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COMPUTING WITH WORDS AND PERCEPTIONS (CWP) —

COMPUTING WITH WORDS AND PERCEPTIONS (CWP) — A PARADIGM SHIFT IN COMPUTING AND DECISION ANALYSIS Lotfi A. Zadeh Computer Science Division Department of EECS UC Berkeley November 25, 2002 URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/

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COMPUTING WITH WORDS AND PERCEPTIONS (CWP) —

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  1. COMPUTING WITH WORDS AND PERCEPTIONS (CWP) — A PARADIGM SHIFT IN COMPUTING AND DECISION ANALYSIS Lotfi A. Zadeh Computer Science Division Department of EECSUC Berkeley November 25, 2002 URL: http://www-bisc.cs.berkeley.edu URL: http://zadeh.cs.berkeley.edu/ Email: Zadeh@cs.berkeley.edu TEL: (510) 642-4959; FAX: (510) 642-1712 SECRETARY: (510) 642-8271; HOME FAX: (510) 526-2433

  2. LOTFI A. ZADEH COMPUTER SCIENCE DIVISION, DEPARTMENT OF EECS UNIVERSITY OF CALIFORNIA BERKELEY, CA 94720-1776 TEL: (510) 642-4959 FAX: (510) 642-1712 SECRETARY: (510) 642-8271 HOME FAX: (510) 526-2433 E-MAIL: zadeh@cs.berkeley.edu

  3. BACKDROP

  4. COMPUTING WITH WORDS AND PERCEPTIONS—A PARADIGM SHIFT IN COMPUTING AND DECISION ANALYSIS • Computing with words and perceptions, or CWP for short, is a mode of computing in which the objects of computation are words, propositions and perceptions described in a natural language. • Perceptions play a key role in human cognition. Humans—but not machines—have a remarkable capability to perform a wide variety of physical and mental tasks without any measurements and any computations. Everyday examples of such tasks are driving a car in city traffic, playing tennis and summarizing a book. LAZ 9-21-02

  5. BASIC PERCEPTIONS attributes of physical objects • distance • time • speed • direction • length • width • area • volume • weight • height • size • temperature sensations and emotions • color • smell • pain • hunger • thirst • cold • joy • anger • fear concepts • count • similarity • cluster • causality • relevance • risk • truth • likelihood • possibility LAZ 11-25-02

  6. DEEP STRUCTURE OF PERCEPTIONS • perception of likelihood • perception of truth (compatibility) • perception of possibility (ease of attainment or realization) • perception of similarity • perception of count (absolute or relative) • perception of causality subjective probability = quantification of perception of likelihood LAZ 11-25-02

  7. FROM NUMBERS TO WORDS • There is a deep-seated tradition in science of striving for the ultimate in rigor and precision • Words are less precise than numbers • Why and where, then, should words be used? • When precise information is not available • When precise information is not needed • When there is a tolerance for imprecision which can be exploited to achieve tractability, simplicity, robustness and low solution cost • When the expressive power of words is greater than the expressive power of numbers LAZ 11-25-02

  8. CONTINUED • One of the major aims of CWP is to serve as a basis for equipping machines with a capability to operate on perception-based information. A key idea in CWP is that of dealing with perceptions through their descriptions in a natural language. In this way, computing and reasoning with perceptions is reduced to operating on propositions drawn from a natural language. LAZ 9-21-02

  9. CONTINUED • In CWP, what is employed for this purpose is PNL (Precisiated Natural Language.) In PNL, a proposition, p, drawn from a natural language, NL, is represented as a generalized constraint, with the language of generalized constraints, GCL, serving as a precisiation language for computation and reasoning, PNL is equipped with two dictionaries and a modular multiagent deduction database. The rules of deduction are expressed in what is referred to as the Protoform Language (PFL). LAZ 9-21-02

  10. CONTINUED • Any measurement-based theory, T, may be generalized to a perception-based theory, Tp, by adding to T the capability to operate on perception-based information. Two generalizations that are of particular importance involve probability theory, PT, and decision analysis, DA. Conceptually, computationally and mathematically, PTp and DAp are significantly more complex than their measurement-based versions. In this instance, as in many others, complexity is the price that has to be paid to reduce the gap between theory and reality. LAZ 9-21-02

  11. KEY POINTS • decisions are based on information • in most realistic settings, decision-relevant information is a mixture of measurements and perceptions • examples: buying a house; buying a stock • existing methods of decision analysis are measurement-based and do not provide effective tools for dealing with perception-based information • a decision is strongly influenced by the perception of likelihoods of outcomes of a choice of action LAZ 8-12-02

