive maps, as fuzzy signed directed graphs, directly represent causal feedback through cycles and allow degrees of influence. Users can combine maps from multiple experts by adding their edge matrices, and the result tends to better capture domain knowledge with larger random expert samples. This matters because many causal models use directed acyclic graphs which forbid loops, and combining them often creates cycles anyway. The approach also makes causal influence transitive, unlike general probabilistic models. It applies these ideas to scenarios like support for insurgency and US-China conflict dynamics.

Core claim

Fuzzy cognitive maps model feedback causal relations in interwoven webs of causality and policy variables as fuzzy signed directed graphs that allow degrees of causal influence and event occurrence. Such models simulate policy scenarios through nonlinear dynamics and forward-chaining inference. Users fuse FCMs from multiple experts by weighting and adding the fuzzy edge matrices, and the combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. FCM causal influence is transitive whereas probabilistic causal influence is not. The paper applies this to public support for insurgency and US-China conflict in the

What carries the argument

Fuzzy signed directed graphs with matrix addition for expert combination and nonlinear dynamics for inference.

Load-bearing premise

Expert-provided fuzzy edge weights accurately capture causal strengths and their matrix addition improves representation with larger random expert samples.

What would settle it

A demonstration that the accuracy of predictions from combined FCMs does not increase or decreases as more experts are added in a domain where the true causal structure is known.

Figures

Figures reproduced from arXiv: 1906.11247 by Bart Kosko, Osonde Osoba.

Figure 1
Figure 1. Figure 1: Fragment of a predator-prey fuzzy cognitive map that describes dolphin [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FCM knowledge combination or fusion by averaging weighted FCM adjacency [PITH_FULL_IMAGE:figures/full_fig_p022_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Learning FCM causal-edge values eij with time-series data from activated causal concept nodes. Figure Note: We can infer the value of this directed causal edge with adaptive inference algorithms such as differential Hebbian learning if the system has access to enough time-series data for both concept nodes. The time-series data may come from survey data or field measurements or expert elicitations. This da… view at source ↗
Figure 4
Figure 4. Figure 4: Learning FCM causal-edge values eij with Google Trends time-series data for three politically charged phrases: Black lives matter, All lives matter, and Blue lives matter. Figure Note: Google Trends time-series data recorded the weekly popularity of these terms in public Google-search activity from January 2014 to February 2017. The time series consisted of 163 ordered samples. The use of BLM-related terms… view at source ↗
Figure 5
Figure 5. Figure 5: PSOT factor-tree model. The figure shows the directed relationships among [PITH_FULL_IMAGE:figures/full_fig_p027_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Two Fuzzy Cognitive Maps of the PSOT factor-tree model. [PITH_FULL_IMAGE:figures/full_fig_p028_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FCM of Allison’s Thucydides’ Trap causal dynamics from [68]. The Thucydides’ Trap FCM predicted war-type patterns between the US and China more often than it predicted peace-type patterns. An exhaustive search of the space of possible (clamped) scenarios found that only under ∼ 20% of scenarios led to lasting 32 [PITH_FULL_IMAGE:figures/full_fig_p032_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Causal edge matrix E for the Thucydides’ trap FCM. E is the adjacency matrix for the FCM’s fuzzy signed directed graph. Each square shows the fuzzy causal edge value eij . The value eij how much the i th concept Ci causes or influences the j th concept Cj . The matrix entries eij in these FCMs are fuzzy values in the bipolar interval [−1, 1]. Uncolored squares indicate the absence of causal influence. Thes… view at source ↗
Figure 9
Figure 9. Figure 9: Spreading causal activation time slices in the Thucydides-trap FCM. Each [PITH_FULL_IMAGE:figures/full_fig_p035_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Average node activations for input scenarios that converge to peaceful [PITH_FULL_IMAGE:figures/full_fig_p037_10.png] view at source ↗
read the original abstract

