The work considers the problem of solving a system of fuzzy relational equations with inf-implication composition and introduces the concepts of a characteristic matrix and attainable components. It is first shown that solving the system is closely related with the covering problem. Further, it is proved that maximal solutions of the system correspond to irredundant coverings of the characteris...

Suppose we have a tournament with edges labelled so that the edges incident with any vertex have at most k distinct labels (and no vertex has outdegree 0). Let m be the minimal size of a subset of labels such that for any vertex there exists an outgoing edge labelled by one of the labels in the subset. It was known that m ? k+1 2 for any tournament. We show that this bound is almost best possib...

In this paper we consider set covering problems with a coefficient matrix almost having the consecutive ones property, i.e., in many rows of the coefficient matrix, the ones appear consecutively. If this property holds for all rows it is well known that the set covering problem can be solved efficiently. For our case of almost consecutive ones we present a reformulation exploiting the consecuti...

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on...

Given a set S of n points in the plane, the disjoint two-rectangle covering problem is to find a pair of disjoint rectangles such that their union contains S and the area of the larger rectangle is minimized. In this paper we consider two variants of this optimization problem: (1) the rectangles are free to rotate but must remain parallel to each other, and (2) one rectangle is axis-parallel bu...

K e y w o r d s S e t c o v e r i n g problems, Fuzzy sets, Fuzzy set-covering problem, Algebraic sum operator. 1. I N T R O D U C T I O N A classical set-covering problem considers the subsets I = {1, 2 , . . . , m} and J = {1, 2 , . . . , n} of integers. A collection p of subset Pj of I is a cover of I, if the union of the members of go is I, i.e., let Pj C I, go = {Pj : j C J0}, J0 C J, go i...

In this paper, we show that both sphere covering problems and optimal polytope approximation of convex bodies are related to optimal Delaunay triangulations, which are the triangulations minimizing the interpolation error between function ‖x‖2 and its linear interpolant based on the underline triangulations. We then develop a new analysis based on the estimate of the interpolation error to get ...

Clinical TempEval 2017 aimed to answer the question: how well do systems trained on annotated timelines for one medical condition (colon cancer) perform in predicting timelines on another medical condition (brain cancer)? Nine sub-tasks were included, covering problems in time expression identification, event expression identification and temporal relation identification. Participant systems we...

In this article, a new genetic algorithm (GA), called the Nash equilibrium sorting (NESGA,) is introduced to identify equilibria for competitive maximal covering location problem with two and three competitors, which combinatorial game theory where it computationally intractable enumerate all decision options of competitors. Although GAs are widely used in optimization, their applications non-c...

The Consecutive-Ones Property (C1P) is a classical concept in discrete mathematics that has been used in several genomics applications, from physical mapping of contemporary genomes to the assembly of ancient genomes. A common issue in genome assembly concerns repeats, genomic sequences that appear in several locations of a genome. Handling repeats leads to a variant of the C1P, the C1P with mu...