Reinstatement of the Extension Principle in Approaching Mathematical Programming with Fuzzy Numbers

Optimization problems in the fuzzy environment are widely studied literature. We restrict our attention to mathematical programming with coefficients and/or decision variables expressed by numbers. Since review of recent literature on shows that extension principle is present through arithmetic but much less involved foundations solution concepts, we believe efforts rehabilitate idea following when deriving relevant descriptions optimal solutions highly needed. This paper identifies current position and role solving involve numbers their models, highlighting indispensability approaching this class problems. After presenting basic ideas optimization, underlying advantages disadvantages different approaches, main methodologies yielding elude principle, then compare them those follow it. also suggest research directions focusing using all stages optimization process.