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FCM Basics

A Fuzzy Cognitive Map (FCM) is a directed graph used to model complex systems. It consists of:

• Concepts (nodes) — the variables, factors, or ideas in your system
• Edges (connections) — directed, weighted relationships between concepts showing causal influence
• Weights — values between -1 and +1 indicating the strength and direction of influence

How FCMs Work

Each concept has an activation level. When you run a simulation, the system iterates: each concept's new value is computed from the weighted sum of incoming influences, passed through a transfer function (sigmoid, hyperbolic tangent, etc.). The system converges to a steady state, oscillates, or becomes chaotic.

When to Use FCMs

FCMs are ideal for modeling "soft" systems where relationships are known qualitatively but hard to quantify precisely: stakeholder mental models, policy analysis, ecological systems, healthcare decision-making, organizational dynamics, and more.

Quick Start Guide

1. Sign up for a free account at get-causality.com/signup
2. Load a demo model from the Home tab to explore the interface
3. Open Model Builder to create your first FCM — add concepts, draw edges, set weights
4. Run analysis from the Model Analysis tab — view metrics, simulate scenarios, run sensitivity analysis
5. Explore tutorials in the Tutorial tab for in-depth guidance on each feature

Keyboard Shortcuts

• Ctrl+Z — Undo last action in Model Builder
• Ctrl+Shift+Z — Redo
• Delete — Remove selected element
• Ctrl+S — Save current model
• Ctrl+A — Select all elements

Account & Plans

Available Plans

All plans include unlimited analyses within their feature set. Annual billing saves 20%. Academic tiers (Academic, Academic Plus, Academic Pro) require .edu email verification.

Academic Tiers

• Free ($0) — Model Builder, single-model analysis. 1 stored survey, 100 responses, 50 concepts/model. Community support.
• Academic ($249/mo) — Adds Multi-Model analysis, full survey platform, goal-seek optimizer. 10 stored surveys, 100 concepts/model. 48h support.
• Academic Plus ($349/mo) — Adds Meta-Model analysis (25+ population-scale analyses). 25 stored surveys, unlimited concepts. 24h support.
• Academic Pro ($449/mo) — Adds Predictive Cognition (deep learning forecasting). 50 stored surveys. Priority 24h support.

Commercial Tiers

• Researcher ($499/mo) — Multi-Model analysis with commercial licensing. 10 stored surveys, unlimited concepts. No .edu required. Priority 24h support.
• Professional ($999/mo) — Multi-Model, Meta-Model, Predictive Cognition, A/B testing, commercial license. 50 stored surveys, 3 team members. 24h support.
• Team ($1,999/mo) — Everything in Professional, plus 100 stored surveys, 10 team members. Priority 12h support.
• Enterprise (Custom) — Unlimited surveys and team members, SSO/SAML, dedicated support, custom deployment. Contact us.

Key Feature Differences

• Commercial use — Researcher, Professional, Team, and Enterprise plans include a commercial license. Academic tiers are for educational use only.
• A/B testing — Available on Professional, Team, and Enterprise plans.
• SSO/SAML — Enterprise only.
• Team collaboration — Professional (3 members), Team (10), Enterprise (unlimited). All other plans are single-user.

Managing Your Account

Visit the Account page to view your current plan, usage statistics, and manage billing. You can upgrade or downgrade at any time. For a full feature comparison, see the pricing page.

Model Builder

The Model Builder is your primary workspace for creating and editing FCMs.

Adding Concepts

Click "Add Concept" in the toolbar or double-click the canvas. Enter a name and optional description. Concepts appear as nodes you can drag to rearrange.

Drawing Edges

Click the edge tool, then click a source concept and drag to the target. Set the weight (-1 to +1) in the dialog. Positive weights indicate positive causal influence; negative weights indicate inhibition.

Importing Models

Import models from CSV, JSON, or adjacency matrix formats. Use the Import button in the toolbar. The builder supports multiple matrix formats and automatically detects concept names from headers.

Saving & Exporting

Models auto-save to your browser's local storage. Use "Save to Cloud" to persist across devices (requires login). Export as JSON, CSV adjacency matrix, or image.

Model Analysis

Analyze a single FCM model's structure and dynamics.

Network Metrics

View density, complexity, hierarchy index, and concept count. Centrality analysis shows which concepts are most influential (outdegree), most influenced (indegree), or most central (betweenness).

Simulation

Run forward inference to see how the system evolves from an initial state. Choose transfer functions (sigmoid, tanh, bivalent, trivalent) and set iteration limits. Visualize convergence with state-vector plots.

