Fuzzy Logic in Mining – Are Right and Wrong Fuzzy Concepts ?

1. Fuzzy Logic in Mining – Are Right and Wrong Fuzzy Concepts? John A. Meech University of British Columbia Norman B. Keevil Institute of Mining Engineering Vancouver, British Columbia, Canada jameech@gmail.com 2014 SUSTAINABLE INDUSTRIAL PROCESSING SUMMIT AND EXHIBITIONSHECHTMAN INTERNATIONAL SYMPOSIUM

2. Fuzzy versus Quasi • You have heard a lot about Quasi-crystals • Now let's consider Logic • Logic is supposedly binary • You are right or you are wrong • But that is always after the fact • How do we describe your state when you are dealing with decision-making under conditions of Uncertainty?

3. What is Fuzzy Logic? When the only tool you have is a hammer, all your problems look like a nail. - Lotfi Zadeh, University of California, Berkeley The Father of Fuzzy Logic • A method to develop approximate solutions that tolerate imprecision • Conventional mathematical models often demand a degree of precision that is difficult to achieve (adaptation may also be a problem) • Models may only work over a small region in time or space, particularly non-linear ones

4. The Whole World is Fuzzy! • We all use FL everyday in a natural way without even realizing it • FL is a method that “computes with words” rather than with numbers • FL deals with how we think about control rather than modeling the process itself • A FL system is how we verbalize our understanding of the process

5. 100 0 Degree of Belief (DoB) Fuzzy Set Terminology

6. Fuzzy Day to Night

7. Fuzzy Set Examples • An automobile changing lanes while passing • The position of the shoreline during tidal inflow or outflow • A door being closed or opened (it's ajar!) • A water valve being opened or closed • A glass of water (Is it half-full or half empty?) • The mixing together of two primary colours • The age of a young customer in a bar (is ID required?) • The time it takes to drive from home to work • The estimated waiting time in a queue

8. Fuzzy Lanes 100 0 Degree of Belief (%) 100 0 Fast Lane Slow Lane

9. Fuzzy Lanes 100 0 Degree of Belief (%) The Car is in the SLOW Lane 100 0 Fast Lane Slow Lane

10. Fuzzy Lanes 100 0 Degree of Belief (%) The Car is in the FAST Lane 100 0 Fast Lane Slow Lane

11. Fuzzy Lanes 100 0 Degree of Belief (%) Oh, oh! Where is the Car? 100 0 Fast Lane Slow Lane

12. Fuzzy Lanes 100 80 60 40 20 0 The Car is almost all in the SLOW Lane but partly in the FAST Lane! Degree of Belief (%) 100 80 60 40 20 0 Fast Lane Slow Lane Let’s replace the Crisp Sets With Fuzzy Sets!

13. Fuzzy Lanes 100 80 60 40 20 0 The Car is half in the SLOW Lane and half in the FAST Lane! Degree of Belief (%) 100 80 60 40 20 0 Fast Lane Slow Lane

14. Fuzzy Lanes 100 80 60 40 20 0 The Car is partly in the SLOW Lane but almost all in the FAST Lane! Degree of Belief (%) 100 80 60 40 20 0 Fast Lane Slow Lane

15. Fuzzy Lanes 100 80 60 40 20 0 Degree of Belief (%) The Car is in the FAST Lane 100 80 60 40 20 0 Fast Lane Slow Lane

16. Fuzzy Statements • I am 90% sure about this. • It is warm today.(same meaning in Yellowknife as in Miami?) • It may rain today. (where, when, how intense, for how long?) • A “recession” is a “decline in GDP” over 2 consecutive quarters. • A “depression” is a severe (10% GDP drop) or prolonged (3-4 year) recession. • “Read my lips: no new taxes” – G.H.W. Bush, 1988 • "It depends on what the meaning of the word 'is' is." – W.J. Clinton, 1998

17. Paradoxes • A man says: Don't Trust Me. Should you trust him? If you do, then you don't! • A politician says: All politicians are liars. Is this true? If so, then he is not a liar. • A card states on one side: The sentence on the other side is false... • On the other side appears: The sentence on the other side is true... How do you interpret this card?

