# New Research

2011/10/01

# Flexible Robust Optimization under Uncertainty

## Decision Support by Fuzzy Mathematical Programming

### Masahiro Inuiguchi(Professor), Tatsushi Nishi(Associate Professor), Masayo Tsurumi(Assistant Profess

Inuiguchi laboratory aims to develop conventional decision sciences and systematic methods as well as intelligent decision aid technologies based on information science and intelligence engineering. Among many research topics such as fuzzy mathematical programming, rough set-based data analysis, combinatorial optimization, discrete algorithms and cooperative game theory, we introduce \"fuzzy mathematical programming\".

\"Fuzziness\" in a narrow sense implies things with unsharp boundaries but in a broad sense it means the general uncertainty. On the other hand, \"mathematical programming\" is a method for computing a solution maximizing/minimizing evaluation function representing profit/cost under certain constraints such as resource restrictions. \"Fuzzy mathematical programming\" is a method for obtaining a solution of a programming problem whose coefficients and constraints are ambiguous and flexible, respectively. In the real world, we may face programming problems in which coefficients are known imprecisely and constraints are given vaguely. Then, for those problems, fuzzy mathematical programming is useful.

Because the given problem is ill-posed, we should first define the solution concept in fuzzy mathematical programming. A solution satisfying constraints and goals with high certainty, a solution satisfying constraints with sufficient certainty, and at the same time, seeking lofty goals, and a solution minimizing the worst regret have been studied. Modeling uncertainty, various solution concepts and their solution methods are fully investigated.