AI planning agents are goal-directed: success is measured in terms of whether or not an input goal is satisfied, and the agent's computational processes are driven by those goals. A decision-theoretic agent, on the other hand, has no explicit goals--- success is measured in terms of its preferences or a utility function that respects those preferences. The two approaches have complementary strengths and weaknesses. Symbolic planning provides a computational theory of plan generation, but under unrealistic assumptions: perfect information about and control over the world and a restrictive model of actions and goals. Decision theory provides a normative model of choice under uncertainty, but offers no guidance as to how the planning options are to be generated. This paper unifies the two approaches to planning by describing utility models that support rational decision making while retaining the goal information needed to support plan generation. We develop an extended model of goals tha...

Real-world scheduling is decision making under vague constraints of different importance, often using uncertain data, where compromises between antagonistic criteria are allowed. We explain in theory and by detailed examples a new combination of fuzzy set based constraints and repair based heuristics that help to model these scheduling problems. We simplify the mathematics needed for a method of eliciting the criteria's importances from human experts. We introduce a new consistency test for configuration changes. This test also helps to evaluate the sensitivity to configuration changes. We describe the implementation of these concepts in our fuzzy constraint library ConFLIP++ and in our heuristic repair library D'ej`aVu. Finally, we present results from scheduling a continuous caster unit in a steel plant.

A large number of problems in production planning and scheduling, location, transportation, finance, and engineering design require that decisions be made in the presence of uncertainty. Uncertainty, for instance, governs the prices of fuels, the availability of electricity, and the demand for chemicals. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to very large-scale optimization models. Decision-making under uncertainty is often further complicated by the presence of integer decision variables to model logical and other discrete decisions in a multi-period or multi-stage setting. This paper reviews theory and methodology that have been developed to cope with the complexity of optimization problems under uncertainty. We discuss and contrast the classical recourse-based stochastic programming, robust stochastic programming, probabilistic (chance-constraint) programming, fuzzy programming, and stochastic dynamic programming. The advantages and shortcomings of these models are reviewed and illustrated through examples. Applications and the state-of-the-art in computations are also reviewed. Finally, we discuss several main areas for future development in this field. These include development of polynomial-time approximation schemes for multi-stage stochastic programs and the application of global optimization algorithms to two-stage and chance-constraint formulations.

This paper explores the implications of approximating a concept based on the Bayesian decision procedure, which provides a plausible unification of the fuzzy set and rough set approaches for approximating a concept. We show that if a given concept is approximated by one set, the same result given by the α-cut in the fuzzy set theory is obtained. On the other hand, if a given concept is approximated by two sets, we can derive both the algebraic and probabilistic rough set approximations. Moreover, based on the well known principle of maximum (minimum) entropy, we give a useful interpretation of fuzzy intersection and union. Our results enhance the understanding and broaden the applications of both fuzzy and rough sets. 1.

Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Abstract. Fuzzy control is a very successful way to transform the expert’s knowledge of the type “if the velocity is big and the distance from the object is small, hit the brakes and decelerate as fast as possible ” into an actual control. To apply this transformation one must: 1) choose fuzzy variables corresponding to words like “small”, “big”; 2) choose operations corresponding to “and ” and “or”; 3) choose a method that transforms the resulting fuzzy variable for a into a single value ā. The wrong choice can drastically affect the quality of the resulting control, so the problem of choosing the right procedure is very important. From mathematical viewpoint these choice problems correspond to non-linear optimization and are therefore extremely difficult. We develop a new mathematical formalism (based on group theory) that allows us to solve the problem of optimal choice and thus: 1) explain why the existing choices are really the best (in some situations); 2) explain a rather mysterious fact that the fuzzy control based on the experts’ knowledge is often better than the control by these same experts; 3) give choice recommendations for the cases when traditional choices do not work. Perspectives of space applications will be also discussed.

The choice of an aggregation function is a common problem in Multi Attribute Decision Making (MADM) systems. The Method of Imprecision (MoI) is a formal theory for the manipulation of preliminary design information that represents preferences among design alternatives with the mathematics of fuzzy sets. The MoI formulates the preliminary design problem as a MADM problem. To date, two aggregation functions have been developed for the MoI, one representing a compensating strategy and one a noncompensating strategy. Much of the prior fuzzy sets research on aggregation functions has been inappropriate for application to engineering design. In this paper, the selection of an aggregation function for MADM schemes is discussed within the context of the MoI. The general restrictions on designappropriate aggregation functions are outlined, and a family of functions, modeling a range of trade-off strategies, is presented. The results are illustrated with an example. Keywords: Fuzzy design; Engineering; Aggregation functions;

From laser-scanned data to feature human model: a system based on

A formal method to allow designers to explicitly make trade-off decisions is presented. The methodology can be used when an engineer wishes to rate the design by the weakest aspect, or by cooperatively considering the overall performance, or a combination of these strategies. The design problem is formulated with preference rankings, similar to a utility theory or fuzzy sets approach. This approach separates the design trade-off strategy from the performance expressions. The details of the mathematical formulation are presented and discussed, along with two design examples: one from the preliminary design domain, and one from the parameter design domain. 1

iii This document and the work it represents was impossible without the support of my wife Ginger. Often one needs non-technical advice to make clear what one is contemplating. Also one always needs a financial supporter. My thesis advisor Erik Antonsson helped focus many of my thoughts. In addition to providing me with technical assistance, he as well provided instruction on the process of conducting academic research, the communication of ideas both orally and written, and the approach to a developing field. I also owe much to my colleagues in the Engineering and Applied Science Division at Caltech. Their comments and advice maintained my comprehension and rigor. Andrew Lewis in particular provided me with invaluable support. Many of the technical proofs were impossible without him. This material and the work it represented were made possible, in part, by a fellowship from the AT&T-Bell Laboratories Ph.D. scholar program, sponsored by the AT&T foundation. Also, the National Science Foundation provided funding under a Presidential Young