A new method for solving linear programming problems using Z-numbers’ ranking

Hasankhani, Fatemeh; Daneshian, Behrouz; Allahviranloo, Tofigh; Khiyabani, Farzin Modarres

doi:10.1007/s40096-021-00446-w

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…Additionally, the Z‐number method has been used in other studies to determine mode selection variables such as hotel selection including unreliable information and various factors that are used as variables in multi‐criteria decision making [25] and to select locations for brigade command posts in the length of combat operations [26]. Moreover, resilience engineering in the health management system [27] and improving resilience capabilities on supply chain performance [28] are also regarded as usages of the Z‐number method. In fact, the use of Z‐number is a new method for ranking data based on the concept of value and ambiguity in decision‐making levels [29], evaluating the coverage analysis of system input data with the type of fuzzy input and output data due to uncertainty in real data [30] and analysing unreliable data failure in reliability with the aim of reducing risk [31].…”

Section: Introductionmentioning

confidence: 99%

Probability modelling of storage based‐smart energy hub considering electric vehicles charging stations performance and demand side management

Javid,

Derakhshan,

Hakimi

2023

IET Renewable Power Gen

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Nowadays, researchers are studying the energy discharging of electric vehicles (EVs) in charging stations. Furthermore, these stations can help maintain the balance of electric energy and reduce costs in the energy hub in the discharging mode. In this regard, this article proposes a probability and possibility approach by the Z‐number method to investigate the uncertainty of the EV owners’ behaviour at charging stations during the discharge of electric energy to the energy hub. Also, here, the uncertainty of electric energy demand, thermal energy, drinking water, and the price of electric energy, thermal energy, drinking water, and electric energy production from a solar power plant has been done by the scenario‐base method. The seawater desalination unit has been modelled to meet the drinking water needs. To check the final results of the proposed method, the mixed integer linear programming (MILP) model has been selected for energy management in the energy hub in the CPLEX optimization solver. The final results show that modelling the behaviour of EV owners in the charging stations using the Z‐number method leads to reduced consumption of some energy carriers in comparison with the fuzzy method in the proposed energy hub.

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Section: Introductionmentioning

confidence: 99%

Probability modelling of storage based‐smart energy hub considering electric vehicles charging stations performance and demand side management

Javid,

Derakhshan,

Hakimi

2023

IET Renewable Power Gen

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“…Although fuzzy-LP and Z-LP are similar in their theoretical solutions, Z-LP techniques are synchronized with the real world. Hasankhani et al [10] proposed a ranking method for Z-numbers for certain linear programming problems that are filled with Z-numbers. This model could be easily applied for all types of constraints, regardless of magnitude.…”

Section: Introduction 1motivationmentioning

confidence: 99%

Z-Number-Based Maximum Expected Linear Programming Model with Applications

Yuan,

Zeng,

Chen

et al. 2023

Mathematics

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In research of a better description for information uncertainty, Z-numbers, which are related to both the objective information and the subjective criticism, were first conceptualized by Zadeh. Because of its neologism, there have been multitudinous attempts toward continuation and expansion of the prototype. In this paper, we mainly study varieties of theoretical preparations for classical Z-numbers and derive the maximum expected linear programming model of Z-numbers, which are constructed on the basis of reliability conversion factors and proliferation on applications due to their simplicity. Firstly, by means of transforming Z-numbers into LR fuzzy intervals through their reliability variable, the credibility distribution and inverse distribution of converted Z-numbers are stated precisely. Then, the operational law of independent variables and its expected value can be derived via credibility distribution. The maximum expected Z-number linear programming model is determined on the basis of previous theoretical preparations, and it transforms from a classical Z-number chance-constrained model into a crisp one. Finally, with the aim of improving the programming method, its application in pragmatic practice with the realistic examples of a supplier section and optimal portfolio problems are enumerated to interpret the effectiveness of our model.

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