  12. KEY POINTS • in most realistic settings: • the outcomes of a decision cannot be predicted with certainty • decision-relevant probability distributions are f-granular • decision-relevant events, functions and relations are f-granular • perception-based probability theory, PTp, is basically a calculus of f-granular probability distributions, f-granular events, f-granular functions, f-granular relations and f-granular counts LAZ 8-12-02

  13. INEVITABILITY OF PROBABILITY • The only satisfactory description of uncertainty is probability. By this I mean that every uncertainty statement must be in the form of a probability; that several uncertainties must be combined using the rules of probability; and that the calculus of probabilities is adequate to handle all situations involving uncertainty…probability is the only sensible description of uncertainty and is adequate for all problems involving uncertainty. All other methods are inadequate… anything that can be done with fuzzy logic, belief functions, upper and lower probabilities, or any other alternative to probability can better be done with probability [Lindley (1987)] LAZ 8-12-02

  14. CONTINUED • The numerous schemes for representing and reasoning about uncertainty that have appeared in the AI literature are unnecessary –probability is all that is needed [Cheesman (1985)] • Probabilities do not exist [de Finetti (1974)] • I do not know why probability theory works as well as it does [Blackwell (1996)] • Probability theory needs an infusion of fuzzy logic to enhance its ability to come to grips with real-world problems [Zadeh (1996)] LAZ 8-12-02

  15. THE BALLS-IN-BOX PROBLEM measurement based • a box contains 20 balls of various kinds • over 70% are white • there are four times as many white balls as black balls • what is the number of black balls? • what is the probability that a ball drawn at random is black? perception-based • 20 about 20 • 70% white most are large • four times several times • how many black balls how many small balls? • Is black is small neither small nor large? LAZ 8-12-02

  16. CONTINUED ASP TSP traveling salesman problem airport shuttle problem i i j j tij = perceived time of travel from i to j cij = measured cost of travel from i to j LAZ 11-25-02

  17. TEST PROBLEM • Prob {Robert is young} is low Prob {Robert is middle-aged} is high Prob {Robert is old} is low • What is the probability that Robert is neither young nor old? LAZ 11-25-02

  18. TEST PROBLEM • A function, Y=f(X), is defined by its fuzzy graph expressed as f1 if X is small then Y is small if X is medium then Y is large if X is large then Y is small (a) what is the value of Y if X is not large? (b) what is the maximum value of Y Y M × L L M S X 0 S M L

  19. BASIC PROBLEMS WITH PT PT

  20. IT IS A FUNDAMENTAL LIMITATION TO BASE PROBABILITY THEORY ON BIVALENT LOGIC • A major shortcoming of bivalent-logic-based probability theory, PT, relates to the inability of PT to operate on perception-based information • In addition, PT has serious problems with • (a) brittleness of basic concepts • (b) the “it is possible but not probable” dilemma LAZ 8-12-02

  21. MEASUREMENT-BASED VS. PERCEPTION-BASED INFORMATION INFORMATION measurement-based numerical perception-based linguistic • it is 35 C • Eva is 28 • probability is 0.8 • Tandy is three years • older than Dana • It is very warm • Eva is young • probability is high • Tandy is a few • years older than Dana • it is cloudy • traffic is heavy • Robert is very honest LAZ 7-22-02

  22. a box contains 20 black and white balls over seventy percent are black there are three times as many black balls as white balls what is the number of white balls? what is the probability that a ball picked at random is white? a box contains about 20 black and white balls most are black there are several times as many black balls as white balls what is the number of white balls what is the probability that a ball drawn at random is white? MEASUREMENT-BASED PERCEPTION-BASED (version 1)

  23. measurement-based X = number of black balls Y2 number of white balls X  0.7 • 20 = 14 X + Y = 20 X = 3Y X = 15 ; Y = 5 p =5/20 = .25 perception-based X = number of black balls Y = number of white balls X = most × 20* X = several *Y X, Y = 20* P = Y/N COMPUTATION (version 1)

  24. BALLS-IN-BOX EXAMPLE (version 2) • a box contains about N balls of various sizes • most are large • there are many more large balls than small balls • what is the number of small balls? • what is the probability that a ball drawn at random is neither large nor small

  25. MEASUREMENT-BASED VS. PERCEPTION-BASED CONCEPTS measurement-basedperception-based expected value usual value stationarity regularity continuous smooth Example of a regular process T= = travel time from home to office on day i. LAZ 8/1/2001

