Ordered weighted average combinatorial optimization: Formulations and their properties

Ordered Weighted Average optimization in Multiobjective Spanning Tree Problem

Extended formulations in combinatorial optimization

This survey is concerned with the size of perfect formulations for combinatorial optimization problems. By “perfect formulation”, we mean a system of linear inequalities that describes the convex hull of feasible solutions, viewed as vectors. Natural perfect formulations often have a number of inequalities that is exponential in the size of the data needed to describe the problem. Here we are p...

Extended Formulations in Combinatorial Optimization

The concept of representing a polytope that is associated with some combinatorial optimization problem as a linear projection of a higherdimensional polyhedron has recently received increasing attention. In this paper (written for the newsletter Optima of the Mathematical Optimization Society), we provide a brief introduction to this topic and sketch some of the recent developments with respect...

Induced Unbalanced Linguistic Ordered Weighted Average

Aggregation operators for linguistic variables usually assume a uniform and symmetrical distribution of the linguistic terms that define the variable. This paper defines the Induced Unbalanced Linguistic Ordered Weighted Average (IULOWA). This aggregator takes into account the fuzzy membership functions of the terms during the aggregation operations of the pairs of terms. There is no restrictio...

Ordered Weighted Average Based Fuzzy Rough Sets

Traditionally, membership to the fuzzy-rough lower, resp. upper approximation is determined by looking only at the worst, resp. best performing object. Consequently, when applied to data analysis problems, these approximations are sensitive to noisy and/or outlying samples. In this paper, we advocate a mitigated approach, in which membership to the lower and upper approximation is determined by...