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.
SlokaB., KantaneI., AvotinsV. and JermolajevaE., Analysis of entrepreneur’s motivation to start business (comparative studies in Latvia in comparison with Canada, USA, Mexico), Eur Integr Stud0(8) (2014),152–158.
2.
HawkinsD.I., New business entrepreneurship in the Japanese economy, J Bus Ventur8(2) (1993), 137–150.
3.
HisrichR.D. and FulopG., The role of women entrepreneurs in Hungary’s transition economy, Int Stud Manag Organ24(4) (1994), 100–117.
4.
TchamyouV.S., The role of knowledge economy in African business, SSRN Electron J8(4) (2016), 1189–1228.
5.
CassarG., The financing of business start-ups, J Bus Ventur19(2) (2004), 261–283.
6.
HuyghebaertN., On the determinants and dynamics of trade credit use: Empirical evidence from business start-ups, J Bus Financ Account33(1–2) (2006), 305–328.
7.
HuyghebaertN., Van de GuchtL. and Van HulleC., The choice between bank debt and trace credit in business start-ups, Small Bus Econ29(4) (2007), 435–452.
8.
MazzarolT., VoleryT., DossN. and TheinV., Factors influencing small business start-ups A comparison with previous research, Int J Entrep Behav Res5(2) (1999), 48–63.
9.
Barba-SánchezV. and Atienza-SahuquilloC., Entrepreneurial behavior: Impact of motivation factors on decision to create a new venture, Investig Eur Dir y Econ la Empres18(2) (2012), 132–138.
10.
SozenE. and O’NeillM., An exploration of the motivations driving newbusiness start-up in the United States craft brewing industry, in Craft Beverages and Tourism, Volume 2, Cham: Springer International Publishing, (2018), 195–212.
11.
TeeceD., PeterafM. and LeihS., Dynamic capabilities and organizational agility: Risk, uncertainty, and strategy in the innovation economy, Calif Manage Rev58(4) (2016), 13–35.
12.
Carrière-SwallowY. and CéspedesL.F., The impact of uncertainty shocks in emerging economies, J Int Econ90(2) (2013), 316–325.
13.
KaufmannA. and Gil AlujaJ., Las matemáticas del azar y de la incertidumbre: elementos básicos para su aplicación en economía, Centro de Estudios Ramín Areces, (1990).
14.
León-CastroE., Espinoza-AudeloL.F., Aviles-OchoaE., MerigóJ.M. and KacprzykJ., A new measure of volatility using induced heavy moving averages, Technol Econ Dev Econ25(4) (2019), 576–599.
15.
YagerR. R., On ordered weighted averaging aggregation operators in multicriteria decisionmaking, IEEE Trans Syst Man Cybern18(1) (1988), 183–190.
16.
Blanco-MesaF., León-CastroE. and MerigóJ.M., A bibliometric analysis of aggregation operators, Appl Soft Comput81 (2019), 105488.
17.
MerigóJ.M. and Gil-LafuenteA.M., Decision-making in sport management based on the OWA operator, Expert Syst Appl38(8) (2011), 10408–10413.
18.
Avilés-OchoaE., Perez-ArellanoL.A., León-CastroE. and MerigóJ.M., Prioritized induced probabilistic distances in transparency and access to information laws, Fuzzy Econ Rev22(1) (2017), 45–55.
19.
Olazabal-LugoM., Leon-CastroE., Espinoza-AudeloL.F., MerigóJ.M. and Gil-LafuenteA.M., Forgotten effects and heavy moving averages in exchange rate forecasting, Econ Comput Econ Cybern Stud Re-search53(4) (2019), 79–96.
20.
CasanovasM. and PlaJ., Selecting investments in start-ups: an OWA-based methodology, East Asian J Bus Econ3(2) (2015), 21–25.
21.
MerigóJ.M., Probabilities in the OWA operator, Expert Syst Appl39(13) (2012), 11456–11467.
22.
HammingR.W., Error detecting and error correcting codes, Bell Syst Tech J29(2) (1950), 147–160.
23.
YagerR.R., Pythagorean membership grades in multicriteria decision making, IEEE Trans Fuzzy Syst22(4) (2014), 958–965.
24.
YagerR.R. and AbbasovA.M., Pythagorean membership grades, complex numbers, and decision making, Int J Intell Syst28(5) (2013), 436–452.
25.
MerigóJ.M. and Gil-LafuenteA.M., New decision-making techniques and their application in the selection of financial products, Inf Sci (Ny)180(11) (2010), 2085–2094.
Romero LunaI., Las PYME en la economía global. Hacia una estrategia de fomento empresarial, Probl del Desarro Rev Latinoam Econ37 (2009), 146.
28.
López-TorresG.C., Maldonado GuzmánG., Pinzón CastroS.Y. and García RamírezR., Colaboración y actividades de innovación en Pymes, Contaduría y Adm61(3) (2016), 568–581.
29.
The World Bank, Doing Business 2016: Measuring Regulatory Quality and Efficiency, 13th ed. Washintong: The World Bank, (2015).