Scenario Analysis

Clamp one or more concept values and observe the steady-state impact on the rest of the system. Compare "what-if" scenarios side by side.

Goal-Seek Optimizer

Specify a target value for a concept and let the optimizer find the minimal interventions needed. Uses differential evolution to handle nonlinear FCM dynamics. Available on Academic plans and above.

Multi-Model Analysis

Compare and combine FCMs from multiple stakeholders. Requires Academic plan or higher.

Importing Multiple Models

Upload a multi-model dataset (CSV with respondent IDs) or combine individual models. The system uses non-zero averaging for aggregation — zeros mean "not asked", not "no relationship".

Core Analyses

• Concept Frequency — How often each concept appears across models
• Edge Frequency — Common relationships across stakeholders
• Combined Model — Aggregated FCM from all stakeholders using non-zero averaging
• Concept Selection — Analyze which concepts respondents selected and why

Statistical Comparisons

• QAP (Quadratic Assignment Procedure) — Test structural similarity between FCM matrices
• Mantel Tests — Correlate distance matrices across models
• Permutation Tests — Non-parametric significance testing for group differences
• Bootstrap Confidence Intervals — Robust estimates, stability analysis, and bias correction for edge weights
• Centrality Comparison — Compare concept importance across groups or models

Structural Analysis

• Cluster Analysis — Within-model (concept centrality, communities, core-periphery) and across-model (model similarity, network clustering)
• Structural Equivalence — Identify concepts that occupy similar structural positions
• Motif Analysis — Detect recurring sub-graph patterns (feed-forward loops, mutual inhibition, etc.)
• Network Dynamics — Analyze system behavior and stability properties
• FCM Loop Influence — Identify and quantify feedback loop impact

Discovery & Harmonization

• Relationship Discovery — Top discoveries, heatmaps, hidden patterns, PCA, absences and gaps, feedback loops, and exhaustive pattern mining with demographic breakdowns
• Concept Harmonization — Align concepts across models with lexical similarity, concept mapping, and merged coverage analysis
• Cross-Tabulation — Compare group differences by demographics or categories with chi-square testing

Meta-Model Analysis

20+ population-scale analyses for large FCM datasets, organized across four assessment phases. Requires Academic Plus plan or higher. All analyses run entirely in your browser using Web Workers and TensorFlow.js — no data leaves your machine.

Phase 1: Data Assessment

• Data Quality — Automated screening of response completion, variance, straight-lining detection, and FCM matrix integrity with participant flagging
• Diagnostics — Distribution statistics, correlation structures, missing data patterns, and identification of low-effort responses
• Validation — Psychometric validation including reliability (Cronbach's alpha, test-retest), outlier detection, multicollinearity checks, normality tests, and construct validity

Phase 2: Descriptive & Statistical

• Concept Preference — Composite preference rankings with James-Stein shrinkage, rank weighting modes, and bootstrap confidence intervals
• Discrete Choice — Models concept selection patterns with grouping variable support
• Network Meta-Analysis — Co-occurrence and correlation networks using Jaccard similarity, Pearson correlation, and association rule mining
• Comparative Analysis — Compare FCM concept rankings and edge weights across subgroups using Welch's t-test or Kruskal-Wallis ANOVA
• FCM Metric Clustering — Cluster participants by structural metrics (Gini, entropy, density, strength) using k-means or hierarchical clustering with silhouette analysis
• Latent Class Analysis — Identify unobserved subgroups using finite mixture models with EM algorithm and BIC/AIC model selection

Phase 3: Causal & Effects

• Total Causal Effects (TCEC) — Compute total causal influence between concept pairs through all direct and indirect paths using matrix power series or Leontief inversion
• Causal Discovery — Structural learning algorithms (PC, GES, LiNGAM, FCI) to validate respondent-drawn causal structure, with Pyodide (Python) or JS fallback
• Bayesian Uncertainty — Posterior distributions on edge weights using Bayesian Ridge Regression with 90%, 95%, and 99% credible intervals
• Monte Carlo Sensitivity — Sample adjacency matrices from weight distributions, compute confidence bands on steady-state activations, and rank edge sensitivity

Phase 4: Machine Learning & Deep Learning

• Respondent Profiling — Predict respondent demographics from FCM structure using Random Forest, Gradient Boosting, or XGBoost with feature importance ranking
• SHAP Explainability — Decompose profiling predictions to show per-respondent attribution of individual classification decisions
• GraphSAGE — Learn multi-dimensional concept embeddings using inductive graph representation; enables community detection, link prediction, and similarity analysis
• Graph Transformer — Learn context-dependent causal connection importance using multi-head self-attention; captures network-dependent edge relevance
• RL Policy Optimization — Evaluate concept interventions using Q-learning to find optimal strategies for maximizing target concept outcomes; identifies levers vs. stressors

