Axiomatic Processes for Asymmetric Allocation Rules under Fuzzy Multicriteria Situations

The present paper is dedicated to investigating weighted allocation rules under fuzzy multicriteria situations. In real-world situations, participants may represent administrative departments of different natures in the management system; participants may be able to perform their duties in the economic model. In addition, participants may adopt relative operating levels to different situations and effectively engage multiple objectives under operational processes. Therefore, considering fuzzy behavior and multicriteria situations, it is reasonable to assign corresponding weights to participants and their relative behavior and to allocate efficiency according to weights in proportion to relative weights, even if it will lead to an asymmetrical situation. In existing studies on fuzzy allocation rules, weights are always given to "participants" or their "operating levels" and then the differences between participants and their operating levels are adjusted. Inspired by the above considerations, relative major results are as follows. (1) By simultaneously assigning weights to participants and their operating levels (strategies), this study seeks to use the supreme marginal variations among operating level vectors to define a new asymmetric allocation rule under fuzzy multicriteria situations. (2) This study further utilizes axiomatic results to illustrate the expedience for this weighted fuzzy asymmetric allocation rule. (3) Finally, an extended index is also proposed by replacing weights with the supreme marginal dedications.