Fuzzy cognitive maps (FCMs) model feedback causal relations in interwoven webs of causality and policy variables. FCMs are fuzzy signed directed graphs that allow degrees of causal influence and event occurrence. Such causal models can simulate a wide range of policy scenarios and decision processes. Their directed loops or cycles directly model causal feedback. Their nonlinear dynamics permit forward-chaining inference from input causes and policy options to output effects. Users can add detailed dynamics and feedback links directly to the causal model or infer them with statistical learning laws. Users can fuse or combine FCMs from multiple experts by weighting and adding the underlying fuzzy edge matrices and do so recursively if needed. The combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample. Many causal models use more restrictive directed acyclic graphs (DAGs) and Bayesian probabilities. DAGs do not model causal feedback because they do not contain closed loops. Combining DAGs also tends to produce cycles and thus tends not to produce a new DAG. Combining DAGs tends to produce a FCM. FCM causal influence is also transitive whereas probabilistic causal influence is not transitive in general. Overall: FCMs trade the numerical precision of probabilistic DAGs for pattern prediction, faster and scalable computation, ease of combination, and richer feedback representation. We show how FCMs can apply to problems of public support for insurgency and terrorism and to US-China conflict relations in Graham Allison's Thucydides-trap framework. The appendix gives the textual justification of the Thucydides-trap FCM. It also extends our earlier theorem [Osoba-Kosko2017] to a more general result that shows the transitive and total causal influence that upstream concept nodes exert on downstream nodes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper argues that Fuzzy Cognitive Maps (FCMs) provide advantages over Directed Acyclic Graphs (DAGs) for modeling causal feedback in complex systems. FCMs are presented as fuzzy signed directed graphs that capture degrees of influence, support nonlinear dynamics and forward inference, allow direct combination of multiple expert models via weighted matrix addition (which tends to improve representation with larger random expert samples), and exhibit transitive causal influence (unlike probabilistic influence in general). The work extends a prior theorem on transitive influence, provides applications to public support for insurgency/terrorism and the Thucydides trap in US-China relations, and includes an appendix with textual justification and the theorem extension.

Significance. If the central claims hold, the framework offers a scalable, feedback-capable alternative for causal modeling and policy simulation that prioritizes pattern prediction, expert fusion, and computational ease over the numerical precision of probabilistic DAGs. The explicit extension of the transitive-influence theorem supplies a formal strengthening of the approach, and the two applications demonstrate concrete utility in conflict and policy domains.

major comments (2)
  1. [Abstract] Abstract: the claim that 'the combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample' is asserted without quantitative validation, simulation results, error analysis, or supporting derivation; this conditional improvement is load-bearing for the stated advantage of FCM combination over DAGs.
  2. [Appendix] Appendix: the extension of the earlier theorem [Osoba-Kosko2017] to a more general result on transitive and total causal influence exerted by upstream nodes is described but the full derivation steps, assumptions, and proof details are not supplied in the visible text, preventing direct verification of the generalized claim.
minor comments (1)
  1. The abstract and introduction could more explicitly separate the modeling advantages (feedback, combination) from the theorem extension to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments highlight areas where the presentation of key claims can be strengthened. We address each major comment below and indicate planned revisions.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'the combined FCM tends to better represent domain knowledge as the expert sample size increases if the expert sample approximates a random sample' is asserted without quantitative validation, simulation results, error analysis, or supporting derivation; this conditional improvement is load-bearing for the stated advantage of FCM combination over DAGs.

    Authors: The claim follows from the standard FCM combination procedure of weighted matrix addition, which is equivalent to averaging expert edge weights. Under the assumption of unbiased random sampling from the expert population, the law of large numbers implies convergence in probability to the population mean edge weights, thereby improving representation of domain knowledge. This is a direct consequence of the linear algebra of the method rather than a new empirical result. We agree the abstract states the property concisely without supporting material. In revision we will qualify the statement, add a short explanatory sentence referencing the averaging property, and include a brief simulation or citation to prior FCM aggregation results to make the conditional improvement explicit. revision: partial

  2. Referee: [Appendix] Appendix: the extension of the earlier theorem [Osoba-Kosko2017] to a more general result on transitive and total causal influence exerted by upstream nodes is described but the full derivation steps, assumptions, and proof details are not supplied in the visible text, preventing direct verification of the generalized claim.

    Authors: The appendix outlines the extension of the transitive-influence result to total causal influence along all paths. We agree that the current description is high-level and that full derivation steps, assumptions (e.g., on the activation function and convergence), and the complete proof would allow direct verification. In the revised version we will expand the appendix to supply the full proof, including all intermediate steps and explicit assumptions. revision: yes

Circularity Check

1 steps flagged

Minor self-citation in theorem extension; central claims remain independent

specific steps
  1. self citation load bearing [Abstract]
    "It also extends our earlier theorem [Osoba-Kosko2017] to a more general result that shows the transitive and total causal influence that upstream concept nodes exert on downstream nodes."