  26. THERE IS A FUNDAMENTAL CONFLICT BETWEEN BIVALENCE AND REALITY • we live in a world in which almost everything is a matter of degree but • in bivalent logic, every proposition is either true or false, with no shades of gray allowed • in fuzzy logic, everything is or is allowed to be a matter of degree • in bivalent-logic-based probability theory only certainty is a matter of degree • in perception-based probability theory, everything is or is allowed to be a matter of degree LAZ 8-12-02

  27. BASIC PERCEPTIONS / F-GRANULARITY • temperature: warm+cold+very warm+much warmer+… • time: soon + about one hour + not much later +… • distance: near + far + much farther +… • speed: fast + slow +much faster +… • length: long + short + very long +…  small medium large 1 0 size LAZ 8-12-02

  28. CONTINUED • similarity: low + medium + high +… • possibility: low + medium + high + almost impossible +… • likelihood: likely + unlikely + very likely +… • truth (compatibility): true + quite true + very untrue +… • count: many + few + most + about 5 (5*) +… subjective probability = perception of likelihood LAZ 8-12-02

  29. CONTINUED • function: if X is small then Y is large +… (X is small, Y is large) • probability distribution: low \ small + low \ medium + high \ large +… • Count \ attribute value distribution: 5* \ small + 8* \ large +… PRINCIPAL RATIONALES FOR F-GRANULATION • detail not known • detail not needed • detail not wanted LAZ 8-12-02

  30. granule L M S 0 S M L PERCEPTION OF A FUNCTION Y f 0 Y medium x large f* (fuzzy graph) perception f f* : if X is small then Y is small if X is medium then Y is large if X is large then Y is small 0 X LAZ 7-22-02

  31. PROBLEMS WITH PT • Bivalent-logic-based PT is capable of solving complex problems • But, what is not widely recognized is that PT cannot answer simple questions drawn from everyday experiences • To deal with such questions, PT must undergo three stages of generalization, leading to perception-based probability theory, PTp LAZ 8-12-02

  32. REASONING WITH PERCEPTIONS—THE UMBRELLA PROBLEM • I am leaving my house. It is likely to rain. Should I take my umbrella? • Let X be the rate of precipitation. My decision is influenced by the probability distribution of X, P. • I do not know P precisely but have a perception of P which may be expressed in symbols as a f-granular probability distribution: P=low\no.rain + low\light.rain + medium\moderate.rain + low\heavy.rain P P (density) medium low X rate of precipitation light medium heavy LAZ 8-26-02

  33. CONTINUED • my decision rule is: take an umbrella if the probability of moderate or heavy rain is high • based on this rule and my perception of P, should I take my umbrella? • plan of solution: (a) using protoformal rules of deduction compute the probability, q, of moderate or heavy rain (b) compare q with high LAZ 8-26-02

  34. FUNDAMENTAL POINTS • the point of departure in perception-based probability theory (PTp) is the postulate: subjective probability=perception of likelihood • perception of likelihood is similar to perceptions of time, distance, speed, weight, age, taste, mood, resemblance and other attributes of physical and mental objects • perceptions are intrinsically imprecise, reflecting the bounded ability of sensory organs and, ultimately, the brain, to resolve detail and store information • perceptions and subjective probabilities are f-granular LAZ 8-26-02

  35. BASIC STRUCTURE OF PROBABILITY THEORY PROBABILITY THEORY measurement- based perception- based frequestist objective bivalent-logic- based fuzzy-logic- based Bayesian subjective PT generalization PTp • In PTp everything is or is allowed to be perception-based LAZ 8-26-02

  36. MEASUREMENT-BASED VS. PERCEPTION-BASED CONCEPTS measurement-basedperception-based expected value usual value stationarity regularity continuous smooth Example of a regular process T= = travel time from home to office on day i. LAZ 8/1/2001

  37. PROBLEMS WITH PT • Bivalent-logic-based PT is capable of solving complex problems • But, what is not widely recognized is that PT cannot answer simple questions drawn from everyday experiences • To deal with such questions, PT must undergo three stages of generalization, leading to perception-based probability theory, PTp LAZ 8-12-02

  38. SIMPLE EXAMPLES OF QUESTIONS WHICH CANNOT BE ANSWERED THROUGH THE USE OF PT • I am driving to the airport. How long will it take me to get there? • Hotel clerk: About 20-25 minutes • PT: Can’t tell • I live in Berkeley. I have access to police department and insurance company files. What is the probability that my car may be stolen? • PT: Can’t tell • I live in the United States. Last year, one percent of tax returns were audited. What is the probability that my tax return will be audited? • PT: Can’t tell LAZ 8-14-02