30.
The World Bank, Doing business 2020: Economy profile of Colombia, Washington, (2020).
31.
PadillaS., ¿Cuál es la mayor preocupación de las pymes? La productividad, El Espectador Bogotá (2018), 1.
32.
Zevallos VallejosE.G., Micro, pequeñas y medianas empresas en América Latina, Rev CEPAL79 (2003), 53–70.
33.
LedermanD., JuliánM., PienknagurS. and Rigolini ResumenJ., El emprendimiento en América latina, muchas empresas y poca innovación, Estud del Banco Mund sobre América Lat y el Caribe (2014), 3–38.
34.
HowaldF., Obstaculos al desarrollo de la Pyme causados por el Estado en Colombia: el caso del sistema tributario, Mexico: McGraw-Hill Interamericana, (2001).
35.
SánchezF., DuqueV. and RuízM., Costos laborales y no laborales y su impacto sobre el desempleo, la duración del desempleo y la informalidad en Colombia, 1980–2007, Doc CEDE (2009).
36.
StokesM., Abrir un negocio en Latinoamérica: Una calle empinada para los jóvenes, ElPaís Buenos Aires, (2015), 1.
37.
KantisH., FedericoJ. and MenéndezC., Políticas de fomento al emprendimiento dinámico en América Latina: tendencias y desafíos, SCIOTECA, (2012).
38.
The World Bank, Doing Business 2019: Training for reform-economy profile Colombia, Washintong, (2019).
39.
MartínezG.C., Anatomía de los ciclos económicos en Colombia 1970–2007, Borradores Econ496 (2008), 1–21.
40.
CEPAL and UN, Las pequeñas y medianas empresas industriales en América Latina y el Caribe | Publicación | Comisión Económica para América Latina y el Caribe, Netherlands (2002).
41.
Cala HederichA., Situación y necesidades de la pequeña y mediana empresa, Rev Civilizar Ciencias Soc y Humanas5(9) (2005), 1–22.
42.
SánchezJ.J., OsorioJ. and BaenaE., Algunas aproximaciones al problema de financiamiento de las pymes en colombia, Sci Tech1(34) (2007).
43.
CEPAL and NU, Apoyando a las PYMES: políticas de fomento en América Latina y el Caribe | Publicación | Comisión Económica para América Latina y el Caribe, Chile, (2011).
44.
GómezL., MartínezJ. and ArzuzaM., Política pública y creación de empresas en Colombia, Rev científica Pensam y Gestión21 (2011), 1–25.
López GaravitoL.F., Historia de la hacienda y el tesoro en Colombia, 1821–1900. Texas: Banco de la República, (1992).
47.
CifuentesA.J., CortésD.G., GarcíaF.C. and PérezD.G., Apuntes contables: revista científica de contabilidad, Apunt Contab11 (2006).
48.
Fajardo CalderónC.L. and Suárez AmayaD.C., Los impuestos en la época de la independencia, su impacto social, evolución e implicaciones en el sistema tributario actual, Criterio Libr10(16) (2012), 293–316.
49.
Placer-MaruriE., Pérez-GonzálezD. and Soto-AcostaP., Efectos de la utilización de la Inteligencia Competitiva en Pymes industriales, 12(4) (2016), 923–941.
50.
MerigóJ.M. and YagerR.R., Generalized moving averages, distance measures and OWA operators, Int J Uncertainty Fuzziness Knowledge-Based Syst21(04) (2013), 533–559.
51.
León-CastroE., Avilés-OchoaE., MerigóJ.M. and Gil-LafuenteA.M., Heavy moving averages and their application in econometric forecasting, Cybern Syst49(1) (2018), 26–43.
52.
LiuJ., ChenH., ZhouL. and TaoZ., Generalized linguistic ordered weighted hybrid logarithm averaging operators and applications to group decision making, Int J Uncertainty Fuzziness Knowledge-Based Syst23(03) (2015), 421–442.
53.
Alfaro-GarcíaV.G., MerigóJ.M., Gil-LafuenteA.M. and KacprzykJ., Logarithmic aggregation operators and distance measures, Int J Intell Syst33(7) (2018), 1488–1506.
54.
Blanco-MesaF., MerigóJ.M. and KacprzykJ., Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory, Knowledge-Based Syst111 (2016), 217–227.
55.
Blanco-MesaF., León-CastroE., MerigóJ.M. and Herrera-ViedmaE., Variances with Bonferroni means and ordered weighted averages, Int J Intell Syst34(11) (2019), 3020–3045.
56.
Blanco-MesaF., León-CastroE., MerigóJ.M. and Herrera-ViedmaE., Variances with Bonferroni means and ordered weighted averages, Int J Intell Syst p. int.22184, (2019).
57.
Blanco-MesaF., León-CastroE. and MerigóJ.M., Covariances with OWA operators and Bonferroni means, Soft Comput (2020), 1–16.
58.
Blanco-MesaF. and MerigóJ.M., Bonferroni distances and their application in group decision making, Cybern Syst51(1) (2020), 27–58.
