Two Squares of Oppositions and Their Applications in Pairwise Comparisons Analysis¹

Issue title: Theory and Practice of Pairwise Comparisons

Guest editors: Ryszard Janicki and Konrad Kułakowski

Article type: Research Article

Authors: Schumann, Andrew^{a; *} | Woleński, Jan^b

Affiliations: [a] University of Information Technology and Management in Rzeszów, Sucharskiego 2, 35-225 Rzeszów, Poland. [email protected] | [b] University of Information Technology and Management in Rzeszów, Sucharskiego 2, 35-225 Rzeszów, Poland

Correspondence: [*] Address for correspondence: University of Information Technology and Management in Rzeszów, Sucharskiego 2, 35-225 Rzeszów, Poland

Note: [1] The research was financed by the National Science Centre in Poland, based on the decision DEC-2012/07/B/HS1/00263, and by the Seventh Framework Programme, FP7-ICT-2011-8

Abstract: This paper examines two main possibilities of pairwise comparisons analysis: first, pairwise comparisons within a lattice, in this case these comparisons can be measurable by numbers; second, comparisons beyond any lattice, in this case these comparisons cannot be measurable in principle. We show that the first approach to pairwise comparisons analysis is based on the conventional square of opposition and its generalization, but the second approach is based on unconventional squares of opposition. Furthermore, the first approach corresponds to lateral inhibition in transmission signals and the second approach corresponds to lateral activation in transmission signals.

Keywords: Logical relations, logical square, logical hexagon, logical octagon, lateral inhibition, lateral activation, pairwise comparison

DOI: 10.3233/FI-2016-1332

Journal: Fundamenta Informaticae, vol. 144, no. 3-4, pp. 241-254, 2016