Cross-Cutting Tools

• Scenario Modeling — Simulate interventions using learned models (GraphSAGE, Transformer, or Causal Discovery) with propagation methods and Monte Carlo uncertainty quantification
• Temporal Analysis — Track how FCM network structure evolves across time periods, including edge weight changes, centrality drift, and structural stability

Predictive Cognition

AI-powered forecasting and synthetic data generation using deep learning models that run in your browser via TensorFlow.js.

This feature is currently under active development and will be available in an upcoming release.

LLM FCM Builder

Coming Soon — Use large language models to automatically generate fuzzy cognitive maps from natural language descriptions, literature reviews, or interview transcripts.

The LLM FCM Builder will allow you to describe a system in plain language and receive a structured FCM with concepts, edges, and weights derived from AI analysis. An API proxy is currently in development to handle CORS and key security.

Surveys

Create and deploy FCM surveys directly from the platform. Collect responses and automatically generate cognitive maps. Requires Academic plan or higher.

Question Types

30+ question types across several categories:

• Input — Text, textarea, email, phone, number, URL
• Selection — Multiple choice, checkboxes, dropdown, scale, matrix/Likert
• Advanced — Ranking, slider, constant sum, NPS, star rating, semantic differential, date/time, file upload
• Research methods — MaxDiff (best-worst scaling), conjoint (CBC), attention check, consent form, heat map
• FCM-specific — Relationship matrix, concept selection, random assignment, interaction matrix, Mad Lib, FCM ranking
• Layout — Question blocks, text/info, section headers, dividers, images, video

Logic & Branching

• Display Logic — Show or hide questions based on previous answers
• Skip Logic — Route respondents to different pages based on conditions
• Question Piping — Insert previous answers into question text
• Carry-Forward — Populate answer options from earlier questions
• Loop/Merge — Repeat question sets for each selected item
• Randomization — Randomize answer order to reduce bias

Distribution

• Direct link — Shareable URL for web distribution
• Email — Send invitations from contact lists with personalization tokens
• SMS — Webhook-based SMS distribution (Twilio)
• QR code — Auto-generated for print distribution
• Embed code — Embed surveys on external websites
• Panel verification — Contact lists, PIN codes, single-use links

Quality & Compliance

• Attention checks — Built-in question type to detect inattentive respondents
• CAPTCHA — reCAPTCHA integration for bot protection
• GDPR consent — Respondent consent enforcement, including Article 9 for special category data
• Data classification — Tag surveys by sensitivity level
• Password protection — Restrict access with a survey password
• Quotas — Set response limits with a sample size calculator

Customization

Custom themes and branding (colors, logo, fonts), rich text editor for question text, custom thank-you pages with redirect URLs, and multi-language translation support.

Response Analytics

• Dashboard — Summary statistics, response counts, completion rates
• Individual responses — View and filter individual submissions
• Cross-tabulation — Multi-variable analysis with chi-square significance testing
• MaxDiff analysis — Best-worst scaling results
• Conjoint analysis — Choice-based conjoint utilities
• Text analytics — Open-ended response analysis
• Export — CSV, JSON, and codebook formats

Automation

Webhook integrations for real-time response notifications, workflow automation with conditional triggers, and A/B testing with variant management and weight distribution (Professional plan and above).

Figure Editor

Create publication-ready figures from your FCM visualizations.

Customization

Adjust node colors, sizes, and labels. Change edge styles, thickness, and curvature. Apply automatic layout algorithms or manually position elements. Add titles, legends, and annotations.

Export Formats

• PNG — High-resolution raster image for presentations and documents
• SVG — Scalable vector format for journals and further editing
• PDF — Print-ready format with embedded vectors

Figures can be generated from individual models, combined models, or analysis results.

Data & Security

Encryption

All personally identifiable information (PII) is encrypted at rest using AES-256. Email addresses are stored as hashes for lookup, never in plaintext. Session tokens use secure, HttpOnly cookies.

Privacy

Meta-Model and deep learning analyses run entirely in your browser. Survey response data is encrypted before database storage. We support GDPR Article 9 consent enforcement for special category data.

Authentication

Login via email/password, Google OAuth, or GitHub OAuth. Enterprise plans support SAML SSO. All sessions are rate-limited with concurrent session caps.

Frequently Asked Questions