## A New Direction in Decision Analysis

(ARO) DAAH 04-961-0341, BISC, (NASA) NCC2-1006, (NASA) NAC2-117, (ONR) N00014-00-1-0621, (ONR) N00014-99-C-0298, (ONR) N00014-96-1-0556, and (ONR) FDN0014991035

Decisions are based on information. More often than not, decision-relevant information is a mixture of measurements and perceptions. For example, in deciding on whether or not to buy a house, what might be called measurement-based information pertains to the price of the house, the taxes, the mortgage rate, age, area, size of the lot, etc., while the perception-based information relates to the appearance of the house, the quality of construction, security, access to public transportation, etc.

Humans have a remarkable capability to make rational decisions based only on perceptions of values of decision variables, without any measurements and any computations. It is this capability that makes it possible for humans to drive in heavy traffic, play golf, park a car, and summarize a story. And it is this capability that the existing methods of decision analysis do not possess.

The incapability of existing methods of decision analysis to operate on perception-based information has a serious implication. More specifically, in most realistic settings, decision-relevant information includes probabilities of possible outcomes and future events. For example, in buying a house, an important consideration might be the probability that prices of houses will be rising in the months ahead. In general, decision-relevant probabilities are subjective and, in essence, are perceptions of likelihood. As perceptions, such probabilities are intrinsically imprecise. Computation with perception-based probabilities is an essential capability which the existing methods of decision analysis do not have.

As an illustration, consider a simple trip-planning problem, I have to fly from city A to city B and need to get there as soon as possible. There are two alternatives: (a) fly to D via B; and (b) fly to D via C. (a) will bring me to D earlier than (b). However, the connection time at B is short, and there is a likelihood that I may miss it, in which case I will have to take the next flight and will arrive in D much later. Neither I nor anyone else knows the numerical value of the probability that I may miss the connection. With this in mind, should I choose (a) or (b)? Decision analysis does not provide an answer to this question.

In perception-based decision analysis, or PDA for short, perception-based information is dealt with through the use of the computational theory of perceptions (CTP). In CTP, the point of departure is not a perception per se, but its description in a natural language. Thus, a perception is equated to its description. In this way, computation with perceptions is reduced to computation with propositions drawn from a natural language.

Reflecting the bounded ability of human sensory organs and, ultimately, the brain, to resolve detail and store information, perceptions are intrinsically imprecise. More specifically, perceptions are f-granular in the sense that (a) the boundaries of perceived classes are fuzzy; and (b) the values of perceived attributes are granulated, with a granule being a clump of values drawn together by indistinguishability, similarity, proximity or functionality. For example, the values of age as a granulated variable might be: young, middle-aged, old, very old, etc. Similarly, the values of probability might be: likely, not very likely, unlikely, etc.

F-granularity of perceptions puts them well beyond the expressive power of existing meaning-representation languages. In CTP, what is employed for meaning representation is precisiated natural language (PNL). A key idea in PNL is that the meaning of a proposition, p, drawn from a natural language, NL, may be represented as a generalized constraint of the form X isr R, where X is the constrained variable that is implicit in p; R is the implicit constraining relation; and r is an indexing variable which identifies the way in which R constrains X. The principal types of constraints are: possibilistic (r=blank); veristic (r=v); probabilistic (r=p); random set (r=rs); fuzzy graph (r=fg); and usuality (r=u). The constraint X isr R is referred to as a generalized constraint form, GC-form, and plays the role of a precisiation of p, p*. A proposition is precisiable if it has a GC-form. The language of GC-forms and their combinations is referred to as the Generalized Constraint Language, GCL. In relation to NL, GCL plays the role of a precisiation language.

Essentially, PNL is a sublanguage of NL which consists of propositions which are precisiable through translation from NL to GCL. More specifically, PNL is equipped with (a) a dictionary from NL to GCL in which the entries are (p, p*); (b) a dictionary from GCL to protoformal language (PFL), in which p* is paired with its abstracted form, e.g., QA's are B's, where p is: most Swedes are tall; and (c) a collection of protoformal rules of deduction which serves as a system for reasoning with perceptions through the use of goal-directed propagation of generalized constraints.

In PNL, perception-based probability distributions are represented as f-granular probability distributions expressed symbolically as P1 \ A1 + --- + Pn \ An, where the Ai are f-granular values of a random variable, X, and the Pi are f-granular values of their respective probabilities, that is, Pi=Prob{X is Ai}. For example, assume that I have to decide on whether to take an umbrella, given my perception that the f-granular probability distribution of rain is: P= low\no rain+low\light rain+high\moderate rain+low\heavy rain. A decision rule, then, may be: Take an umbrella if the perception of the probability distribution of rain is P. An important part of PDA is a collection of rules for computing with and ranking of f-granular probability distributions.

In spirit as well as in substance, perception-based decision analysis represents a radical departure from existing measurement-based methods. Basically, what PDA adds to decision analysis is a collection of concepts and techniques for basing decisions on perception-based information, with the understanding that measurement-based information is a special case.

A concomitant of progression from measurement-based to perception-based decision analysis is a shift from universal, normative decision principles to customized decision rules which are application-and context-dependent. This is an unavoidable consequence of striving for a rapprochment with the reality of making decisions in an environment of pervasive uncertainty, imprecision and partial truth.

* Professor in the Graduate School and Director, Berkeley Initiative in Soft Computing (BISC), Computer Science Division, Department of EECS, University of California, Berkeley, CA 94720-l776; Telephone: 5l0-642-4959; Fax: 5l0-642-l7l2; E-mail: zadeh@cs.berkeley.edu. Research supported in part by ONR N00014-00-1-0621, ONR Contract N00014-99-C-0298, NASA Contract NCC2-1006, NASA Grant NAC2-117, ONR Grant N00014-96-1-0556, ONR Grant FDN0014991035, ARO Grant DAAH 04-961-0341 and the BISC Program of UC Berkeley.

Send mail to the author : (zadeh@cs.berkeley.edu)

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