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Using Fuzzy Cognitive Maps to Model Policy Issues in the face of Uncertainty and Limited Data

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Brian Gregor, Oregon Analytics

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Using Fuzzy Cognitive Maps to Model Policy Issues in the face of Uncertainty and Limited Data

  1. 1. Using Fuzzy Cognitive Maps to Model Policy Issues in the face of Uncertainty and Limited Data Portland State University Friday Seminar February 17, 2017 Brian Gregor, P.E. – Oregon Systems Analytics
  2. 2. Outline • Background on Fuzzy Cognitive Maps (FCM) and their usefulness for modeling issues involving uncertainty; • The mathematical formulation of an FSDM and how it differs from common FCM models; • Open source software for building and running an FSDM; and, • Results of research with ODOT and OSU on modeling the potential effects of new transportation technologies and services using an FSDM.
  3. 3. Business as usual planning is no longer adequate •Increasing ‘automobility’ is no longer a foregone conclusion; •Disruptive technologies and services are emerging; •EVs and more fuel efficient vehicles are making it necessary to pursue new revenue sources; •Substantial environmental constraints are apparent There is a lot of uncertainty about how things will play out. 3
  4. 4. Example of uncertainty about future vehicle miles traveled (VMT) 4 1980 2000 2020 2040 2060 20406080100120140 Year Annual2010$(thousands) Exponential Grow th Linear Grow th 1980 2000 2020 2040 2060 0.100.150.200.250.300.350.40 Year MilesPer2010$ Exponential Decline Linear Decline 1980 2000 2020 2040 2060 10000150002000025000 Year AnnualMiles Exp Grow th & Decline Exp Grow th & Lin Decline Lin Grow th & Exp Decline Lin Grow th & Decline Miles Per Driver=VMT Number of Drivers x Miles Per DriverPer Capita GDP x = Per Capita GDP Miles Per Driver
  5. 5. Models enhance our ability to reason about the future even when there is uncertainty Everyone is a modeler to some extent. In most cases we use mental models to help us reason. We are accustomed to using mental models to reason about questions that involve uncertainty. Due to our limited abilities to think in systems terms, our mental models are limited as well. Differences in our mental models leads to conflict. Computer models can “reason” about large systems in a consistent manner. Proper use of computer models can help produce consensus.
  6. 6. Soft computing methods are useful for modeling systems involving uncertainty and imprecision • Fuzzy cognitive maps (FCMs) describe causal systems as directed graphs. • Nodes identify concepts of interest: values between 0 and 1. • Edges show causal connections. Arrows point from cause to effect. • Edge weights indicate magnitude and direction of causality. • Typically expressed as linguistic variables: e.g. low, medium, high. • Translated to fuzzy numbers or values between -1 and 1 (most common approach) • Expert opinion commonly used in development. Ozesmi, Ecological Modelling, 176 (2004) 43–64
  7. 7. Standard FCM math and its limitations 𝑟′ = 𝑓 𝑖=1 𝑛 𝑤𝑖 ∗ 𝑐′𝑖 𝑓( activation function Fuzzy cognitive maps are neural networks with feedback. Issues • Weights relate the states of concepts rather than changes in state. • Meaning of iteration is unclear. • Meaning of the activation function is unclear. • Need to invert concepts to avoid negative weights. • Convergence can be problem and results may not make sense. If graph contains cycle(s), iterate to convergence (if it does converge)
  8. 8. Fuzzy System Dynamics Model (FSDM) • Weights are similar to elasticities. Their meanings are clear. • Sensitivity functions modify weights as a function of concept value. • Causal concept(s) of interest are incremented in small steps. • If model contains one or more cycles, calculations are iterated to convergence. • Node values in range of 0-100 (% of maximum assumed real value) 𝑤 = 𝑟′ − 𝑟 𝑟 𝑐′ − 𝑐 𝑐 ∆𝑟 = 𝑠 𝑟 ∗ 𝑖 𝑛 𝑠𝑐 ∗ 𝑤𝑖 ∗ ∆𝑐𝑖 + 1 − 1 0 20 40 60 80 100 0.00.20.40.60.81.0 Concept Level SensitivityFactor Causal Sensitivity Receiving Sensitivity sc = causal sensitivity sr = receiving sensitivity
  9. 9. Running the FSDM 0 100 200 300 400 500 52545658 All Increments Iteration PercentCongestedVMT 0 5 10 15 20 25 30 51.051.151.251.351.451.551.6 First 3 Increments Iteration PercentCongestedVMT Causal concept(s) of interest are incremented in small steps. • Elasticities relate small changes in cause to effect; and • Large changes don’t happen immediately. With each increment of the causal concept(s), if there are cycles (i.e. feedback loops), the model is iterated to convergence. • Iterations calculate successive orders of effects. Although time is not explicit in the model, it can be approximated by increments to causal concept(s) of interest. Iterations to reach convergence Net effect of one increment Causal variable(s) of interest are incremented in small steps Iteration to convergence with each increment Example: Effect of Density Change on Congestion
