ELECTRE TRI-nB, pseudo-disjunctive: axiomatic and combinatorial results
Denis Bouyssou, Thierry Marchant, Marc Pirlot
TL;DR
The paper investigates the axiomatic structure of ELECTRE TRI-nB in its pseudo-disjunctive form, revealing that its analysis is more intricate than the pseudo-conjunctive counterpart. It proves that while linear partitions unify several models, the pseudo-disjunctive framework $ETRI ext{-}nB ext{-}pd$ does not collapse to the $E$-based representations, and it presents two targeted characterizations for simplification: binary-attribute settings and a restricted $F^{u}$-case under high data quality. A key combinatorial thread links representability to maximal antichains in products of chains, leading to exact and asymptotic counts $d_F$ and $d_E$, with explicit lower bounds and numerical results. Collectively, the results illuminate fundamental differences in expressivity between pseudo-conjunctive and pseudo-disjunctive variants and provide a foundation for further enumeration and structural analysis in ELECTRE TRI-nB.
Abstract
ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes into ordered categories. It is an extension of ELECTRE TRI-B, using several limiting profiles, instead of just one, to delimit each category. ELECTRE TRI-nB comes in two flavours: pseudo-conjunctive and pseudo-disjunctive. In a previous paper we have characterized the ordered partitions that can be obtained with ELECTRE TRI-nB, pseudo-conjunctive, using a simple axiom called linearity. The present paper is dedicated to the axiomatic analysis of ELECTRE TRI-nB, pseudo-disjunctive. It also provides some combinatorial results.