Optimistic Fuzzy Weighted Average

The fuzzy weighted average (FWA) is used in many engineering problems where aggregation of fuzzy information is dealt with. In this framework, many algorithms have been proposed to compute efficiently the FWA according to Zadeh's extension principle. However, due to fuzzy interval calculus, the exact solution presents a characteristic that may be viewed as an important drawback. Indeed, replacing each individual by the fuzzy weighted average in the assessment of the population score leads to a result different from the original one. The presented work is an attempt to propose an optimistic counterpart for the FWA that eliminates the mentioned characteristic, possibly undesirable. Actually, the optimistic FWA is computed by using a modified division operator. When existing, the latter is the inverse operator of the fuzzy multiplication. Contrary to the conventional FWA, the optimistic one can be computed by a sequence of elementary arithmetic operations.