Traditionally, logic has been used for substantiation of a claim and sometimes, mathematical proofs helped to substantiate a scientific statement. Actually, logic has greatly helped human beings to easily understand and believe many subjects. Mathematics and its application also followed the same objective in a different manner. Perhaps, we have been applying a combination of logic and mathematics in several cases instinctively the traces of which are observable in our personal lives. Integration of logic with most widely used mathematical methods has significantly been effective in major decision making and long-run predictions. In current work, we consider the effects of two cases of such integrations called fuzzy logic. These two methods and examples of their applications are only trivial examples of an extensive knowledge. Here, we address some applications of fuzzy average for predictions and decision making in a fuzzy environment.

One of the activities involved in the construction of all refineries and most industries is movement, lifting and installation of light and heavy equipment by means of various cranes. In the event of an accident as a result of these activities, such consequences as damage to equipment, manpower injury or death seem probable. The basis of the research is to categorize various types of cranes and type of accident happened to them since the beginning of 1389 (2010) until the end of 1393 (2014) in the refinery project phase 14 of South Pars in Iran, and explore the link between type of accident and type of crane by using a linear programming modeling. Sampling from the population with N cranes was performed, which was chosen using n Morgan table. Causes of accidents were investigated in three classes; machine causes, human factor, and environmental conditions for cranes. The cranes under study are in four main types namely overhead, hydraulic, tower, and crawler. Drawing on causes of accidents and types of crane, a model of linear programming is developed, for which the first constraint of each model was reported for guidelines of risk evaluation of phase 14 refinery and the second constraint for pairwise investigation of accident factors in an attempt to take account of accident factors mentioned in accident reports. LP models were predicted in three modes namely causal, machine-human, machine-environmental, and environmental-human factors, and for each problem an optimal level is determined for objective function and the corresponding optimal solution. Given the final table of each LP models, some results were obtained that can serve as an instrument for making proper decision by crane supervisors and operators of heavy lifting in an effort to increase safety and secure better control of accident factors in each of crane types.