Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

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A prioritized aggregation operator-based approach to multiple criteria decision making using interval-valued intuitionistic fuzzy sets: A comparative perspective

Information Sciences ◽

10.1016/j.ins.2014.05.018 ◽

2014 ◽

Vol 281 ◽

pp. 97-112 ◽

Cited By ~ 46

Author(s):

Ting-Yu Chen

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Multiple Criteria Decision Making ◽

Intuitionistic Fuzzy Sets ◽

Aggregation Operator ◽

Multiple Criteria ◽

Comparative Perspective ◽

Intuitionistic Fuzzy ◽

Prioritized Aggregation Operator ◽

Interval Valued

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Multiple criteria decision making based on Hamy mean operators under the environment of spherical fuzzy sets

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201708 ◽

2021 ◽

pp. 1-26

Author(s):

Muhammad Sarwar Sindhu ◽

Tabasam Rashid ◽

Agha Kashif

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Closed Interval ◽

Multiple Criteria Decision Making ◽

Score Function ◽

Vital Role ◽

Multiple Criteria ◽

Uncertain Information ◽

Membership Degree ◽

Picture Fuzzy Sets

Aggregation operators are widely applied to accumulate the vague and uncertain information in these days. Hamy mean (HM) operators play a vital role to accumulate the information. HM operators give us a more general and stretchy approach to develop the connections between the arguments. Spherical fuzzy sets (SpFSs), the further extension of picture fuzzy sets (PcFSs) that handle the data in which square sum of membership degree (MD), non-membership degree (NMD) and neutral degree (ND) always lie between closed interval [0, 1]. In the present article, we modify the HM operators like spherical fuzzy HM (SpFHM) operator and weighted spherical fuzzy HM (WSpFHM) operator to accumulate the spherical fuzzy (SpF) information. Moreover, various properties and some particular cases of SpFHM and the WSpFHM operators are discussed in details. Also, to compare the results obtained from the HM operators a score function is developed. Based on WSpFHM operator and score function, a model for multiple criteria decision-making (MCDM) is established to resolve the MCDM problem. To check the significance and robustness of the result, a comparative analysis and sensitivity analysis is also performed.

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