The importance of correct and clear decisions during a complex difficult situation is very easy to understand, but not so achieve. Especially in situations where decision-makers must decide under time pressure uncertainty. For instance, typical crisis have such characteristics. Given the uncertainty, subjectivity ambiguity human knowledge, are also characterized by conflicting interests. In thi...

The Pakistanian Acorus calamus (Fam.: Araceae) is locally found (Nasir, 1978) in Chitral, Peshawar, Jhelum valley, Thalawan valley, Mandi and Kashmir. The common name of A. calamus is sweet flag. It is found in marshy places and along the river banks from 600-2000m. The rootstock (modified stem) commonly called as rhizome, is medicinal and yields an essential oil used in the manufacture of soap...

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Motivated by hypergraph decomposition algorithms, we introduce the notion of edge-induced vertex-cuts and compare it with the well-known notions of edge-cuts and vertex-cuts. We investigate the complexity of computing minimum edge-induced vertex-cuts and demonstrate the usefulness of our notion by applications in network reliability and constraint satisfaction.

Recently, fuzzy multi-sets have come to the forefront of scientists’ interest and been used in algebraic structures such as multi-groups, multi-rings, anti-fuzzy multigroup (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize knowledge about structure γ)-anti-multi-fuzzy a way, notion is an application multi sets theory group. The concept complement set that generalizes both theories ...

Split cuts represent the most widely used class of cutting planes currently employed by state-of-the-art branch-and-cut solvers for mixed integer linear programming. Rank-1 cuts often have better numerical properties than higher rank cuts. In this paper, we study several heuristics to generate new families of strong rank-1 split cuts, by considering integer linear combinations of the rows of th...

The split cuts of Cook, Kannan and Schrijver are general-purpose valid inequalities for integer programming which include a variety of other well-known cuts as special cases. To detect violated split cuts, one has to solve the associated separation problem. The complexity of split cut separation was recently cited as an open problem by Cornuéjols & Li [10]. In this paper we settle this question...

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...