A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...

Given a set U of n distinct numbers, we are interested in preprocessing them, so that subsequent rrembership queries of the form ‘Is y E U?’ can be answered quickly. For example, if one sorts the elements of U, then each query can be answerred in pg(n + I)1 comparisons by a binary search. This may be contrasted with the situation where no preprocessing is done, when n comparisons are needed to ...

Markov chains having the same stationary distribution can be partially ordered by performance in the central limit theorem. We say that one chain is at least as good as another in the e ciency partial ordering if the variance in the central limit theorem is at least as small for every L( ) functional of the chain. Peskun partial ordering implies e ciency partial ordering [25, 30]. Here we show ...