    Transitivity of FCM causal influence is supported solely by extension of prior work by the same authors rather than an independent external result, though this property is not load-bearing for the core modeling and combination claims.

full rationale

The paper presents FCMs as a modeling framework defined directly by fuzzy signed directed graphs and matrix addition for combination. The improvement claim is explicitly conditional on expert samples approximating random samples, with no fitting of parameters to target outcomes. The only self-citation is the appendix extension of the authors' prior theorem on transitivity, which supports a secondary property but is not invoked to justify or derive the primary advantages over DAGs. No self-definitional loops, fitted predictions, or load-bearing self-citation chains appear in the derivation.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the domain assumption that causal relations admit fuzzy signed directed-graph representations with cycles and that expert weights can be meaningfully added; no new entities are postulated and no parameters are fitted to data within the paper itself.

free parameters (1)
  • fuzzy edge weights
    Expert-assigned or learned values in [-1,1] that define the model; these are inputs rather than parameters fitted to the paper's own results.
axioms (2)
  • domain assumption Causal systems can be represented as fuzzy signed directed graphs that permit cycles and nonlinear dynamics
    Invoked throughout the abstract as the foundation for FCMs versus DAGs.
  • domain assumption Matrix addition of expert FCMs yields a combined model whose quality improves with random expert sample size
    Stated as the justification for the combination procedure.

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discussion (0)

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Agentic Chunking and Bayesian De-chunking of AI Generated Fuzzy Cognitive Maps: A Model of the Thucydides Trap

    cs.AI 2026-05 unverdicted novelty 6.0

    Agentic chunking generates overlapping fuzzy cognitive maps from text that mix into a representative FCM, with Bayesian de-chunking producing posterior maps; applied to Thucydides Trap, 7/8 maps predict war upon stimu...

Reference graph

Works this paper leans on

71 extracted references · 71 canonical work pages · cited by 1 Pith paper

  1. [1]

    Fuzzy cognitive maps of public support for insur- gency and terrorism

    O. A. Osoba and B. Kosko, “Fuzzy cognitive maps of public support for insur- gency and terrorism”, The Journal of Defense Modeling and Simulation, vol. 14, no. 1, pp. 17–32, 2017

    work page 2017

  2. [2]

    Fuzzy cognitive maps

    B. Kosko, “Fuzzy cognitive maps”,International Journal of man-machine studies, vol. 24, no. 1, pp. 65–75, 1986

    work page 1986

  3. [3]

    A review of fuzzy cognitive maps research during the last decade

    E. I. Papageorgiou and J. L. Salmeron, “A review of fuzzy cognitive maps research during the last decade”, IEEE Transactions on Fuzzy Systems, vol. 21, no. 1, pp. 66–79, 2013

    work page 2013

  4. [4]

    Glykas, Ed., Fuzzy cognitive maps

    M. Glykas, Ed., Fuzzy cognitive maps. Springer, 2010

    work page 2010

  5. [5]

    Papageorgiou, Fuzzy cognitive maps for applied sciences and engineering: From fundamentals to extensions and learning algorithms, ser

    E. Papageorgiou, Fuzzy cognitive maps for applied sciences and engineering: From fundamentals to extensions and learning algorithms, ser. Intelligent Sys- tems Reference Library. Springer Berlin Heidelberg, 2013,ISBN : 9783642397394. [Online]. Available: https : / / books . google . com / books ? id = S3LGBAAAQBAJ. 38

    work page 2013

  6. [6]

    A review of fuzzy cognitive maps in medicine: Taxonomy, methods, and applications

    A. Amirkhani, E. I. Papageorgiou, A. Mohseni, and M. R. Mosavi, “A review of fuzzy cognitive maps in medicine: Taxonomy, methods, and applications”, Computer methods and programs in biomedicine, vol. 142, pp. 129–145, 2017

    work page 2017

  7. [7]

    The potential impact of brexit on the energy, water and food nexus in the uk: A fuzzy cognitive mapping approach

