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Issue:Solving I-fuzzy number linear programming problems via Tanaka and Asai approach

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Title of paper: Solving I-fuzzy number linear programming problems via Tanaka and Asai approach
Author(s):
Abha Aggarwal
University School of Basic and Applied Sciences, Guru Gobind, Singh Indraprastha University, Delhi-110078, India
abha@ipu.ac.in
Aparna Mehra
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
apmehra@maths.iitd.ac.in
Suresh Chandra
Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khas, New Delhi-110016, India
chandras@maths.iitd.ac.in
Imran Khan
University School of Basic and Applied Sciences, Guru Gobind, Singh Indraprastha University, Delhi-110078, India
imranalig_khan@yahoo.co.in
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 23, 2017, Number 5, pages 85—101
Download:  PDF (296 Kb  Kb, File info)
Abstract: This paper proposes an extension of Tanaka and Asai approach to study Atanassov’s I-fuzzy linear programming problems where problem parameters are prescribed by I-fuzzy numbers. In literature, there are various indices based ranking function approaches for solving such I-fuzzy linear programming problems, e.g., Li [26], Li et al. [27], Dubey and Mehra [18] and Dubey et al. [19]. One major issue with these approaches is that the solution so obtained depends on the specific choice of the ranking function. The primary advantage of the proposed method is that, it is independent of any transformation and also provides the precise degrees of belief and disbelief of the optimal solution in achieving the goals set by the decision maker. It is shown that solving such an optimization problem is equivalent to solving a non-linear programming problem. A small numerical example is included as an illustration.
Keywords: I-fuzzy set, Triangular I-fuzzy numbers, I-fuzzy mathematical programming, I-fuzzy parameters.
AMS Classification: 90C72
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