Successive Proportional Additive Numeration Using Fuzzy Linguistic Labels (Fuzzy Linguistic SPAN)

The SPAN (Successive Proportional Additive Numeration or Social Participatory Allocation Network) is a procedure that converts individual judgments into a group decision. The procedure is based on a voting design by which individual experts allocate their votes iteratively between their preferred options and other experts. The process ends when all the votes are allocated to options, and the one with the highest number of votes is selected. The method requires the experts to specify an exact allocation of votes to both options and other experts. The Fuzzy Linguistic SPAN allows experts to allocate their votes using linguistic labels such as “most of” or “a few”, and determine the preferred option. This method is demonstrated using the Max–Min aggregation function used to develop a proportional representation of the option and member voting schemes. The method is also demonstrated using the LOWA aggregation function. The Fuzzy Linguistic SPAN method is beneficial since the linguistic voting process is easier for the experts and significantly reduces the computational process compared to the traditional SPAN. The paper presents the method and two examples with comparisons to the numerical SPAN method.