In our daily life we have to make many decisions and sometimes in a single day we met the situations when correct decision is very compulsory to handle some complicated situations. However, in a professional environment, we need decision-making (DM) techniques to determine the finest alternative from the given alternatives. In this manuscript, we develop one of the finest DM techniques by employing interpreted aggregation operators (AOs). Furthermore, to aggregate the collection of a finite number of information into a singleton set, the Bonferroni mean (BM) operator plays a very beneficial and dominant role. The BM operator is massively powerful than the averaging/geometric operators because they are the specific cases of the BM operator. Based on the above advantages-we initiate the notion of bipolar complex fuzzy BM (BCFBM) operator, bipolar complex fuzzy normalized weighted BM (BCFNWBM) operator and bipolar complex fuzzy ordered weighted BM (BCFOWBM) operator. Furthermore, some well-known and useful properties and results of the initiated operators will be established. We will also apply the described AOs, and evaluate a DM technique, called multi-attribute DM (MADM) to prove the trustworthiness and practicality of the evaluated theory. Finally, to compare the presented work with some prevailing operators, we illustrate some examples and try to evaluate the graphical interpretation of the established work to improve the worth of the proposed theory.
Citation: Tahir Mahmood, Ubaid ur Rehman, Zeeshan Ali, Muhammad Aslam. Bonferroni mean operators based on bipolar complex fuzzy setting and their applications in multi-attribute decision making[J]. AIMS Mathematics, 2022, 7(9): 17166-17197. doi: 10.3934/math.2022945
In our daily life we have to make many decisions and sometimes in a single day we met the situations when correct decision is very compulsory to handle some complicated situations. However, in a professional environment, we need decision-making (DM) techniques to determine the finest alternative from the given alternatives. In this manuscript, we develop one of the finest DM techniques by employing interpreted aggregation operators (AOs). Furthermore, to aggregate the collection of a finite number of information into a singleton set, the Bonferroni mean (BM) operator plays a very beneficial and dominant role. The BM operator is massively powerful than the averaging/geometric operators because they are the specific cases of the BM operator. Based on the above advantages-we initiate the notion of bipolar complex fuzzy BM (BCFBM) operator, bipolar complex fuzzy normalized weighted BM (BCFNWBM) operator and bipolar complex fuzzy ordered weighted BM (BCFOWBM) operator. Furthermore, some well-known and useful properties and results of the initiated operators will be established. We will also apply the described AOs, and evaluate a DM technique, called multi-attribute DM (MADM) to prove the trustworthiness and practicality of the evaluated theory. Finally, to compare the presented work with some prevailing operators, we illustrate some examples and try to evaluate the graphical interpretation of the established work to improve the worth of the proposed theory.
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Tahir Mahmood, Ubaid ur Rehman, Zeeshan Ali, Muhammad Aslam. Bonferroni mean operators based on bipolar complex fuzzy setting and their applications in multi-attribute decision making[J]. AIMS Mathematics, 2022, 7(9): 17166-17197. doi: 10.3934/math.2022945
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