IJPAM: Volume 21, No. 4 (2005)
INCREASING LEVELS OF UNCERTAINTY
Department of Computer and Mathematical Sciences
University of Houston - Downtown
Houston, Texas 77002, USA
Department of Information Technology
University of Texas at El Paso
El Paso, Texas 79968, USA
Department of Mathematical Sciences
Indiana University - Purdue University at Indianapolis
Indianapolis, Indiana 46202, USA
Abstract.This paper outlines a paradigm for decision-making under various levels of uncertainty. The basic components of the general model are a finite state space and a finite set of possible actions (decisions). Each (state, action) pair induces a probability distribution over the space of possible outcomes. Associated with each (state, action, outcome) triple is a benefit function, which is modeled as a fuzzy set. Initially we consider the case in which the distribution over the state space is known. Our decision is based on the expected (fuzzy) benefit. Further uncertainty regarding the state space is modeled by postulating a family of probability distributions on the state space. In this scenario expected benefit is defined in terms of a Choquet integral. We also consider an approach based on maximum entropy.
Next we consider the case in which uncertainty is not expressible as a belief function. In this context we extend the concept of a Choquet integral.
Finally we define a preference relation on the distributions over the
outcome space. We invoke the concept of fuzzy subsethood to make comparisons. We also use the concepts of positive responsiveness, weak
dominance and weak independence to establish our preferences.
Received: April 10, 2005
AMS Subject Classification: 68T05, 68T37
Key Words and Phrases: decision making, fuzzy benefit function, Choquet integral, preference relation, subsethood
Source: International Journal of Pure and Applied Mathematics