Abstract

The objective of the paper is to present an extension of the ordered weighted average (OWA) operator, probability OWA (POWA) operator, distance measures and Pythagorean membership grades. These new operators are called the Pythagorean membership grade OWA distance (PMGOD) operator and the probabilistic Pythagorean membership grade OWA distance (PPMGOD) operator. This extension includes in one formulation the ability to measure the ideal vs. real situation of the distance operators, the weighting vector and reordering step of the OWA operator and the way in which it includes uncertainty based on the satisfaction of the criteria of the Pythagorean membership degree. These propositions are applied to new business ventures in the city of Colombia, where the decision maker can express his/her concerns about the uncertainty and probabilities of the current business environment and, thus, generate a better decision-making process.