Doctor of Philosophy, Systems Science
(specialization in Intelligent Systems), May 2000
Binghamton University, Binghamton, NY
Uncertainty Theory – uncertainty measures and imprecise probabilities
Soft computing – fuzzy logic, neural networks, and probabilistic reasoning
Intelligent – Information Systems – expert and knowledge-based systems
Systems Optimization – mathematical and engineering optimization techniques
Masters of Science, Systems Science, May 1998
Binghamton University, Binghamton, NY
Bachelors of Arts, Mathematics, June 1991
University of California at Berkeley, Berkeley, CA
I am interested in the development of tools from soft computing, intelligent systems and uncertainty-based information to be applied to information rich environments such as genomics and economic forecasting. In such environments information is so abundant as to make uncertainty and ambiguity an unavoidable feature of the landscape. Thus, strategic management of uncertainty becomes critical for maximizing information extraction while ensuring that the derived results are bias free and not over fit.
I completed my doctoral work under the direction of Professor George J. Klir in the area of generalized information theory (GIT), a field in which Professor Klir literally wrote the book . As the name suggests, GIT is a generalization of classical information theory as developed by Claude Shannon . GIT adopts the notion of uncertainty-based information from classical information theory. The term uncertainty-based information is intended to emphasize the parallel notions of uncertainty as an information deficiency and of information as uncertainty reduction, as well as to distinguish this type of information from other notions of information such as descriptive (or algorithmic) information.
The necessity for a generalized information theory derives directly from the creation and wide spread acceptance in the second half of the twentieth century of alternative mathematical formalizations of uncertainty. Until recently, probability theory was the only available theory for formalizing uncertainty. This is no longer the case. New uncertainty formalisms include the Dempster-Shafer theory of evidence , imprecise probabilities  and possibility theory . My doctoral dissertation  overviewed current uncertainty formalisms, summarized the current state of affairs of uncertainty-based information measures and proposed several new candidate measures for generalizing the Shannon entropy to probability-like measures such as the basic or mass assignment of Dempster and Shafer.
In addition to the generalization of probability measures to more general monotone measures the equally important notion of set is also undergoing a generalization from the classical notion of a crisp set in which membership is a yes or no question to the modern notion of a fuzzy set  in which partial membership is characterized by a value between 0 (no membership) and 1 (full membership). Another generalization of the notion of set is the rough set  in which sets are characterized by upper and lower approximations.
These complementary generalizations of measures and sets have greatly enhanced the expressiveness with which we are able to model cognitive processes. Such modeling capabilities are increasingly in demand as the complexity of the information systems we manage grows. Together with tools from soft computing such as neural networks and genetic algorithms, they permit us to emulate that most remarkable of information processing systems, the human mind, as well as to build decision support systems that aid decision makers in fulfilling their responsibilities.
1. Dubois, D. and Prade, H. , Possibility Theory. Plenum Press, New York.
2. Klir, G. J. and Wierman M.J. , Uncertainty-Based Information: Elements of Generalized Information Theory. Physica-Verlag/Springer-Verlag, Heidelberg and New York.
3. Klir, G. J. and Yuan, B. , Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice Hall, PTR, Upper Saddle River, NJ.
4. Pawlak, Z. , Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer, Boston. Shafer G. , A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton, NJ
5. Shafer G. , A Mathematical Theory of Evidence. Princeton Univ. Press, Princeton, NJ.
6. Shannon, C. E. , “The mathematical theory of communication.” The Bell System Technical J., 27, pp. 379-423, 623-656.
7. Smith, R. M. , Generalized Information Theory: Resolving Some Old Questions and Opening Some New Ones. Ph.D. Dissertation, Binghamton University æ SUNY, Binghamton.
8. Walley, P. , Statistical Reasoning With Imprecise Probabilities. Chapman and Hall, London.
Fraser, A., Smith, R., Smyth, P. and Vixie, K., “Persistence and recurrence in atmospheric circulation.” Proceedings of the 29th Symposium on the Interface of Computing Science and Statistics, 1997.
Smith, R.M. and Bedau, M.A., “The emergence of complex ecologies in ECHO.” Proceedings of the NECSI Complex Systems Conference, Addison-Wesley, 1998
Smith, R.M. and Klir, G.J., “On measuring uncertainty in evidence theory.” Proceedings of the North American Fuzzy Information Society, IEEE, 1999. Klir, G.J. and Smith R.M., “Recent developments in generalized information theory.” International Journal of Fuzzy Systems 1(1), 1999.
Smith, R.M., Generalized Information Theory: Resolving Some Old Questions and Opening Some New Ones. Ph.D. Dissertation, Binghamton University, Binghamton, NY, 2000.
Klir, G.J. and Smith, R.M., “On measuring uncertainty and uncertainty-based information.” Annals of Mathematics and Artificial Intelligence, invited paper for special issue on representations of uncertainty, 2001.