S. Bozóki and T. Rapcsák, On Saaty???s and Koczkodaj???s inconsistencies of pairwise comparison matrices, Journal of Global Optimization, vol.3, issue.3, pp.157-175, 2008.
DOI : 10.1007/s10898-007-9236-z

R. Brunelli, Template Matching Techniques in Computer Vision, 2010.
DOI : 10.1002/9780470744055

M. Brunelli and M. Fedrizzi, Axiomatic properties of inconsistency indices for pairwise comparisons, Journal of the Operational Research Society, vol.41, issue.3, pp.66-67
DOI : 10.1016/S0377-2217(98)00109-X

URL : http://arxiv.org/pdf/1306.6852

M. Brunelli, Studying a set of properties of inconsistency indices for pairwise comparisons, Annals of Operations Research, vol.52, issue.3, pp.1507-08826
DOI : 10.1016/j.dss.2011.11.022

B. Cavallo and L. Apuzzo, A general unified framework for pairwise comparison matrices in multicriterial methods, International Journal of Intelligent Systems, vol.22, issue.12, pp.377-398, 2009.
DOI : 10.1007/BF02688991

B. Cavallo, L. Apuzzo, and M. Squilllante, Pairwise Comparison Matrices over Abelian Linearly Ordered Groups: A Consistency Measure and Weights for the Alternatives, Studies in Fuzziness and Soft Computing, vol.305, pp.49-64, 2010.
DOI : 10.1007/978-3-642-35635-3_4

G. Crawford and C. Williams, The analysis of subjective judgment matrices; A project AIR FORCE report prepared for united states air force report number R, pp.2572-2573, 1985.

Z. Duszak and W. W. Koczkodaj, Generalization of a new definition of consistency for pairwise comparisons, Information Processing Letters, vol.52, issue.5, pp.5-273, 1994.
DOI : 10.1016/0020-0190(94)00155-3

R. Janicki, On a pairwise comparison-based consistent non-numerical ranking, Logic Journal of IGPL, vol.34, issue.1, pp.197-217, 2009.
DOI : 10.1037/h0070288

S. Farinelli, Geometric arbitrage theory and market dynamics, Journal of Geometric Mechanics, vol.7, issue.4, pp.431-471, 2015.
DOI : 10.3934/jgm.2015.7.431

URL : http://www.aimsciences.org/journals/doIpChk.jsp?paperID=11784&mode=full

S. Farinelli and S. Vasquez, Gauge invariance, geometry and arbitrage the journal of investment strategies, p.2366, 2012.

J. Fülöp, A method for approximating pairwise comparison matrices by consistent matrices, Journal of Global Optimization, vol.15, issue.3, pp.423-442, 2008.
DOI : 10.1007/978-1-4757-2809-5

G. Friedman, Survey Article: An elementary illustrated introduction to simplicial sets, Rocky Mountain Journal of Mathematics, vol.42, issue.2, pp.42-44
DOI : 10.1216/RMJ-2012-42-2-353

URL : http://doi.org/10.1216/rmj-2012-42-2-353

M. Gromov, Metric structures in Riemannian and non-Riemannian spaces, 1997.

M. Hirsch, , 1997.

K. Illinski, Gauge geometry of financial markets, Journal of Physics A: Mathematical and General, vol.33, issue.1, pp.5-14, 2000.
DOI : 10.1088/0305-4470/33/1/102

R. Janicki and W. W. Koczkodaj, A weak order solution to a group ranking and consistencydriven pairwise comparisons Appl, Math. Comp, pp.94-227, 1998.

R. Janicki and Y. Zhai, On a paiwise-based consistent non-numerical ranking, Logic Journal of IGPL, vol.4, issue.4, pp.1-10, 2011.

S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol.1, 1963.

W. W. Koczkodaj, A new definition of consistency of pairwise comparisons, Mathematical and Computer Modelling, vol.18, issue.7, pp.79-84, 1993.
DOI : 10.1016/0895-7177(93)90059-8

URL : https://doi.org/10.1016/0895-7177(93)90059-8

W. W. Koczkodaj, J. Magnot, J. Mazurek, J. F. Peters, H. Rakhshani et al., On normalization of inconsistency indicators in pairwise comparisons, International Journal of Approximate Reasoning, vol.86, pp.73-79, 2017.
DOI : 10.1016/j.ijar.2017.04.005

URL : http://arxiv.org/pdf/1702.07205

W. W. Koczkodaj and J. Magnot, A Geometric Framework for the Inconsistency in Pairwise Comparisons

W. W. Koczkodaj and R. Szwarc, Axiomatization of inconsistency indicators for pairwise comparisons, International Journal of Approximate Reasoning, vol.94, pp.4-485, 2014.
DOI : 10.1016/j.ijar.2017.12.001

