Fuzzy Logic-Based Disaster Mitigation and Extreme Event Detection Dan Tamir, Naphtali D. Rishe, and...
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Transcript of Fuzzy Logic-Based Disaster Mitigation and Extreme Event Detection Dan Tamir, Naphtali D. Rishe, and...
Fuzzy Logic-Based Disaster Mitigation and Extreme Event Detection
Dan Tamir, Naphtali D. Rishe, and Abraham Kandel
© 2015 Tamir, Rishe, Kandel
Prelude
We need a FORMAL understanding of the relations between uncertainty, that is immersed in disaster mitigation programs (DMP), and Fuzzy Logic. Just as the FORMAL notions of computer science have immensely benefited software and hardware design, a formal treatment of DMP should also lend to significant advances in the way that these programs and systems are developed and designed in the future.
Preparedness
Swans come in different shades of Gray:White Swans,Gray Swans, Black Swans,
So, in fact, all Swans are Gray
Preparedness
Swans come in different shades of Gray:White Swans,Gray Swans, Black Swans,
Second Generation Swans
Yes. But then, there are the
Some Disasters are Black Swans
The Black Swan is an outlier and it carries an extreme adverse impact
After the Fact: It is explainable and predictable Low predictability and large adverse impact What you don’t know is far more relevant than what
you do know
Well…, you did not connect the dotsI was completely
surprised
Some Disasters are Gray Swans
The Gray Swan is an unlikely event It can be anticipated It carries an extreme adverse impact
But you were not prepared for the second shock and the
aftermath
We were completely prepared for this disaster
Ramification of Unanticipated Disasters
No recipe for success Leadership is key Trying to adhere to a set of “best practices” which
have been set ahead of time and used in training and ramification exercises can help reducing cost and risk
Improvisation In addition, existing Swans might (are likely to)
spawn unanticipated second generation Swans
Example: the 9/11 collapse of the Twins
Can I take a course on leadership?
Ramification of Anticipated Disasters
Leadership is key Following instructions derived from set of
“best practices” which have been set ahead of time and used in training and ramification exercises
However, existing Swans might (and are likely to) spawn second generation SwansFor example, nuclear radiation following a
tsunami
Only computers follow instructions
Second Generation Swans
Second generation Swans are Swans that are generated and / or detected while the disaster is in effect.
A Gray Swan, might (and according to the Murphy lows is likely to) spawn a Black Swan.
Generally, second generation Swans evolve late and fast.
Hence, this introduces a more challenging detection problem
Second Generation Gray Swans
Even in the extreme cases where the nature of the disaster is known, preparedness plans are in place, and analysis, evaluation, and simulations of the disaster management procedures have been performed, the amount and magnitude of “surprises” that accompany the real disaster pose an enormous demand
Detecting relatively slow evolving [first generation] Gray Swans before the disaster occurs and relatively fast evolving second generation Gray Swans requires an adequate set of uncertainty management tools
Primo, currently more people are dying from self inflicted wounds (e.g., smoking) then from disasters. Disaster, however, have potential for extreme (deadly) impact. Secundo, disasters, cause outrage, fear, and chaos. In failing to address disaster, we betray those who had high hopes for us. People say “focus.” This is a great virtue if you are a brain surgeon or a chess player. The last thing you need to do when you deal with outliers and uncertainty is to “focus.” Treso, as Yogi Berra said “It is tough to make predictions, especially about the future” and “you got to be very careful if you don't know where you're going, because you might not get there.”
Examples of Gray Swans
• Bangladeshi factory collapse; Iceland volcano eruption • Arab Spring - a seemingly White Swan that spawns a Gray
Swan that spawns a Gray Swan that spawns a grey Swan– Civil war in Syria
• Fukushima - tsunami followed by nuclear radiation and risk of meltdown of nuclear facilities in the area.