    G. Ziv, E. Watson, D. Young, D. C. Howard, S. T. Larcom, and A. J. Tanentzap, “The potential impact of brexit on the energy, water and food nexus in the uk: A fuzzy cognitive mapping approach”, Applied Energy, vol. 210, pp. 487–498, 2018

    work page 2018

  8. [8]

    Analyzing the impact of social factors on homelessness: A fuzzy cognitive map approach

    V . K. Mago, H. K. Morden, C. Fritz, T. Wu, S. Namazi, P. Geranmayeh, R. Chattopadhyay, and V . Dabbaghian, “Analyzing the impact of social factors on homelessness: A fuzzy cognitive map approach”, BMC medical informatics and decision making, vol. 13, no. 1, p. 94, 2013

    work page 2013

  9. [9]

    Fuzzy sets

    L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, pp. 338–353, 1965

    work page 1965

  10. [10]

    Fuzzy logic

    B. Kosko and S. Isaka, “Fuzzy logic”,Scientific American, vol. 269, no. 1, pp. 62– 7, 1993

    work page 1993

  11. [11]

    Abstraction and pattern classification

    R. Bellman, R. Kalaba, and L Zadeh, “Abstraction and pattern classification”, Journal of Mathematical Analysis and Applications, vol. 13, no. 1, pp. 1–7, 1966

    work page 1966

  12. [12]

    J. D. Sterman, Business dynamics: Systems thinking and modeling for a complex world, HD30. 2 S7835 2000. 2000

    work page 2000

  13. [13]

    Learning structures of conceptual models from observed dynamics using evolutionary echo state networks

    H. Abdelbari and K. Shafi, “Learning structures of conceptual models from observed dynamics using evolutionary echo state networks”, Journal of Artificial Intelligence and Soft Computing Research, vol. 8, no. 2, pp. 133–154, 2018

    work page 2018

  14. [14]

    Pearl, Causality

    J. Pearl, Causality. Cambridge university press, 2009

    work page 2009

  15. [15]

    Quantization effects on the equi- librium behavior of combined fuzzy cognitive maps

    R. Taber, R. R. Yager, and C. M. Helgason, “Quantization effects on the equi- librium behavior of combined fuzzy cognitive maps”, International Journal of Intelligent Systems, vol. 22, no. 2, pp. 181–202, 2007

    work page 2007

  16. [16]

    Fuzzy cognitive map architectures for medical decision support systems

    C. D. Stylios, V . C. Georgopoulos, G. A. Malandraki, and S. Chouliara, “Fuzzy cognitive map architectures for medical decision support systems”, Applied Soft Computing, vol. 8, no. 3, pp. 1243–1251, 2008

    work page 2008

  17. [17]

    Virtual worlds as fuzzy cognitive maps

    J. A. Dickerson and B. Kosko, “Virtual worlds as fuzzy cognitive maps”, in Virtual Reality Annual International Symposium, 1993., 1993 IEEE, IEEE, 1993, pp. 471–477

    work page 1993

  18. [18]

    Fuzzy Systems as Universal Approximators

    B. Kosko, “Fuzzy Systems as Universal Approximators”, IEEE Transactions on Computers, vol. 43, no. 11, pp. 1329–1333, Nov. 1994. 39

    work page 1994

  19. [19]

    Kosko, Fuzzy engineering

    B. Kosko, Fuzzy engineering. Prentice Hall, 1996

    work page 1996

  20. [20]

    Bayesian inference with adaptive fuzzy priors and likelihoods

    O. Osoba, S. Mitaim, and B. Kosko, “Bayesian inference with adaptive fuzzy priors and likelihoods”, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 41, no. 5, pp. 1183–1197, Oct. 2011, ISSN : 1083-4419. DOI: 10.1109/TSMCB.2011.2114879

    work page doi:10.1109/tsmcb.2011.2114879 2011

  21. [21]

    Causal inference using potential outcomes: Design, modeling, decisions

    D. B. Rubin, “Causal inference using potential outcomes: Design, modeling, decisions”, Journal of the American Statistical Association, vol. 100, no. 469, pp. 322–331, 2005

    work page 2005

  22. [22]

    G. W. Imbens and D. B. Rubin,Causal inference in statistics, social, and biomed- ical sciences. Cambridge University Press, 2015

    work page 2015

  23. [23]

