Geodesic
A Pythagorean Hesitant Fuzzy Programming Approach and Its Application to Multi Objective Reliability Optimization Problem
Yugoslav journal of operations research, Tome 34 (2024) no. 2, p. 201 .

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Decision-making problems can often be effectively solved using traditional optimization methods that have a clearly defined configuration. However, in real-world scenarios, decision-makers frequently encounter doubt or hesitation, making it challenging to precisely specify certain parameters. As a result, they often seek input from different experts, leading to conflicting values and varying levels of satisfaction among decisionmakers. This uncertainty and lack of crisp values make decision-making problems inherently non-deterministic. In this paper, a novel Pythagorean hesitant fuzzy (PHF) programming method is designed to address the challenges of optimization problems with multiple objectives. Here PHF aggregation operators are used to aggregate the PHF memberships and non-memberships of the objectives. Additionally, to account the uncertainties of the parameters of the optimization problem Parabolic Pythagorean fuzzy number is used and centroid method is applied for defuzzification. We solved an example of multi objective optimization problem of manufacturing system to demonstrate our proposed method and finally, presented a case study on reliability optimization model for Life Support Systems, where the primary objectives are to maximize system reliability and minimize cost. The result is compared with other existing methods by degree of closeness.
Classification : 03B52 90C29
Keywords: Parabolic Pythagorean fuzzy number, Pythagorean hesitant fuzzy set, Pythagorean hesitant fuzzy aggregation operator, Multi objective reliability optimization 
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     author = {Swarup Jana and Sahidul Islam},
     title = {A {Pythagorean} {Hesitant} {Fuzzy} {Programming} {Approach} and {Its} {Application} to {Multi} {Objective} {Reliability} {Optimization} {Problem}},
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     year = {2024},
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Swarup Jana; Sahidul Islam. A Pythagorean Hesitant Fuzzy Programming Approach and Its Application to Multi Objective Reliability Optimization Problem. Yugoslav journal of operations research, Tome 34 (2024) no. 2, p. 201 . http://geodesic.mathdoc.fr/item/YJOR_2024_34_2_a0/