• 9/11 NYC attack followed by the collapse of the Twins• Y2K (was this a wolf-wolf-wolf ignited by grid?) • Financial Markets (1987, 2008), Madoff• 1998 Long-Term Capital Management• Yom Kippur War• December 7, 1941 - Pearl Harbor• Lincoln, Kennedy, Sadat, and Rabin assassinations
Black Swans and Fairy Tales
Robert Merton, Jr., and Myron Scholes were founding partners in the large speculative trading firm called Long-Term Capital Management, or LTCM. It was a collection of people with top-notch resumes, from the highest ranks of academia. They were considered geniuses. The ideas of portfolio theory inspired their risk management of possible outcomes - thanks to their sophisticated “calculations.” They managed to enlarge the ludic fallacy to industrial proportions.
Then, during the summer of 1998, a combination of large events, triggered by a Russian financial crisis, took place that lay outside their models. It was a Black Swan. LTCM went bust and almost took down the entire financial system with it.
Monstrous amount of risk.
The 9/11 Attack
What did we learn from the 9/11 episode?• We have learned precise rules for avoiding
Islamic proto-terrorists and tall buildings• We do not learn rules, just facts and only facts• Black Swan is a suckers problem - it occurs
relative to your expectations
Expectations Killed the Turkey
• Expectations are based on induction• Expectations are based on perception• Expectations can be dead wrong• It's what the Turkey doesn't know...
Expectations Killed the Turkey
Some people are like the Turkey. Exposed to a major first generation or second generation Gray Swans without being aware of it, while others play reverse Turkey (using Fuzzy logic) prepared for Swans of any Gray level or generation that might surprise others.
Hiding in Plain Sight
• Black Swans are not impossible to predict• Black Swans exist because we choose to
ignore the data that allows us to anticipate them
• The Black Swan is a suckers problem. In other words it occurs relative to your expectation.
The Problem of Induction
Mathematical induction is sound , but intuitive induction is dangerous• Observed events do not always determine the
future• Induction does not account for outliers• Induction hides the Gray Swan; it removes the
Gray Swan from “the equation.”
Induction in Mediocristan
• In Mediocristan there are no consequential variations from expectations
• Induction is great for Mediocristan Induction fails in Extremistan
We Live in Extremistan
We pretend to live in Mediocristan by• Generalizing• Creating explanations based on patterns• Discarding the possibility of a Black SwanWe DO live in Extremistan• Do not be the Turkey
When Missing a Train is Painless
Jean-Olivier Tedesco said “I don't run for trains.” Missing a train is only painful if you run after it. In disaster mitigation terms, this means that you are exposed to the improbable only if you let it control you.
Poincare
Poincare's reasoning was simple: as you project into the future you may need an increasing amount of precision about the dynamics of the process that you are modeling, since your error rate grows very rapidly. The problem is that near precision is impossible since the degradation of your forecast compounds abruptly.
Easier Than you Think: The Problem of Decision Under Fuzziness
Looking into Fuzzy tools is motivated by the fact that precision is costly. Precise information is costly to obtain, costly to store, and costly to manipulate and retrieve.
Avoid being a sucker.
Na Na Na Na Na Na
The Rarer the Event, the Fuzzier the Odds
Detection of a looming disaster is similar to cancer detection:The finding of a single malignant tumor proves that you have cancer, but the absence of such a finding cannot allow you to say with certainty that you are cancer-free.
Not so bad tools
1. Fuzzy Switching Mechanisms2. Fuzzy Expected Value3. Fuzzy Relational Data Bases, Fuzzy Expert Systems and
Fuzzy Dynamic Forecasting (FDEs)4. Fuzzy Data-Mining and Fuzzy social Network
Architectures (FSNA)5. Value-at-Risk (VaR) under Fuzzy uncertainty6. Non-cooperative Fuzzy games and Fuzzy Prisoners
Dilemma game7. Fuzzy logic driven web crawlers and web-bots
Fuzzy Switching Mechanisms
Fuzzy switching mechanisms can serve as a tool for making decisions with insufficient dataHazardous variable imply imprecision in the systemThe imprecision stems from lack of sharp input transitionsThe fuzzy switching theory can serve as a tool for identifying hazardous transients
Fuzzy Expectations and The Theory of Typicality
In essence, the theory of Fuzzy sets is aimed at the development of a body of concepts and techniques for dealing with sources of uncertainty or imprecision that are non-statistical in nature.
