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Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation

Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation

Huda E. Khalid
Copyright: © 2020 |Pages: 16
ISBN13: 9781799825555|ISBN10: 1799825558|ISBN13 Softcover: 9781799825562|EISBN13: 9781799825579
DOI: 10.4018/978-1-7998-2555-5.ch004
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MLA

Khalid, Huda E. "Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation." Neutrosophic Sets in Decision Analysis and Operations Research, edited by Mohamed Abdel-Basset and Florentin Smarandache, IGI Global, 2020, pp. 82-97. https://doi.org/10.4018/978-1-7998-2555-5.ch004

APA

Khalid, H. E. (2020). Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation. In M. Abdel-Basset & F. Smarandache (Eds.), Neutrosophic Sets in Decision Analysis and Operations Research (pp. 82-97). IGI Global. https://doi.org/10.4018/978-1-7998-2555-5.ch004

Chicago

Khalid, Huda E. "Geometric Programming Dealing With Neutrosophic Relational Equations Under the (Max-Min) Operation." In Neutrosophic Sets in Decision Analysis and Operations Research, edited by Mohamed Abdel-Basset and Florentin Smarandache, 82-97. Hershey, PA: IGI Global, 2020. https://doi.org/10.4018/978-1-7998-2555-5.ch004

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Abstract

The neutrosophic relation equations are important elements of neutrosophic mathematics, and it can be widely applied in power systems, neutrosophic comprehensive evaluation. The aim of this chapter is to find the minimal solutions for the neutrosophic relation geometric programming having (V, Λ) operator. In this chapter, a max-min method has been built for finding an optimal solution in the neutrosophic relation equations, and a new characteristic matrix has been defined which is an important step to test the consistency of the system Aοx=b and for finding all effective paths that lead to the set of all quasi-minimum solutions. The gained results are reasonable and harmonized with those results in Khalid's work. The method overcomes the problems of poor convergence efficiency inherited from the stochastic hill-climbing method or genetic algorithms. The suggested algorithm has the intersection column method which was proposed to find the effective paths that neglect the fallacious paths, and two new theorems were presented to deal with the optimal solution for (NREGP).

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