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Multi-criteria ranking across importance measures for stochastic networks

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Abstract

The identification of the components important to the performance of a system provides insight into decisions such as which components to protect against failure or where to add redundancy to ensure system function. However, there are many perspectives on “importance,” including consideration of purely topological characteristics or consideration of how components enable flow in a network. And even within these broad perspectives, there are different ways to quantify importance. With this in mind, we offer a means to aggregate across different perspectives of importance to provide a more holistic ranking of components. We specifically consider networks with a stochastic nature to their capacities, as the calculation of importance can change based on such variability. We make use of a multi-criteria decision analysis technique under uncertainty, Fuzzy TOPSIS, to aggregate different importance measures given variability in network link capacities. Our proposed approach is illustrated with a case study based on the Colombia highway transportation network.

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Data Availability

Data are available upon request.

Abbreviations

IM:

Importance measure

\(NIM\) :

Number of importance measures

\({G}_{W}=\left(V,E,W\right)\) :

Weighted graph

\(V\) :

Set of nodes

\(E\) :

Set of links connecting two nodes

\(W\) :

Set real numbers that represent the capacity of the links

\(NODES=|V|\) :

Number of nodes in the network

\(LINKS=|E|\) :

Number of links in the network

\(EIM\) :

Matrix \(LINKS\times NIM\) of importance measures such that element \(\left(k,l\right)\) of \(EIM\) is the evaluation of IM \(l\) for link \(k\)

\({Wmin}_{k}\) :

Lower limit of the nominal capacity \({W}_{k}\), \(k=1,\dots ,LINKS\)

\({Wmax}_{k}\) :

Upper limit of the nominal capacity \({W}_{k}\), \(k=1,\dots ,LINKS\)

\({P}_{k}\) :

Percentage of the nominal capacity, \(k=1,\dots ,LINKS\)

DEMATEL:

Decision making trial and evaluation laboratory

PROMETHEE:

Preference ranking organization method for enrichment evaluations

TOPSIS:

Technique for order preference by similarity to ideal solution

\(NSIMUL\) :

Number of scenarios of possible links capacities

\(FEIM\) :

Fuzzy matrix \(EIM\), whose entries are triangular fuzzy numbers

\(Nfuzzy\) :

Number of sets of fuzzy weights for sensitivity analysis

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Authors and Affiliations

  1. Faculty of Engineering, Universidad Central de Venezuela, Caracas, Venezuela

    Claudio M. Rocco

  2. School of Industrial and Systems Engineering, University of Oklahoma, 202 W. Boyd St., Rm. 124, Norman, OK, 73019, USA

    Kash Barker & Andrés D. González

Authors
  1. Claudio M. Rocco
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  2. Kash Barker
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  3. Andrés D. González
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Correspondence to Kash Barker.

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Rocco, C.M., Barker, K. & González, A.D. Multi-criteria ranking across importance measures for stochastic networks. Life Cycle Reliab Saf Eng 12, 187–196 (2023). https://doi.org/10.1007/s41872-023-00225-7

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