Attribute Partitioning in Multiple Attribute Decision Making Problems for a Decision with a Purpose - a Fuzzy Approach

摘要

This work introduces a methodology to find solutions corresponding to different purposes in a multiple attribute decisionmaking problem under fuzzy environment. The discernment of purpose-based solutions becomes important when the problem is defined vaguely and solution is targeted to heterogeneous population. Depending on the purpose, for which the solution is sought, the attributes are identified and weighted in an appropriate proportion. The level of similarity between a pair of attributes plays an important role to determine the aggregated value of attributes specific to a purpose. Our work determines the similarity levels between a pair of attributes by calculating their maximum attainability in presence of each other. The achievement of an attribute in presence of another is represented as a fuzzy set in the unit interval. The crisp equivalents of the fuzzy sets in the unit interval are used to define their simultaneous satisfaction denoted as 1-step relation. The 1-step relation is extended to (m-1)-step relation to calculate the degree of attainability of the same pair of attributes in the presence of m (all) attributes. The different levels of (m-1)-step relations generate several partitions of the attributes corresponding to multiple purposes in the multiple attribute decision-making problems. The degree of fulfilment of the purposes in the alternatives are numerically derived by first taking weighted average of attributes within the equivalence classes of a partition and then aggregating the values corresponding to equivalence classes through ordered weighted averaging. The methodology is illustrated with a numerical example.