    P. K. Davis, D. Manheim, W. L. Perry, and J. S. Hollywood,Causal models and exploratory analysis in heterogeneous information fusion for detecting potential terrorists. RAND Corporation, 2015

    work page 2015

  24. [24]

    Using causal mod- els in heterogeneous information fusion to detect terrorists

    P. K. Davis, D. Manheim, W. L. Perry, and J. Hollywood, “Using causal mod- els in heterogeneous information fusion to detect terrorists”, in 2015 WINTER SIMULATION CONFERENCE (WSC), IEEE, 2015, pp. 2586–2597

    work page 2015

  25. [25]

    Fuzzy knowledge combination

    B. Kosko, “Fuzzy knowledge combination”, International Journal of Intelligent Systems, vol. 1, no. 4, pp. 293–320, 1986

    work page 1986

  26. [26]

    Hidden patterns in combined and adaptive knowledge networks

    ——, “Hidden patterns in combined and adaptive knowledge networks”, Interna- tional Journal of Approximate Reasoning, vol. 2, no. 4, pp. 377–393, 1988

    work page 1988

  27. [27]

    Knowledge processing with fuzzy cognitive maps

    R. Taber, “Knowledge processing with fuzzy cognitive maps”,Expert Systems with Applications, vol. 2, no. 1, pp. 83–87, 1991

    work page 1991

  28. [28]

    Generalized mixture representations and combinations for additive fuzzy systems

    B. Kosko, “Generalized mixture representations and combinations for additive fuzzy systems”, in Neural Networks (IJCNN), 2017 International Joint Confer- ence on, IEEE, 2017, pp. 3761–3768

    work page 2017

  29. [29]

    Additive Fuzzy Systems: From Generalized Mixtures to Rule Continua

    ——, “Additive Fuzzy Systems: From Generalized Mixtures to Rule Continua”, International Journal of Intelligent Systems, vol. 33, no. 8, pp. 1573–1623, 2018

    work page 2018

  30. [30]

    Generalized belief propagation

    J. S. Yedidia, W. T. Freeman, and Y . Weiss, “Generalized belief propagation”, in Advances in Neural Information Processing Systems, 2001, pp. 689–695

    work page 2001

  31. [31]

    Dynamic bayesian networks: Representation, inference and learning

    K. P. Murphy, “Dynamic bayesian networks: Representation, inference and learning”, PhD thesis, UNIVERSITY OF CALIFORNIA, BERKELEY, 2002

    work page 2002

  32. [32]

    Graphical models, exponential families, and variational inference

    M. J. Wainwright and M. I. Jordan, “Graphical models, exponential families, and variational inference”, Foundations and TrendsR⃝ in Machine Learning, vol. 1, no. 1–2, pp. 1–305, 2008. 40

    work page 2008

  33. [33]

    Approximating probabilistic inference in bayesian belief networks is np-hard

    P. Dagum and M. Luby, “Approximating probabilistic inference in bayesian belief networks is np-hard”, Artificial intelligence, vol. 60, no. 1, pp. 141–153, 1993

    work page 1993

  34. [34]

    Russell, P

    S. Russell, P. Norvig, and E. Davis,Artificial intelligence : A modern approach, ser. Always learning. Pearson Education, Limited, 2016, ISBN : 9781292153964. [Online]. Available: https : / / books . google . com / books ? id = XS9CjwEACAAJ

    work page 2016

  35. [35]

    Learning bayesian networks is np-complete

    D. M. Chickering, “Learning bayesian networks is np-complete”, in Learning from data, Springer, 1996, pp. 121–130

    work page 1996

  36. [36]

    Large-sample learning of bayesian networks is np-hard

    D. M. Chickering, D. Heckerman, and C. Meek, “Large-sample learning of bayesian networks is np-hard”, Journal of Machine Learning Research, vol. 5, no. Oct, pp. 1287–1330, 2004

    work page 2004

  37. [37]

    Pearl, Probabilistic reasoning in intelligent systems: Networks of plausible inference, ser

    J. Pearl, Probabilistic reasoning in intelligent systems: Networks of plausible inference, ser. Morgan Kaufmann series in representation and reasoning. Elsevier Science, 2014, ISBN : 9780080514895. [Online]. Available: https://books. google.com/books?id=mn2jBQAAQBAJ

    work page 2014

  38. [38]

    The variational bayesian em algorithm for in- complete data: With application to scoring graphical model structures

