Choquet integral optimisation with constraints and the buoyancy property for fuzzy measures

Beliakov, Gleb; Liu, James N. K.

doi:10.1016/j.ins.2021.07.032

Cited by 15 publications

(5 citation statements)

References 34 publications

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“…It is worth noted that, since the main structure of the proposed scheme is based on the graph theory equipped with binary nodes and branches structures, considering the system graph matrix in (n+e+s) dimensions where s represents the system switching conditions, it is possible to evaluate the criteria (1)-( 7) at each time moving window through online working mode. In this case, there are two time moving windows Δt 1 = (2 s .ne + log n) and Δt 2 = (ne +s) required in which using the Landau function [28] as the main objective function O(f) and developing the parameters, the system weighted and unweighted parameters are evaluated [29]. In the case of large PDSs with multiple operating conditions, the size of graph dimension is significantly increased which leads to enormous computations.…”

Section: Criterion 7: the Aggregated Node Validation (Anv)mentioning

confidence: 99%

“…In this section, the CI algorithm [29] is proposed to evaluate proposed online index developed in (1)- (8). The conceptual structure of the CI algorithm based on proposed seven criteria as input features, is shown in Figure 1.…”

Section: Developing the Proposed Choquet Algorithm To Evaluate The Sy...mentioning

confidence: 99%

“…In this case, there are two time moving windows Δ t 1 = (2 s . ne + log n ) and Δ t 2 = ( ne + s ) required in which using the Landau function [28] as the main objective function O ( f ) and developing the parameters, the system weighted and unweighted parameters are evaluated [29]. In the case of large PDSs with multiple operating conditions, the size of graph dimension is significantly increased which leads to enormous computations.…”

Section: Developing Online Parameters To Evaluate the Pds Resiliency ...mentioning

confidence: 99%

“…Noting that, considering reverse ordering for OWA, the weights will be corresponded with the largest inputs. Also, for proofing fuzzy functions, Möbius inversion or expressed in what is referred to a Möbius representation is performed while the Möbius representation is invertible via the so‐called Zeta transform, and hence from any fuzzy measure, the standard representation can be provided [29].…”

Section: Developing Online Parameters To Evaluate the Pds Resiliency ...mentioning

confidence: 99%

“…In this case, fuzzy presents a set of function rules in which all possible incorporations of the main criteria are provided. The performance and complexity of Choquet Integral is an exponential 2 n function, where n presents the number of criteria through main resiliency objective function [29].…”

Section: Developing the Proposed Choquet Algorithm To Evaluate The Sy...mentioning

confidence: 99%

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Online evaluation of the distribution system resiliency criteria using Choquet‐based graph technique

Ranjbar

2023

IET Generation Trans & Dist

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Nowadays, due to network expansions, system operators are dealing with natural events including system failures. Evaluating the system readiness to maintain the network interconnections during severe faults are known as an important challenge of today's distribution networks. To do this, this paper presents an online non‐model‐based scheme of evaluating the system resiliency and supplying critical loads within severe natural conditions. In this case, by developing system resiliency as multi‐metric decision making problem and proposing the Choquet integral and graph theoretic methodology, the system resiliency is evaluated. The proposed resiliency scheme is an online non‐model‐based approach can be used for all distribution system configurations with the potential of natural event failures. In this case, by proposing online resiliency criteria based on the system critical loads and branches and developing the proposed criteria on Choquet integral scheme in the form of optimization procedure, the system resiliency is evaluated. The validity of the proposed approach is carried out on two different systems including the IEEE 123‐bus test system and the Consortium for Electric Reliability Technology Solutions (CERTS) microgrid. Simulation results present effectiveness of the proposed scheme to provide proper protective switching strategy and design the system resiliency criteria for future distribution systems.

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Section: Criterion 7: the Aggregated Node Validation (Anv)mentioning

confidence: 99%

Section: Developing the Proposed Choquet Algorithm To Evaluate The Sy...mentioning

confidence: 99%

Section: Developing Online Parameters To Evaluate the Pds Resiliency ...mentioning

confidence: 99%

Section: Developing Online Parameters To Evaluate the Pds Resiliency ...mentioning

confidence: 99%

Section: Developing the Proposed Choquet Algorithm To Evaluate The Sy...mentioning

confidence: 99%

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Online evaluation of the distribution system resiliency criteria using Choquet‐based graph technique

Ranjbar

2023

IET Generation Trans & Dist

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Choquet integral‐based measures of economic welfare and species diversity

Beliakov

Liu

2021

Int J of Intelligent Sys

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Measures of diversity, spread and inequality can be important indicators in domains as diverse as ecology, economics and health. One of the key characteristics of such indices is the Pigou–Dalton (P‐D) principle, also known as the principle of progressive transfers, whereby proportional redistribution from larger to smaller arguments should increase (or decrease, depending on the context) the overall measure of social or economic welfare, diversity and so on. Previous studies have identified the ordered weighted averaging operators as being appropriate for welfare measurement, subject to conditions on the weighting vectors. We propose the Choquet integral, defined with respect to a capacity or fuzzy measure, as a candidate for defining nonsymmetric measures of welfare. This allows for importance and interaction to be modelled between inputs while still satisfying the P‐D principle. We extend the buoyancy concept to fuzzy measures and characterise the resulting classes of buoyant and antibuoyant fuzzy measures. We then turn to the problem of optimisation of the Choquet integral subject to linear constraints, which in the case of antibuoyant fuzzy measures permits an efficient linear programming solution.

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Multi-agent collaborative conceptual design method for robotic manufacturing systems in small- and mid-sized enterprises

Zheng,

Du,

Sun

et al. 2023

Computers & Industrial Engineering

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Choquet integral optimisation with constraints and the buoyancy property for fuzzy measures

Cited by 15 publications

References 34 publications

Online evaluation of the distribution system resiliency criteria using Choquet‐based graph technique

Online evaluation of the distribution system resiliency criteria using Choquet‐based graph technique

Choquet integral‐based measures of economic welfare and species diversity

Multi-agent collaborative conceptual design method for robotic manufacturing systems in small- and mid-sized enterprises

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