Fuzzy rough bi-level multi-objective nonlinear programming problems

Elsisy, M. A.; Sayed, Mohamed A. El

doi:10.1016/j.aej.2019.12.002

Cited by 14 publications

(2 citation statements)

References 26 publications

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“…The previous articles did not use the approach of operations using α-cut. Other work [46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

Ammar,

Abd-Elrazek,

Radwan

2024

Sohag Journal of Sciences

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In this paper, we introduce a new operation on alpha cut for fuzzy rough and fully fuzzy rough multi-objective quadratic programming problems. Realistic quadratic programming problems often encounter uncertainty as well as indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy and fuzzy rough approaches are applied to such a problem. This paper proposes an effective method to solve the problem of fully fuzzy and fuzzy rough multi-objective quadratic programming where all the variables and parameters are fully fuzzy rough and fuzzy rough triangular numbers. Firstly, a fuzzy rough multi-objective quadratic problem has turned into an equivalent rough multi-objective quadratic programming problem with α-cut. Moreover, from the problem obtained, four crisp multi-objective quadratic programming problems are generated, and the resulting problems are solved as a crisp quadratic programming problem using a weighted method. We use Kuhn-Tucker conditions to solve the four crisp quadratic programming problems. An algorithm to solve (FRMOQP) problem with α-cut will be introduced. An illustrative example will be given. Secondly, a fully fuzzy rough multi-objective quadratic problem has turned into an equivalent fully rough multi-objective quadratic programming problem. Moreover, from the problem obtained four crisp multi-objective quadratic programming problems are generated, and the resulting problems are solved as a crisp quadratic programming problem using a weighted method. An algorithm to solve problems will be introduced. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.

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“…The previous articles did not use the approach of operations using α-cut. Other work [46][47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

Ammar,

Abd-Elrazek,

Radwan

2024

Sohag Journal of Sciences

View full text Add to dashboard Cite

show abstract

“…Garai, et al [11], developed a multi-objective multi-item inventory model with fuzzy rough coefficients. Elsisy and Elsayed [12], develop bilevel multi-objective nonlinear programming problem (BMNPP), in which the objective functions have fuzzy nature and the constraints represented as a rough set. Midya and Roy [13], introduced an analysis of the interval programming utilizing rough interval Pandian, et al [14] proposed level-bound method for solving fully fuzzy interval integer transportation problem Ammar and Eljarbi [15] proposed an algorithm for solving fuzzy rough multi-objective integer linear fractional programming problem.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction

Ahmed¹

2021

AJAMS

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This paper is focused on estimating the parameter of Exponential distribution under right-censored data with cure fraction. The maximum likelihood estimation and Bayesian approach were used. The Bayesian method is implemented using gamma, Jeffreys, and extension of Jeffreys priors with two loss functions, which are; squared error loss function and Linear Exponential Loss Function (LINEX). The methods of the Bayesian approach are compared to maximum likelihood counterparts and the comparisons are made with respect to the Mean Square Error (MSE) to determine the best for estimating the parameter of Exponential distribution under right-censored data with cure fraction. The results show that the Bayesian with gamma prior under LINEX loss function is a better estimation of the parameter of Exponential distribution with cure fraction based on right-censored data.

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An interval method to measure the uncertainty of basic probability assignment

Deng

2022

Soft Comput

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Fuzzy rough bi-level multi-objective nonlinear programming problems

Cited by 14 publications

References 26 publications

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

α-Cut Approach for Solving Fuzzy Rough Multi-Objective Quadratic Programming Problem

Bayesian Methods and Maximum Likelihood Estimations of Exponential Censored Time Distribution with Cure Fraction

An interval method to measure the uncertainty of basic probability assignment

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