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A novel approach to MADM problems using Fermatean fuzzy Hamacher prioritized aggregation operators

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Abstract

A generalized form of union and intersection on FFS can be formulated from a generalized t-norm (TN) and t-conorm (TCN). Hamacher operations such as Hamacher product and Hamacher sum are good alternatives to produce such product and sum. The Hamacher operations can generate more flexible and more accurate results in decision-making process due to the working parameter involved in these operations. The intuitionistic fuzzy set, briefly as IFS and its extension involving Pythagorean fuzzy set (PFS) and Fermatean fuzzy set (FFS), are all effective tools to express uncertain and incomplete cognitive information with membership, nonmembership and hesitancy degrees. The Fermatean fuzzy set (FF-set) carries out uncertain and imprecise information smartly in exercising decision making than IFS and PFS. By adjusting the prioritization of attributes in FF environment, in this course of this article, we first device new operations on FF information using prioritized attributes and by employing HTN and HTCN, we discuss the basic operations. Induced by the Hamacher operations and FF-set, we propose FF Hamacher arithmetic and also geometric aggregation operators (AOs). In the first section, we introduce the concepts of an FF Hamacher prioritized AO and FF Hamacher prioritized weighted AO. In the second part, we develop FF Hamacher prioritized geometric operator (GO) and FF Hamacher prioritized weighted GO. We study essential properties and a few special cases of our newly proposed operators. Then, we make use of these proposed operators in developing tools which are key factors in solving the FF multi-attribute decision-making situations with prioritization. The university selection phenomena are considered as a direct application for analysis and to demonstrate the practicality and efficacy of our proposed model. The working parameter considered in these AOs is analyzed in different existing and proposed AOs. Further, comparison analysis is conducted for the authenticity of proposed & existing operators.

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Authors and Affiliations

  1. Department of Mathematics, Abdul Wali Khan University, Mardan, KP, Pakistan

    Asmatullah Jan, Asghar Khan & Minhaj Afridi

  2. Department of Mathematics and Physics, Nanjing Institute of Technology, Jiangning, Nanjing, China

    Waqar Khan

Authors
  1. Asmatullah Jan
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  2. Asghar Khan
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  3. Waqar Khan
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  4. Minhaj Afridi
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Contributions

Khan and Khan discussed and formulated the measures. Jan and Afridi wrote the paper together.

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Correspondence to Asghar Khan.

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Jan, A., Khan, A., Khan, W. et al. A novel approach to MADM problems using Fermatean fuzzy Hamacher prioritized aggregation operators. Soft Comput 25, 13897–13910 (2021). https://doi.org/10.1007/s00500-021-06308-w

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