This paper describes an extension of a classical network reliability problem to the multi-state case. The two-terminal reliability (2TR) problem assumes a network and its elements can be in either a working or a failed state. However, many practical networks are built of elements that may operate in more than two states. The major focus of this study is to develop a methodology for obtaining th...

We propose general separation procedures for generating cuts for the stable set polytope, inspired by a procedure by Rossi and Smriglio and applying a lifting method by Xavier and Campêlo. In contrast to existing cut-generating procedures, ours generate both rank and non-rank valid inequalities, hence they are of a more general nature than existing methods. This is accomplished by iteratively s...

In this paper, some kinds of cut sets for R̄-fuzzy sets are introduced and their properties are given. Moreover, the decomposition theorems and representation theorems on R̄-fuzzy sets are obtained based on different cut sets. Finally, the axiomatic definition of cut set for R̄-fuzzy set is introduced which characterizes the common properties of cut set.

Hajnal, A. and N. Sauer, Cut-sets in infinite graphs and partial orders. Discrete Mathematics 117 (1993) 113-125. The set S c V(U) is a cut-set of the vertex v of a graph 9 if v is not adjacent to any vertex in S and, for every maximal clique C of Q, ({v} u S) n C # 0. S is a cut-set of the element v of a partial order 9 if S is a cut-set of v in the comparability graph of 8. Given upper bounds...

I prove that the Boolean Prime Ideal Theorem is equivalent, under some weak set-theoretic assumptions, to what will call Cut-for-Formulas Cut-for-Sets Theorem: for a set F and binary relation ⊢ on P ( ) $\mathcal {P}(F)$ , if finitary, monotonic, satisfies cut formulas, then it also sets. deduce CF/CS from Ultrafilter twice; each proof uses different order-theoretic variant of Tukey-Teichmüller...

Abstract Let V be a set of n vertices, $${\mathcal M}$$ M m labels, and let $${\textbf{R}}$$ R an $$m \times n$$ m × n matrix ofs independent Bernoulli random variables with probability success p ; columns are incidence...