    M. J. Beal and Z. Ghahramani, “The variational bayesian em algorithm for in- complete data: With application to scoring graphical model structures”, Bayesian statistics, vol. 7, J. Bernardo, M. Bayarri, J. Berger, A. Dawid, D Heckerman, A. Smith, M West, et al., Eds., pp. 453–464, 2003

    work page 2003

  39. [39]

    Variational bayesian learning of directed graphical models with hidden variables

    ——, “Variational bayesian learning of directed graphical models with hidden variables”, Bayesian Analysis, vol. 1, no. 4, pp. 793–831, 2006

    work page 2006

  40. [40]

    Kosko, Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence

    B. Kosko, Neural networks and fuzzy systems: A dynamical systems approach to machine intelligence. Prentice Hall, 1991

    work page 1991

  41. [41]

    Probability measures of fuzzy events

    L. A. Zadeh, “Probability measures of fuzzy events”, Journal of mathematical analysis and applications, vol. 23, no. 2, pp. 421–427, 1968

    work page 1968

  42. [42]

    Probabilities of conditionals and conditional probabilities

    D. Lewis, “Probabilities of conditionals and conditional probabilities”, The Philo- sophical Review, vol. 85, pp. 297–315, 1976

    work page 1976

  43. [43]

    Probabilities of conditionals and conditional probabilities–part two

    ——, “Probabilities of conditionals and conditional probabilities–part two”, The Philosophical Review, vol. 95, no. 4, pp. 581–589, 1986

    work page 1986

  44. [44]

    Probable Equality, Superpower Sets, and Superconditionals

    B. Kosko, “Probable Equality, Superpower Sets, and Superconditionals”,Interna- tional Journal of Intelligent Systems, vol. 19, pp. 1151–1171, Dec. 2004. 41

    work page 2004

  45. [45]

    Outline of a new approach to the analysis of complex systems and decision analysis

    L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision analysis”, IEEE Transactions on Systems, Man, and Cybernetics, vol. 3, no. 1, pp. 28–44, 1973

    work page 1973

  46. [46]

    The noisy expectation-maximization algorithm for multiplicative noise injection

    O. Osoba and B. Kosko, “The noisy expectation-maximization algorithm for multiplicative noise injection”, Fluctuation and Noise Letters, p. 1 650 007, 2016

    work page 2016

  47. [47]

    Fuzzy Entropy and Conditioning

    B. Kosko, “Fuzzy Entropy and Conditioning”, Information Sciences, vol. 40, no. 2, pp. 165–174, 1986

    work page 1986

  48. [48]

    Virtual worlds as fuzzy cognitive maps

    J. A. Dickerson and B. Kosko, “Virtual worlds as fuzzy cognitive maps”,Pres- ence, vol. 3, no. 2, pp. 173–189, 1994

    work page 1994

  49. [49]

    M. W. Hirsch, S. Smale, and R. L. Devaney,Differential equations, dynamical systems, and an introduction to chaos. Academic press, 2012

    work page 2012

  50. [50]

    Aggregating probabilistic forecasts from incoherent and abstaining experts

    J. B. Predd, D. N. Osherson, S. R. Kulkarni, and H. V . Poor, “Aggregating probabilistic forecasts from incoherent and abstaining experts”,Decision Analysis, vol. 5, no. 4, pp. 177–189, 2008

    work page 2008

  51. [51]

    Preference functions that score rankings and maximum likelihood estimation

    V . Conitzer, M. Rognlie, and L. Xia, “Preference functions that score rankings and maximum likelihood estimation.”, in IJCAI, vol. 9, 2009, pp. 109–115

    work page 2009

  52. [52]

    When do noisy votes reveal the truth?

