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Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Year of Publication: 2016
Mohamed A. H. El_Hawy, Khaled T. Wassif, Hesham A. Hefny, Hesham A. Hassan

Mohamed A H El_Hawy, Khaled T Wassif, Hesham A Hefny and Hesham A Hassan. Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers. International Journal of Computer Applications 155(14):42-50, December 2016. BibTeX

	author = {Mohamed A. H. El_Hawy and Khaled T. Wassif and Hesham A. Hefny and Hesham A. Hassan},
	title = {Hybrid Fuzzy-Linear Programming with Shadowed Fuzzy Numbers},
	journal = {International Journal of Computer Applications},
	issue_date = {December 2016},
	volume = {155},
	number = {14},
	month = {Dec},
	year = {2016},
	issn = {0975-8887},
	pages = {42-50},
	numpages = {9},
	url = {},
	doi = {10.5120/ijca2016912577},
	publisher = {Foundation of Computer Science (FCS), NY, USA},
	address = {New York, USA}


Linear programming problem in an environment that includes different types of uncertainties represents real-world situations. In such situations, different forms of uncertain data parameters are commonly found in that problem. Fuzzy sets and their extensions are important tools of representing vague information. For decades, a lot of approaches are developed to solve fuzzy-linear programming problems. The existence of hybrid types of uncertainties in the fuzzy-linear programming problem imposes a real challenge to solve it. There is a need for introducing an efficient methodology to transform different types of uncertainties into a unified form. This paper introduces a new approach to solve hybrid fuzzy-linear programming using an improved version of shadowed fuzzy numbers (SFNs). SFNs are useful transformation tool for different types of uncertainties. They have the advantage of preserving the characteristics of uncertainty for different types of fuzzy sets used in the problem.


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Shadowed sets , Fuzzy numbers , Intuitionistic fuzzy numbers , Non-specificity measure , Entropy measure , Fuzzy linear programming