URL : http://arxiv.org/pdf/1307.6272

W. W. Koczkodaj and J. Sybowski, Axiomatization of Inconsistency Indicators for Pairwise Comparisons Matrices Revisited

W. W. Koczkodaj and J. Magnot, Axiomatization of Inconsistency Indicators for Pairwise Comparisons Matrices

W. W. Koczkodaj and R. Urban, Axiomatization of inconsistency indicators for pairwise comparisons, International Journal of Approximate Reasoning, vol.94, pp.18-29, 2018.
DOI : 10.1016/j.ijar.2017.12.001

W. W. Koczkodaj, J. Szybowski, and E. Wajch, Inconsistency indicator maps on groups for pairwise comparisons, International Journal of Approximate Reasoning, vol.69, pp.2-81, 2016.
DOI : 10.1016/j.ijar.2015.11.007

M. Lahby, C. Leghris, and A. Adib, Network Selection Decision based on handover history in Heterogeneous Wireless Networks, International Journal of Computer Science and Telecommunications, vol.3, issue.2, pp.2012-2033

I. Kolar, P. W. Michor, and J. Slovak, Natural operations in differential geometry Springer, 1993.

A. Kriegl and P. W. Michor, The convenient setting for global analysis Mathematical surveys and monographs, 2000.

W. Lawvere and S. Schanuel, Conceptual Mathematics: A First Introduction to Categories, 1997.
DOI : 10.1017/CBO9780511804199

M. Lane and S. , Categories for the Working Mathematician Graduate Texts in, Mathematics, vol.5, 1998.

G. Mack, Gauge theory of things alive, Nuclear Physics B - Proceedings Supplements, vol.42, issue.1-3, pp.923-925, 1995.
DOI : 10.1016/0920-5632(95)00423-7

J. Magnot, Structure groups and holonomy in infinite dimensions, Bulletin des Sciences Math??matiques, vol.128, issue.6, pp.6-513, 2004.
DOI : 10.1016/j.bulsci.2004.03.005

J. Magnot, AMBROSE???SINGER THEOREM ON DIFFEOLOGICAL BUNDLES AND COMPLETE INTEGRABILITY OF THE KP EQUATION, International Journal of Geometric Methods in Modern Physics, vol.158, issue.09, p.9, 2013.
DOI : 10.1007/978-1-4612-1104-4_13

J. Magnot, q-deformed Lax equations and their differential geometric background Lambert University Publishing, 2015.

J. Magnot, A mathematical bridge between discretized gauge theories in quantum physics and approximate reasoning in pairwise comparisons Adv, Article ID 7496762, 2018.

J. Magnot, Abstract, Demonstratio Mathematica, vol.21, issue.1, pp.8-16, 2018.
DOI : 10.1142/S0219887813500436

J. Magnot, Remarks on a new possible discretization scheme for gauge theories, to appear in Int, J. Theor. Phys

T. Saaty, A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology, vol.15, issue.3, pp.234-281, 1977.
DOI : 10.1016/0022-2496(77)90033-5

J. Milnor, Remarks on infinite-dimensional Lie groups, Relativity, groups and topology, II (Les Houches, 1983), pp.1007-1057, 1984.

F. J. Peters, Computational Proximity: Excursions in the Topology of Digital Images, p.437, 2016.

J. Ramik, Pairwise comparison matrix with fuzzy elements on alo-group, Information Sciences, vol.297, pp.236-253, 2015.
DOI : 10.1016/j.ins.2014.11.010

B. Sengupta, A. Tozzi, G. K. Cooray, P. K. Douglas, and K. J. Friston, Towards a Neuronal Gauge Theory, PLOS Biology, vol.72, issue.3, 2016.
DOI : 10.1371/journal.pbio.1002400.s009

URL : https://doi.org/10.1371/journal.pbio.1002400

A. Tozzi, J. F. Peters, C. Chafin, D. De-falco, and J. S. Torday, Progress in Biophysics and Molecular Biology, 2018.

H. Whitney, Geometric Integration Theory Princeton University Press, 1957.

H. Yamabe, On an arcwise connected subgroup of a Lie group; Osaka Math, J, vol.2, pp.13-14, 1950.

K. Young, Foreign exchange markets as a lattice gauge theory Amer, J. Phys, vol.67, pp.10-862, 1999.

Y. Zhai, Non numerical ranking based on pairwise comparisons PhD thesis, Mc Master university, LAREMA, université d'Angers, Boulevard Lavoisier, F-49045 Angers cedex 01, 2010.

L. Jeanne-d, Arc, 30 avenue de Grande Bretagne, F-63000 Clermont-Ferrand