    I. Caragiannis, A. D. Procaccia, and N. Shah, “When do noisy votes reveal the truth?”, in PROCEEDINGS OF THE FOURTEENTH ACM CONFERENCE ON ELECTRONIC COMMERCE, ACM, 2013, pp. 143–160

    work page 2013

  53. [53]

    Stochastic optimal linear estimation and control

    J. S. Meditch, “Stochastic optimal linear estimation and control”, 1969

    work page 1969

  54. [54]

    D. O. Hebb, The organization of behavior: A neuropsychological approach. John Wiley & Sons, 1949

    work page 1949

  55. [55]

    Differential Hebbian learning

    B. Kosko, “Differential Hebbian learning”, in AIP Conference Proceedings , vol. 151, 1986, pp. 277–282

    work page 1986

  56. [56]

    Mill, A system of logic, ratiocinative and inductive: Being a connected view of the principles of evidence and the methods of scientific investigation, ser

    J. Mill, A system of logic, ratiocinative and inductive: Being a connected view of the principles of evidence and the methods of scientific investigation, ser. A System of Logic, Ratiocinative and Inductive: Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation v. 1. John W. Parker, 1843. [Online]. Available: https...

    work page

  57. [57]

    Unsupervised learning in noise

    B. Kosko, “Unsupervised learning in noise”, IEEE Transactions on Neural Net- works, vol. 1, no. 1, pp. 44–57, 1990. 42

    work page 1990

  58. [58]

    Being bayesian about network structure. a bayesian approach to structure discovery in bayesian networks

    N. Friedman and D. Koller, “Being bayesian about network structure. a bayesian approach to structure discovery in bayesian networks”, Machine learning, vol. 50, no. 1-2, pp. 95–125, 2003

    work page 2003

  59. [59]

    A computational model of public support for insurgency and terrorism: A prototype for more-general social-science modeling

    P. K. Davis and A. O’Mahony, “A computational model of public support for insurgency and terrorism: A prototype for more-general social-science modeling”, RAND Corporation, 2013

    work page 2013

  60. [60]

    P. K. Davis, E. V . Larson, Z. Haldeman, M. Oguz, and Y . Rana,Understanding and influencing public support for insurgency and terrorism. RAND Corporation, 2012

    work page 2012

  61. [61]

    D. A. Snow, S. A. Soule, and H. Kriesi, The Blackwell companion to social movements. John Wiley & Sons, 2008

    work page 2008

  62. [62]

    Ibrahim, The Al Qaeda reader: The essential texts of osama bin laden’s terrorist organization

    R. Ibrahim, The Al Qaeda reader: The essential texts of osama bin laden’s terrorist organization. Broadway Books, 2007

    work page 2007

  63. [63]

    Nawaz, Radical: My journey from Islamist extremism to a democratic awak- ening

    M. Nawaz, Radical: My journey from Islamist extremism to a democratic awak- ening. Random House, 2015

    work page 2015

  64. [64]

    P. K. Davis and K. Cragin,Social science for counterterrorism: Putting the pieces together. RAND Corporation, 2009

    work page 2009

  65. [65]

    Experiments in multiresolution modeling (MRM)

    P. K. Davis and J. H. Bigelow, “Experiments in multiresolution modeling (MRM)”, RAND Corporation, 1998

    work page 1998

  66. [66]

    Primer for building factor trees to represent social-science knowl- edge

    P. K. Davis, “Primer for building factor trees to represent social-science knowl- edge”, in PROCEEDINGS OF THE WINTER SIMULATION CONFERENCE, Winter Simulation Conference, 2011, pp. 3121–3135

    work page 2011

  67. [67]

    The Thucydides Trap: Are the US and China headed for war?

    G. Allison, “The Thucydides Trap: Are the US and China headed for war?”, The Atlantic, vol. 24, 2015

    work page 2015

  68. [68]

    [Online]

    ——, Destined for War: Can America and China Escape Thucydides’s Trap? Houghton Mifflin Harcourt, 2017, ISBN : 9780544935334. [Online]. Available: https://books.google.com/books?id=CtmpDAAAQBAJ

    work page 2017

  69. [69]

    Thucydides, History of the Peloponnesian War; Translated by Benjamin Jowett, 1998

    work page 1998

  70. [70]

    The clash of civilizations?

    S. P. Huntington, “The clash of civilizations?”,Foreign affairs, pp. 22–49, 1993

    work page 1993

  71. [71]

    deep” neural classifiers. The spreading activation also roughly resembles the routed messages in message-passing probabilistic inference on DAGs. Such messages propagate “evidence

    ——, The clash of civilizations and the remaking of world order. Penguin Books India, 1997. 43 Mathematical Appendix: FCM Causal Influence Theo- rems This appendix states and proves the two main theorems on downstream causal influence in a FCM. Both theorems apply to any two concept nodes in a FCM. Theorem 1 shows the transitive effect that upstream concept ...

    work page 1997