More Tools
1. Complex and Multidimensional Fuzzy Sets, Logic, and Systems
2. Neuro Fuzzy based Logic, and Systems – Scalar, complex, and multidimensional variants
3. Fuzzy Clustering– Dynamic and Incremental Clustering– Operating in Scalar, complex, and
multidimensional Spaces
Complex and Multidimensional Fuzzy Sets, Logic, and Systems
The Cartesian representation of the pure complex grade of membership is given in the following way:
Where and, the real and imaginary components of the pure complex fuzzy grade of membership, are real value fuzzy grades of membership. That is, and can get any value in the interval. The polar representation of the pure complex grade of membership is given by:
Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of cyclic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction
Complex and Multidimensional Fuzzy Sets, Logic, and Systems
The definition of complex Fuzzy sets, logic and systems can be extended to multidimensional fuzzy sets, logic and systems, thereby enabling inference in highly uncertain domains. In specific domains represented by linguistic variables.
Moreover, the definition can be used for the construction of multidimensional Neuro-Fuzzy inference systems (described later) and for incremental fuzzy clustering in a multidimensional feature space composed of linguistic variables (described later).
Neuro-Fuzzy systems• The term Neuro-Fuzzy systems refers to combinations of artificial neural
networks and Fuzzy logic.• Neuro-Fuzzy systems enable modeling human reasoning via fuzzy
inference systems along with the modeling of human learning via the learning and connectionist structure of neural networks.
• Neuro-Fuzzy systems can serve as highly efficient mechanisms for inference and learning under uncertainty. Furthermore incremental learning techniques can enable observing outliers and the Fuzzy inference can allow these outliers to coexist (with low degrees of membership) with “main-stream” data. As more information about the outliers becomes available, the information, and the derivatives of the rate of information flow can be used to identify potential Black Swans that are hidden in the outliers
• The classical model of Neuro-Fuzzy systems can be extended to include multidimensional Fuzzy logic and inference systems in numerical domains and in domains characterized by linguistic variables.
Dynamic and Incremental Fuzzy Clustering
• Clustering is a widely used mechanism for pattern recognition and classification.
• Fuzzy clustering (e.g., the Fuzzy C-means) enables patterns to become members of more than one cluster. – Additionally, it enables maintaining clusters that represent outliers through
low degree of membership.– These clusters would be discarded in clustering of hard (vs. Fuzzy) data.
• Incremental and dynamic clustering (e.g., the incremental Fuzzy ISODATA) enable the clusters’ structures to change as information is accumulated. – Again, this is a strong mechanism for enabling identification of unlikely events
(i.e., Black Swans) without premature discarding of these events
Dynamic and Incremental Fuzzy Clustering
• The clustering can be performed in a traditional feature space composed of numerical measurements of feature values.
• Alternatively, the clustering can be performed in a multidimensional Fuzzy logic space where the features represent values of linguistic variables
• The combination of powerful classification capability, adaptive and dynamic mechanisms, as well as the capability to consider uncertain data, maintain data with low likelihood of occurrence, and use a combination of numerical and linguistic values makes this tools one of the most promising tools for detecting Black Swans.
To Be
• Accelerate delivery of technical capabilities to win the current fight
• Prepare for an uncertain future
Be prepared
To Be
• Accelerate delivery of technical capabilities to win the current fight
• Prepare for an uncertain future• Reduce the cost, acquisition time, and risk of
major defense / disaster mitigation acquisition programs
• Develop world class science, technology, engineering and mathematics (STEM) capabilities for the Agencies and the Nation.