Applications of intuitionistic fuzzy set aggregation operators in transport multi-factor project evaluation

Abstract

An intuitionistic fuzzy set (IFS) is a generalisation of a fuzzy set characterised by a truth membership function and a false membership function. The former is a lower bound on the grade of membership of the evidence in favour of a particular element belonging to the set and the latter is a lower bound on the negation of that element belonging to the set derived from evidence against that element belonging to the set. A similar concept is a vague set, though vague sets have been shown to be identical to IFSs. In the context of project evaluation, an IFS may be used to represent the degree to which a project satisfies a criterion and the degree to which it does not. Aggregation of such IFSs has been considered in recent years to identify a best project in terms of several criteria or factors. A particular desirable way to aggregate IFS is in terms of an ordered weighted average (OWA) which can be expressed in different forms such as arithmetic and geometric. In an OWA operator, weights are applied to the position of an element in the aggregation. In addition, hybrid OWA operators may be developed to not only weight the position of elements in the aggregation but the element itself. An example is given relating to the Kuranda Range Road upgrade (Queensland, Australia) which is limited by grade, poor overtaking opportunities, poor horizontal alignment and other constraints and the road is expected to become increasingly congested over the next few years. A more flexible multi-factor decision method is used to identify a ‘best’ project from a set of four alternative projects.