  10. 10. Steps for Creating a FSDM • Define the concepts being modeled • Descriptive names (and abbreviations) • e.g. Relative auto capacity (RelAutoCap) • Meaning and, if possible, how measured • e.g. Freeway equivalent lane-miles of freeways and arterials per 1000 persons • Plausible range of values • e.g. 0.5 – 5.0 • Group the concepts into related sets to simplify model development and understanding, for example: • Transportation technologies and services • Travel behavior and outcomes • Specify the causal relationships and direction of causality • Positive: increase causes increase • Negative: increase causes decrease • Specify the relative magnitude of weights: VL, L, ML, M, MH, H, VH • VH: Mathematical identity relationships • H: Direct and immediate relationships • M: Causal variable is major determinant but effect depends on other factors too. • Specify scenarios • Starting values of all concepts • Changes to values of causal concepts of interest.
  11. 11. Software for building and running FSDM models • Demonstration to show how models are specified and run • https://github.com/gregorbj/FSDM_GUI
  12. 12. Modeling the potential effects of new transportation technologies and services • Research sponsored by the Oregon Department of Transportation • Project manager: Alex Bettinardi • Research Team: Oregon Systems Analytics & Oregon State University • Brian Gregor (OSA) • Haizhong Wang (OSU) • Rachel Vogt (OSU) • Autonomous vehicles • Owned autonomous vehicles • Shared autonomous vehicles • Connected vehicles • Intelligent infrastructure • Mobile Technologies • Demand-responsive transportation services • Light-weight electric vehicles (e.g. electric bicycles)
  13. 13. Model of transportation technologies and services
  14. 14. Model of travel outcomes
  15. 15. Model of connections between technologies/services and outcomes
  16. 16. Testing the Travel Behaviors & Outcomes Sub-model 2000 4000 6000 8000 10000 12000 20406080 Density vs. Congestion Population Weighted Density PercentofVMTinCongestion 47 Metropolitan Areas PDX Model 2000 4000 6000 8000 10000 12000 6000800010000120001400016000 Density vs. Vehicle Travel Population Weighted Density PerCapitaVMT 47 Metropolitan Areas PDX Model 2000 4000 6000 8000 10000 12000 0.750.800.850.90 Density vs. Speed Population Weighted Density RatioofCongestedvs.UncongestedSpeed 47 Metropolitan Areas PDX Model 2000 4000 6000 8000 10000 12000 65707580 Density vs. Auto Ownership Population Weighted Density %HavingAccesstoMoreThan1Vehicle 47 Metropolitan Areas PDX Model Doubled Density Scenario Comparison of Model Results with Data for 93 Metropolitan Areas 1.0 1.2 1.4 1.6 1.8 2.0 20406080 Highway Capacity vs. Congestion Relative Highway Capacity PercentofVMTinCongestion 93 Metropolitan Areas PDX Model 1.0 1.2 1.4 1.6 1.8 2.0 6000800010000120001400016000 Highway Capacity vs. Vehicle Travel Relative Highway Capacity PerCapitaVMT 93 Metropolitan Areas PDX Model 1.0 1.2 1.4 1.6 1.8 2.0 0.750.800.850.90 Highway Capacity vs. Speed Relative Highway Capacity RatioofCongestedvs.UncongestedSpeed 93 Metropolitan Areas PDX Model 1.0 1.2 1.4 1.6 1.8 2.0 707274767880 Highway Capacity vs. Auto Ownership Relative Highway Capacity PercentageofHouseholdswith1orFewerVehicles 93 Metropolitan Areas PDX Model Increased Road Capacity Scenario Comparison of Model Results with Data for 93 Metropolitan Areas Double Density Scenario Comparison with 47 Metropolitan Areas Increase Road Capacity Scenario Comparison with 47 Metropolitan Areas
  17. 17. Test of increasing capacity and increasing density
  18. 18. Test of increasing capacity and reducing autonomous vehicle cost
  19. 19. Conclusions Models can be useful in every planning domain. • We need simple models for policy development as well as complex models for project development. It is useful to model systems for which there is uncertainty. • Enforces consistency in reasoning. • Helps form consensus. FSDM is a promising modeling approach for policy matters that involve uncertainty. • The process of model development helps bring rigor to policy discussions. • Models can accommodate uncertainty. • Can be easily modified to test different assumptions.
  20. 20. Next Steps ODOT independent review underway • Transportation futures model: evaluating model and developing and evaluating alternatives. • Evaluating usability of FSDM software. Improve documentation and awareness • Publish in journals • Other More work needed to improve the method and model. • Sensitivity function theory. • Use fuzzy numbers for weights. • Guidance on establishing weights.
  21. 21. Contacts: FSDM software and algorithms Brian Gregor, Oregon Systems Analytics: gregor@or-analytics.com https://github.com/gregorbj/FSDM_GUI Transportation Futures Research Haizhong Wang, Oregon State University: Haizhong.Wang@oregonstate.edu Alex Bettinardi, Oregon Department of Transportation: Alexander.O.BETTINARDI@odot.state.or.us Brian Gregor, Oregon Systems Analytics: gregor@or-analytics.com Acknowledgements: This research was partially supported through funding from the Oregon Department of Transportation and the Federal Highway Administration, U.S. Department of Transportation. Contacts and Acknowledgements

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