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AIMS Mathematics

2023, Volume 8, Issue 3: 6036-6063. doi: 10.3934/math.2023305
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Analysis of Einstein aggregation operators based on complex intuitionistic fuzzy sets and their applications in multi-attribute decision-making

  • 1.
    Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan
  • 2.
    Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan
  • 3.
    Department of Mathematics, Deanship of Applied Sciences Umm Al-Qura University, Makkah, Saudi Arabia
  • Received: 24 October 2022 Revised: 07 December 2022 Accepted: 19 December 2022 Published: 29 December 2022

  • MSC : 03B52, 68T27, 68T37, 94D05, 03E72

  • The main influence of this analysis is to derive two different types of aggregation operators under the consideration of algebraic t-norm and t-conorm and Einstein t-norm and t-conorm for CIF set theory. Because these operators are very effective for evaluating the collection of information into a singleton preference. For this, first, we discover the Algebraic and Einstein operational laws for CIF sets. Then, we aim to discover the theory of CCIFWA, CCIFOWA, CCIFWG, CCIFOWG operators and their valuable properties "idempotency, monotonicity and boundedness" and results. Furthermore, we also derive the theory of CCIFEWA, CCIFEOWA, CCIFEWG, CCIFEOWG operators and their valuable properties "idempotency, monotonicity, and boundedness" and results. Some special cases of the derived work are also described in detail. Finally, we illustrate a MADM procedure under the consideration of derived operators to enhance the worth of the presented information. Finally, we compare the presented operators with various existing operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.

    Citation: Wajid Azeem, Waqas Mahmood, Tahir Mahmood, Zeeshan Ali, Muhammad Naeem. Analysis of Einstein aggregation operators based on complex intuitionistic fuzzy sets and their applications in multi-attribute decision-making[J]. AIMS Mathematics, 2023, 8(3): 6036-6063. doi: 10.3934/math.2023305

    Related Papers:

  • The main influence of this analysis is to derive two different types of aggregation operators under the consideration of algebraic t-norm and t-conorm and Einstein t-norm and t-conorm for CIF set theory. Because these operators are very effective for evaluating the collection of information into a singleton preference. For this, first, we discover the Algebraic and Einstein operational laws for CIF sets. Then, we aim to discover the theory of CCIFWA, CCIFOWA, CCIFWG, CCIFOWG operators and their valuable properties "idempotency, monotonicity and boundedness" and results. Furthermore, we also derive the theory of CCIFEWA, CCIFEOWA, CCIFEWG, CCIFEOWG operators and their valuable properties "idempotency, monotonicity, and boundedness" and results. Some special cases of the derived work are also described in detail. Finally, we illustrate a MADM procedure under the consideration of derived operators to enhance the worth of the presented information. Finally, we compare the presented operators with various existing operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.


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