The inclusion-based LINMAP method for multiple criteria decision analysis within an interval-valued Atanassov's intuitionistic fuzzy environment

The purpose of this paper is to develop an inclusion-based LINMAP (i.e., Linear Programming Technique for Multidimensional Analysis of Preference) method for multiple criteria decision analysis that is based on interval-valued Atanassov's intuitionistic fuzzy sets. Using the inclusion comparison possibility in the interval-valued Atanassov's intuitionistic fuzzy context, an inclusion-based index of interval-valued Atanassov's intuitionistic fuzzy numbers is proposed that considers positive and negative ideals. An inclusion-based consistency index and an inclusion-based inconsistency index to measure the concordance and discordance, respectively, between paired comparison judgments are suggested. An inclusion-based LINMAP model is constructed using a linear programming technique to determine the optimal criterion weights and obtain the corresponding comprehensive inclusion-based index for each alternative. Then, the priority order of the alternatives can be acquired according to the comprehensive inclusion-based indices. The feasibility of the proposed method is illustrated using a practical problem that relates to the selection of bridge construction methods. A comparative analysis of other relevant decision-making methods is conducted to validate the effectiveness of the developed methodology.