Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment

Abdullah Ali H. Ahmadini; Firoz Ahmad; Abdullah Ali H. Ahmadini; Firoz Ahmad

doi:10.3934/math.2021269

AIMS Mathematics

2021, Volume 6, Issue 5: 4556-4580. doi: 10.3934/math.2021269

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Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment

Abdullah Ali H. Ahmadini ¹,
Firoz Ahmad ^{2,3
,
,}

1.
Department of Mathematics, Faculty of Sciences, Jazan University, Jazan, SAUDI ARABIA
2.
Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, INDIA
3.
SQC&OR Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700108, INDIA

Received: 24 September 2020 Accepted: 03 February 2021 Published: 22 February 2021
MSC : 03B52, 03F55, 62J05, 62J99

The existence of neutral /indeterminacy degrees reflects the more practical aspects of decision-making scenarios. Thus, this paper has studied the intuitionistic fuzzy multiobjective linear programming problems (IFMOLPPs) under neutrosophic uncertainty. To highlight the degrees of neutrality in IFMOLPPs, we have investigated the neutrosophic optimization techniques with intuitionistic fuzzy parameters. The marginal evaluation of each objective is determined by three different membership functions, such as truth, indeterminacy, and falsity membership degrees under the neutrosophic environment. The marginal evaluation of each objective function is elicited by various sorts of membership functions such as linear, exponential, and hyperbolic types of membership functions, which signifies an opportunity for decision-makers to select the desired membership functions. The developed neutrosophic optimization technique is implemented on existing numerical problems that reveal the validity and applicability of the proposed methods. A comparative study is also presented with other approaches. At last, conclusions and future research directions are addressed based on the proposed work.
Citation: Abdullah Ali H. Ahmadini, Firoz Ahmad. Solving intuitionistic fuzzy multiobjective linear programming problem under neutrosophic environment[J]. AIMS Mathematics, 2021, 6(5): 4556-4580. doi: 10.3934/math.2021269

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Abstract

The existence of neutral /indeterminacy degrees reflects the more practical aspects of decision-making scenarios. Thus, this paper has studied the intuitionistic fuzzy multiobjective linear programming problems (IFMOLPPs) under neutrosophic uncertainty. To highlight the degrees of neutrality in IFMOLPPs, we have investigated the neutrosophic optimization techniques with intuitionistic fuzzy parameters. The marginal evaluation of each objective is determined by three different membership functions, such as truth, indeterminacy, and falsity membership degrees under the neutrosophic environment. The marginal evaluation of each objective function is elicited by various sorts of membership functions such as linear, exponential, and hyperbolic types of membership functions, which signifies an opportunity for decision-makers to select the desired membership functions. The developed neutrosophic optimization technique is implemented on existing numerical problems that reveal the validity and applicability of the proposed methods. A comparative study is also presented with other approaches. At last, conclusions and future research directions are addressed based on the proposed work.

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