The real world is complex; complexity in the world generally arises from uncertainty in the form of ambiguity. For systems with little complexity, hence little uncertainty, closed-form mathemat- ical expressions provide precise descriptions of the systems. For the most complex systems where few numerical data exist and where only ambiguous or imprecise information may be available, Fuzzy set theory (FST) provides a way to understand system behavior. Fuzzy modeling approaches provides the appropriate framework to describe and treat uncertainty when there is lack of evidence available or lack of certainty in evidence, that the standard proba- bilistic reasoning methods are not appropriate. FST was developed by Zadeh [8], since then it has been applied to the fields of opera- tions research, management science, artificial intelligence/expert systems, statistics and many other fields. In 1976, Zimmermann [9] first introduced FST into conventional LP problems. He considered LP problems with a fuzzy goal and fuzzy constraints. Since then, fuzzy linear programming has been developed in a number of directions.
In the light of our literature review about decision making in biomass to energy supply chains, we can conclude that there is scarcely any research on biomass to energy supply chain planning models that employs fuzzy modeling approach. Among them, Aviso et al. [10] developed an LP model with fuzzy input output analysis to optimize supply chains under water footprint constraints. Tong et al. [11] developed a multiperiod MILP model for optimal design and planning of a hydrocarbon biofuel supply chain integrated with existing petroleum refineries. They applied fuzzy possibilistic pro- gramming to their model.
Most of the models applied for the energy systems design work for different objectives such as satisfying minimum system costs and minimum level of harmful gas emissions, and a set of technological, economic, environmental and social constraints. Multi dimensionality of the sustainability goal and complexity of energy systems make multicriteria and multiobjective deci- sion making (MODM) methods increasingly popular for sus- tainable energy systems. Although goal programming (GP) is one of the most powerful MODM approaches in practical deci- sion making it is rarely used in biomass to energy conversion systems design.