A structured solution framework for fuzzy minimum spanning tree problem and its variants under different criteria

Ke Wang (), Yulin Zhou, Guichao Tian and Mark Goh ()
Additional contact information
Ke Wang: Shanghai University
Yulin Zhou: Shanghai University
Guichao Tian: Shanghai Institute of Science and Technology Management
Mark Goh: National University of Singapore

Fuzzy Optimization and Decision Making, 2021, vol. 20, issue 4, No 4, 497-528

Abstract: Abstract This paper develops a unified and structured solution framework for the minimum spanning tree (MST) problem and its variants (e.g., constrained MST problem and inverse MST problem) on networks with fuzzy link weights. It is applicable to any additive decision criterion under fuzziness (e.g., expected value, value at risk, and conditional value at risk), for generalized cases that the link weights may be represented by arbitrary types of fuzzy variables. It also applies to the entropy criterion while the link weights are continuous fuzzy variables. Following the optimality conditions of the fuzzy MST under different decision criteria proved first in this paper, it is shown that the MST problem and its variants on a fuzzy network can be converted into equivalent deterministic counterparts on their corresponding crisp networks. Consequently, these problems can be effectively solved via their deterministic counterparts without fuzzy simulation, and meanwhile, the performance of the trees under a specified criterion is precisely measured. The accuracy and efficiency are both significantly improved compared with other fuzzy simulation-based approaches. Numerical examples illustrate the superiority of the proposed solution framework. Furthermore, some new theoretical conclusions on the MST problem under fuzziness are also presented.

Keywords: Fuzzy network; Minimum spanning tree; Path optimality condition; Conditional value at risk; Entropy (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10700-021-09352-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:fuzodm:v:20:y:2021:i:4:d:10.1007_s10700-021-09352-1

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10700

DOI: 10.1007/s10700-021-09352-1

Access Statistics for this article

Fuzzy Optimization and Decision Making is currently edited by Shu-Cherng Fang and Boading Liu

More articles in Fuzzy Optimization and Decision Making from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().