  39. CONTINUED • Robert is a professor. Almost all professors have a Ph.D. degree. What is the probability that Robert has a Ph.D. degree? • PT: Can’t tell • I am talking on the phone to someone I do not know. How old is he? • My perception: Young • PT: Can’t tell • Almost all A’s are B’s. Almost all B’s are C’s. What fraction of A’s are C’s? • PT: Between 0 and 1 • The Robert example • The balls-in-box example • The trip-planning example • The umbrella example LAZ 8-23-02

  40. THE TRIP-PLANNING PROBLEM • I have to fly from A to D, and would like to get there as soon as possible • I have two choices: (a) fly to D with a connection in B; or (b) fly to D with a connection in C • if I choose (a), I will arrive in D at time t1 • if I choose (b), I will arrive in D at time t2 • t1 is earlier than t2 • therefore, I should choose (a) ? B (a) A D (b) C LAZ 7-30-02

  41. CONTINUED • now, let us take a closer look at the problem • the connection time, cB , in B is short • should I miss the connecting flight from B to D, the next flight will bring me to D at t3 • t3 is later than t2 • what should I do? decision = f ( t1 , t2 , t3 ,cB ,cC ) existing methods of decision analysis do not have the capability to compute f reason: nominal values of decision variables ≠observed values of decision variables LAZ 7-30-02

  42. CONTINUED • the problem is that we need information about the probabilities of missing connections in B and C. • I do not have, and nobody has, measurement-based information about this probabilities • whatever information I have is perception-based • with this information, I can compute perception-based granular probability distributions of arrival times in D for (a) and (b) • the problem is reduced to ranking of granular probability distributions Note: subjective probability = perception of likelihood LAZ 8-12-02

  43. THE KERNEL PROBLEM —THE SIMPLEST B-HARD DECISION PROBLEM time of arrival missed connection 0 alternatives a b • decision is a function of and perceived probability of missing connection • strength of decision LAZ 8-19-02

  44. CRISP PARETO OPTIMALITY LEADS TO COUNTERINTUTIVE CONCLUSIONS gain gain gain gain b b b b a a a a 1) all 2) many 3) not sure 4) no one b > a LAZ 08-10-02

  45. PERCEPTION-BASED GRANULAR PROBABILITY DISTRIBUTION probability P3 P2 P1 0 arrival time (AT) A2 A1 A3 P(AT) = P1\A1 +P2\A2 + P3\A3 Prob {AT is Ai } is Pi LAZ 7-30-02

  46. BRITTLENESS (DISCONTINUITY) • Almost all concepts in PT are bivalent in the sense that a concept, C, is either true or false, with no partiality of truth allowed. For example, events A and B are either independent or not independent. A process, P, is either stationary or nonstationary, and so on. An example of brittleness is: If all A’s are B’s and all B’s are C’s, then all A’s are C’s; but if almost all A’s are B’s and almost all B’s are C’s, then all that can be said is that proportion of A’s in C’s is between 0 and 1. LAZ 8-14-02

  47. THE DILEMMA OF “IT IS POSSIBLE BUT NOT PROBABLE” • A simple version of this dilemma is the following. Assume that A is a proper subset of B and that the Lebesgue measure of A is arbitrarily close to the Lebesgue measure of B. Now, what can be said about the probability measure, P(A), given the probability measure P(B)? The only assertion that can be made is that P(A) lies between 0 and P(B). The uniformativeness of this assessment of P(A) leads to counterintuitive conclusions. For example, suppose that with probability 0.99 Robert returns from work within one minute of 6pm. What is the probability that he is home at 6pm? LAZ 8-14-02

  48. BRITTLENESS OF PROBABILISTIC COMPUTATIONS p: with probability 0.9, Robert returns from work at 6pm ± 10 min. q: what is the probability, r, that Robert is home at 6 pm? 6:11pm? 5:49 pm? answer: 0≤ r ≤1 ; answer: r ≥ 0.9 ; answer: r ≤ 0.1 p: with probability 0.9, Robert returns from work at 6 pm ± 1 min. q: what is the probability, r, that Robert is home at 6 pm? 6:01 pm? 5:59 pm? answer: 0≤ r ≤1; answer: r ≥ 0.9 ; answer: r ≤ 0.1 1.0 0.9 0.1 0 5:50 6:10 LAZ 8-14-02

  49. CONTINUED U U B B A A A B: proper subset of A A= proper subset of B LAZ 8-14-02

  50. CONTINUED • Using PT, with no additional information or the use of the maximum entropy principle, the answer is: between 0 and 1. This simple example is an instance of a basic problem of what to do when we know what is possible but cannot assess the associated probabilities or probability distributions. A case in point relates to assessment of the probability of a worst case scenario. LAZ 8-14-02

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