Topic
Upper set
About: Upper set is a research topic. Over the lifetime, 32 publications have been published within this topic receiving 350 citations. The topic is also known as: upset.
Papers
TL;DR: New concepts of efficiency for uncertain multi-objective optimization problems are presented by replacing the set ordering with other set orderings by analyzing the connection between the concept of minmax robust efficiency presented by Ehrgott et al.
Abstract: In this paper we present new concepts of efficiency for uncertain multi-objective optimization problems. We analyze the connection between the concept of minmax robust efficiency presented by Ehrgott et al. (Eur J Oper Res, 2014, doi:
10.1016/j.ejor.2014.03.013
) and the upper set less order relation $$\preceq _s^u$$
introduced by Kuroiwa (1998, 1999). From this connection we derive new concepts of efficiency for uncertain multi-objective optimization problems by replacing the set ordering with other set orderings. Those are namely the lower set less ordering (see Kuroiwa 1998, 1999), the set less ordering (see Nishnianidze in Soobshch Akad Nauk Gruzin SSR 114(3):489–491, 1984; Young in Math Ann 104(1):260–290, 1931, doi:
10.1007/BF01457934
; Eichfelder and Jahn in Vector Optimization. Springer, Berlin, 2012), the certainly less ordering (see Eichfelder and Jahn in Vector Optimization. Springer, Berlin, 2012), and the alternative set less ordering (see Ide et al. in Fixed Point Theory Appl, 2014, doi:
10.1186/1687-1812-2014-83
; Kobis 2014). We analyze the resulting concepts of efficiency and present numerical results on the occurrence of the various concepts. We conclude the paper with a short comparison between the concepts, and an outlook to further work.
80 citations
12 Oct 1993
TL;DR: In generalized approximation spaces, the lower and upper set approximations are defined and the introduced notions with different types of relation approximation are illustrated.
Abstract: We generalize the notion of an approximation space introduced in [3]. In generalized approximation spaces we define the lower and upper set approximations. We illustrate the introduced notions with different types of relation approximation.
44 citations
TL;DR: This work investigates two set scalarization functions of type sup-inf, which are extensions of the oriented distance of Hiriart-Urruty and uses these functions to characterize the lower and upper set less preorders of Kuroiwa and the strict lower and strict upper set relations.
Abstract: In the framework of normed spaces ordered by a convex cone not necessarily solid, we consider two set scalarization functions of type sup-inf, which are extensions of the oriented distance of Hiriart-Urruty. We investigate some of their properties and, moreover, we use these functions to characterize the lower and upper set less preorders of Kuroiwa and the strict lower and strict upper set relations. Finally, we apply the obtained results to characterize several concepts of minimal solution to a set optimization problem defined by a set-valued map. Minimal and weak minimal solutions with respect to the lower and upper set less relations are between the concepts considered. Illustrative examples are also given.
30 citations
Journal Article•
[...]
TL;DR: In this paper, the authors introduced the notion of a Γ-CI-algebras, and investigated the relationship between Γ -ideals, Γ subalgeses, and upper sets in these structures.
Abstract: The purpose of this paper is to introduce the notion of a Γ-CI-algebras, we study Γ-ideals, Γ-subalgebras and upper sets in Γ-CI-algebras. Some characterizations of Γ-ideals and Γ-subalgebras are obtained. Moreover, we investigate relationships between Γ-ideals, Γ-subalgebras and upper sets in Γ-CI-algebras.
25 citations
TL;DR: Representations for U are obtained and shown to correspond to certain multidimensional partitions of integers and various notions in statistics and reliability theory are considered.
Abstract: Let U be an upper set contained in the finite discrete lattice L = {1,..., D1} ×... × {1,..., Dp}. Representations for U are obtained and shown to correspond to certain multidimensional partitions of integers. It is shown that for p = 3, the number of possible upper sets in L is $\prod_{t=0}^{D3-1} \left{D1 + D2 + t\atop D1}\right\Big/\left{D1 + t\atop D1}\right$ . Various other representation and enumeration results are obtained for related settings. Considered are a variety of applications to multivariate positive dependence and various notions in statistics and reliability theory.
18 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2020 | 3 |
| 2019 | 2 |
| 2018 | 1 |
| 2017 | 2 |
| 2015 | 4 |
| 2014 | 5 |