18. Paradoxes Bertrand Russell's Famous Paradox: “All rules have exceptions.” Is this a rule? If so, then what is its exception? • The Liar's Paradox represented by "This sentence is false." can only be understood as a half truth. It can never be a true statement and it never can be a false statement.

19. Fuzzy vs. Binary Binary Approach to Assessing a Decision

20. Fuzzy vs. Binary Fuzzy Approach to Assessing a Decision 0 100 -C.L. C.L. 100 100 C.L. 100 – C.L. 0 Confidence Level (C.L.) = 70%

21. Fuzzy vs. Binary Fuzzy Approach to Assessing a Decision 0 100 -C.L. C.L. 100 100 C.L. 100 – C.L. 0 Confidence Level (C.L.) = 60%

22. Fuzzy vs. Binary Fuzzy Approach to Assessing a Decision 0 100 -C.L. C.L. 100 100 C.L. 100 – C.L. 0 Confidence Level (C.L.) = 80%

23. Managing Uncertainty • FL gives an evolutionary approach to adapt • FL model is simple and intuitive • Decision-making involves 3 states • Accept • Reject • Wait (or Hold) • As evidence mounts, we move towards a conclusion

24. NEW IDEA! The process is evolutionary. It begins with an idea or theory being formulated. At this stage, belief in the theory must “Wait for More Information”. Data are classified into variables that support or deny the theory. Weights are developed to assign the relative importance of each variable and an assembly of all facts is made to derive a current Degree of Belief in the theory. Wait for More Information 100 75 67 50 33 25 0 0 25 33 50 67 75 100 Data are gathered and applied in a way that the Degree of Belief (DoB) in “Wait for More Information” drops. The DoBdepends on the relative importance of contradictory and supportive evidence. START A Confidence Level (CL) is selected. If the current DoB exceeds CL, the theory is Accepted. If the current DoB is less than 100 – CL, the theory is Rejected. When a certain amount of evidence is collected, the theory may become “Worthy of Consideration”. Supportive Evidence Contradictory Evidence WORTHY OF CONSIDERATION DoB Reject Accept Accept CL = 67 Reject Accept 0 25 33 50 67 75 100 Neither supportive nor contradictory

25. Weighting the Evidence • Each new piece of evidence possesses three components • Contribution to the Degree of Belief in ACCEPT - DOBAccept • Contribution to the Degree of Belief in REJECT - DOBReject • Contribution to the Degree of Belief in WAIT - DOBWait • DOBAccept can be a complement of DOBReject but not necessarily • DOBWait = 0 if  DOBAccept and DOBReject are complementary • Knowledge of any two  DoBs allows the third to be calculated • DOBAccept is calculated using fuzzy sets and weights • Small influence: weight = 0.1 (can be variable, i.e., type II) • Medium influence: weight = 0.2 (can be variable, i.e., type II) • Large influence: weight = 0.3 (can be variable, i.e., type II) • The boundary between each zone is fuzzy (i.e., a type II set) • Confidence Level is also a type II fuzzy set selected by an expert

26. Example: Climate Change • CO2 is a Greenhouse Gas (radiative forcing) • Atmospheric CO2 levels are increasing • Increase due to fossil fuel combustion • Temperature levels are increasing (or not) • Degree of heating affected by feedback issues • Albedo, Clouds, Particulate matter, El Nino/La Nina • Extreme weather events, sea levels rising • Oops – there has been no warming for 17 years. • Conclusion: we should "wait for more info"

27. Conclusion • FL provides a natural way of modeling how we think and speak about subjects • FL is much better than binary logic in dealing with real-world problems • FL gives an evolutionary way to make decisions about complex subjects • The process is easy to understand and use

28. Thanks for listening!Questions?