Averaging aggregation operators under the environment of <i>q</i>-rung orthopair picture fuzzy soft sets and their applications in MADM problems

Sumbal Ali; Asad Ali; Ahmad Bin Azim; Ahmad ALoqaily; Nabil Mlaiki; Sumbal Ali; Asad Ali; Ahmad Bin Azim; Ahmad ALoqaily; Nabil Mlaiki

doi:10.3934/math.2023452

AIMS Mathematics

2023, Volume 8, Issue 4: 9027-9053. doi: 10.3934/math.2023452

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Averaging aggregation operators under the environment of q-rung orthopair picture fuzzy soft sets and their applications in MADM problems

1.
Department of Mathematics & Statistics, Hazara University, Mansehra, 21120, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University. Riyadh, 11586, Saudi Arabia
3.
School of computer, Data, and Mathematical Sciences, Western Sydney University, Australia-Sydney-2150

Received: 31 October 2022 Revised: 04 February 2023 Accepted: 06 February 2023 Published: 10 February 2023
MSC : 60L70, 68N17

q-Rung orthopair fuzzy soft set handles the uncertainties and vagueness by membership and non-membership degree with attributes, here is no information about the neutral degree so to cover this gap and get a generalized structure, we present hybrid of picture fuzzy set and q-rung orthopair fuzzy soft set and initiate the notion of q-rung orthopair picture fuzzy soft set, which is characterized by positive, neutral and negative membership degree with attributes. The main contribution of this article is to investigate the basic operations and some averaging aggregation operators like q-rung orthopair picture fuzzy soft weighted averaging operator and q-rung orthopair picture fuzzy soft order weighted averaging operator under the environment of q-rung orthopair picture fuzzy soft set. Moreover, some fundamental properties and results of these aggregation operators are studied, and based on these proposed operators we presented a stepwise algorithm for MADM by taking the problem related to medical diagnosis under the environment of q-rung orthopair picture fuzzy soft set and finally, for the superiority we presented comparison analysis of proposed operators with existing operators.
Citation: Sumbal Ali, Asad Ali, Ahmad Bin Azim, Ahmad ALoqaily, Nabil Mlaiki. Averaging aggregation operators under the environment of q-rung orthopair picture fuzzy soft sets and their applications in MADM problems[J]. AIMS Mathematics, 2023, 8(4): 9027-9053. doi: 10.3934/math.2023452

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Abstract

q-Rung orthopair fuzzy soft set handles the uncertainties and vagueness by membership and non-membership degree with attributes, here is no information about the neutral degree so to cover this gap and get a generalized structure, we present hybrid of picture fuzzy set and q-rung orthopair fuzzy soft set and initiate the notion of q-rung orthopair picture fuzzy soft set, which is characterized by positive, neutral and negative membership degree with attributes. The main contribution of this article is to investigate the basic operations and some averaging aggregation operators like q-rung orthopair picture fuzzy soft weighted averaging operator and q-rung orthopair picture fuzzy soft order weighted averaging operator under the environment of q-rung orthopair picture fuzzy soft set. Moreover, some fundamental properties and results of these aggregation operators are studied, and based on these proposed operators we presented a stepwise algorithm for MADM by taking the problem related to medical diagnosis under the environment of q-rung orthopair picture fuzzy soft set and finally, for the superiority we presented comparison analysis of proposed operators with existing operators.

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