We present a decision tree evaluation method integrated with a common framework for analyzing multi-attribute decisions under risk, where information is numerically imprecise. The approach extends the use of additive and multiplicative utility functions for supporting evaluation of imprecise statements, relaxing requirements for precise estimates of decision parameters. Information is modeled i...

We covered Riemann integrals in the first three weeks in MA502 this semester (Chapter 11 in [1]). This report explores a necessary and sufficient condition for determining Riemann integrability of f(x) solely from its properties. This condition is known as Lebesgue’s criterion and elucidating the proof of this condition is the aim of this report. This report revisits the concepts learnt in MA50...

The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false i...

We consider the problem of inductively inferring a grammar for a language, given (positive) examples of the language and putative (possibly faulty) grammars for the complement of the language. The criterion of success is identification in the limit, defined by E. M. Gold (1967, Inform. and Control 10, 447 474). Additional information is useful insofar as it allows the identification of language...

We generalize the classical expected-utility criterion by weakening transitivity to Suzumura consistency. In the absence of full transitivity, reflexivity and completeness no longer follow as a consequence of the system of axioms employed and a richer class of rankings of probability distributions results. This class is characterized by means of standard expected-utility axioms in addition to S...

Developing the infrastructures for preventing non-communicable diseases is one of the most important goals of healthcare context in recent years. In this regard, the number and capacity of preventive healthcare facilities as well as assignment of customers to facilities should be determined for each region. Besides the accessibility, the utility of customers is a determinative factor in partici...

We consider the problem of scheduling exception handlers in real-time systems that operate under runtime uncertainties including those on execution times, activity arrivals, and failure occurrences. The application/scheduling model includes activities and their exception handlers that are subject to time/utility function (TUF) time constraints and an utility accrual (UA) optimality criterion. A...