The Use of Interval-Valued Probability Measures in Fuzzy Linear Programming: a constraint set approach

This paper uses a constraint set approach to linear programming problems with equality constraints whose coefficients and/or right-hand side values could be uncertain. We consider three types of uncertainty: probabilistic, fuzzy/possibilistic, and interval. The constraint set generated by the linear constraints under uncertainty is illdefined and difficult to generate. Our approach computes an inner constraint set and an outer constraint set. Optimization is then carried out using these two sets using interval-valued probability approaches. We discuss the requisite associated semantics. Keywords--inverval-valued probability measure, random sets, inner constraint set, outer constraint set.

• Type: Journal
• Year: 2009
• Where: EUSFLAT
• Authors: Phantipa Thipwiwatpotjana, Weldon A. Lodwick
• Keywords: EUSFLAT 2009, Fuzzy Logic, Inner Constraint, Outer Constraint, Requisite Associated Semantics