Associated Fuzzy Probabilities in MADM with Interacting Attributes: Application in Multi-Objective Facility Location Selection Problem

Abstract

For decreasing service centers’ selection risks in emergency facility location selection, it is crucial to have selected candidate service centers within deeply detailed facility location selection model. To achieve this, a new approach developed in this article involves two stages. In the first stage, the fuzzy multi-attribute group decision making (MAGDM) model for evaluation of the selection of candidate service centers is created. For the aggregation of experts’ assessments of candidate service centers (with respect to attributes) aggregation operators’ approach is used. Experts’ assessments are presented in fuzzy terms with semantic form of triangular fuzzy numbers. For the deeply detailed facility location selection modeling and for the intellectual activity of experts in their evaluations, pairwise interactions between attributes of MAGDM model are considered in the construction of the second-order additive triangular fuzzy valued fuzzy measure (TFVFM). The associated triangular fuzzy probability averaging (As-TFPA) aggregation operators’ family is constructed with respect to TFVFM. Analytical properties of the As-TFPA operators are studied. The new operators are certain extensions of the well-known Choquet integral operator. The extensions, in contrast to the Choquet aggregation, consider all possible pair-wise interactions of the attributes by introducing associated fuzzy probabilities of a TFVFM. At the end of the first stage, a candidate service center’s selection index is defined as As-TFPA operator’s aggregation value on experts’ assessments with respect to attributes. At the second stage, fuzzy multi-objective facility location set covering problem (MOFLSCP) is created for facility location selection optimal planning with new criteria: (1) maximization of candidate service centers selection index and classical two criteria, (2) minimization of the total cost needed to open service centers and (3) minimization of number of agents needed to operate the opened service centers. For the constructed two-stage methodology a simulation example of emergency service facility location planning for a city is considered. The example gives the Pareto fronts obtained by As-TFPA operators, the Choquet integral-TFCA operator and well-known TOPSIS approach, for optimal selecting candidate sites for the servicing of demand points. The comparative analysis identifies that the differences in the Pareto solutions, obtained by using As-TFPA operators and TFCA operator or TOPSIS aggregation, are also caused by the fact that TFCA operator or TOPSIS approach considers the pair interaction indexes for only one consonant structure of attributes. While new As-TFPA aggregations provide all pairwise interactions for all consonant structures.