Pythagorean membership grade distance aggregation: An application to new business ventures

Issue title: Fuzzy systems and applications in innovation and sustainability

Guest editors: Ernesto Leon-Castro, Fabio Blanco-Mesa, Victor Alfaro-Garcia, Anna M. Gil-Lafuente and Jose M. Merigo

Article type: Research Article

Authors: Mariño-Becerra, Gladys^a | Blanco-Mesa, Fabio^{a; *} | León-Castro, Ernesto^b

Affiliations: [a] Facultad de Ciencias Económicas y Administrativas, Escuela de Administración de Empresas, Universidad Pedagógica y Tecnológica de Colombia, Av. Central del Norte 39-115, Tunja, Colombia | [b] Facultad de Ciencias Económicas y Administrativas, Universidad Católica de la Santísima Concepción, Alonso de Ribera, Concepción, Chile

Correspondence: [*] Corresponding author. Fabio Blanco-Mesa, E-mail: [email protected].

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.

Keywords: Pythagorean membership grades, distance operators, OWA operator, start business, decision making.

DOI: 10.3233/JIFS-189189

Journal: Journal of Intelligent & Fuzzy Systems, vol. 40, no. 2, pp. 1827-1836, 2021