Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

Abstract

Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.