Sukanto Bhattacharya

Fuzziness and funds allocation in portfolio optimization

Each individual investor is different, with different financial goals, levels of risk tolerance and personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It is really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook – essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about 24 questions that each has to be answered with values from 1 to 5. The questions range from personal background to what the customer expects from an investment. A fuzzy logic system has been designed for the evaluation of the answers to the above questions. The notion of fuzziness with respect to funds allocation is investigated.

Recognition and Resolution of “Comprehension Uncertainty” in AI

Handling uncertainty is an important component of most intelligent behaviour – so uncertainty resolution is a key step in the design of an artificially intelligent decision system (Clark, 1990). Like other aspects of intelligent systems design, the aspect of uncertainty resolution is also typically sought to be handled by emulating natural intelligence (Halpern, 2003; Ball and Christensen, 2009). A three-valued extension of classical (i.e. binary) fuzzy logic was proposed by Smarandache (2002) when he coined the term “neutrosophic logic” as a generalization of fuzzy logic to such situations where it is impossible to de-fuzzify the original fuzzy–valued variables via some tractable membership function into either of set T or its complement TC where both T and TC are considered crisp sets. In these cases one has to allow for the possibility of a third unresolved state intermediate between T and TC.