A New Interval Arithmetic Approach to Solve the Trapezoidal Intuitionistic Fuzzy Linear Programming Problem

Linear programming Problem (LPP) is intended to assist executives in making decisions. It is a mathematical technique to determine the best allocation of resources such as labour, employees, components, machinery, and other facilities in order to achieve a specific goal. The parameters in our real-l...

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Bibliographic Details
Published in:IAENG international journal of applied mathematics Vol. 54; no. 2; pp. 262 - 276
Main Authors: Sanjana, R, Ramesh, G
Format: Journal Article
Language:English
Published: Hong Kong International Association of Engineers 01.02.2024
Subjects:
Fuzzy sets
Interval arithmetic
Linear programming
Numerical methods
Parameters
Robustness (mathematics)
Simplex method
ISSN:1992-9978, 1992-9986
Online Access:Get full text
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Summary:Linear programming Problem (LPP) is intended to assist executives in making decisions. It is a mathematical technique to determine the best allocation of resources such as labour, employees, components, machinery, and other facilities in order to achieve a specific goal. The parameters in our real-life situations are hazy and imprecise. The Intuitionistic Fuzzy Set (IFS) is a tool for dealing with decision-making issues under uncertainty. Due to various types of complexity, determining the accurate Membership Function (MF) by an ordinary fuzzy set is not always possible. Interval numbers are thus used to describe the unpredictability. LPP is resolved in this study using novel interval arithmetic operations with Trapezoidal Intuitionistic Fuzzy Numbers (TrIFNs) as parameters. In order to obtain the optimal solution, LPP is solved using three methods: Simplex Method (SM), Robust Two Step Method (RTSM) and Alternative Solution Method (SOM-2). Additionally, the proposed methods are numerically shown, and results are compared and represented diagrammatically.
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ISSN:1992-9978
1992-9986