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Multiple attribute decision-making Pythagorean vague normal operators and their applications for the medical robots process on surgical system

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Abstract

The Pythagorean vague normal set is a concept that involves more uncertainty than fuzzy sets, vague sets, interval valued fuzzy sets and subsequently has more substantial application in decision making. Several new approaches to multiple attribute decision-making problems are explored using Pythagorean vague normal set. The Pythagorean vague normal set is a generalization of Pythagorean interval-valued normal fuzzy set. In addition to the vague set, Pythagorean interval-valued fuzzy set has been extended to the Pythagorean vague set. We define Pythagorean vague normal numbers along with some of their fundamental operations. As a result, the Pythagorean vague number concept with normal fuzzy number has been consolidated, and we have defined the Pythagorean vague normal number. An interesting idea of Pythagorean vague normal weighted averaging, Pythagorean vague normal weighted geometric, generalized Pythagorean vague normal weighted averaging, and generalized Pythagorean vague normal weighted geometric operators is discussed. These operators are used in the multiple attribute decision-making approach and an algorithm that uses them. We illustrate the interplay between the extended Euclidean distance and Hamming distance using a numerical example. This communication discusses the Pythagorean vague normal set properties based on different algebraic operations. This approach is more realistic and easier to understand and it identifies the most effective solution more quickly. It is becoming more common for hospitals and other healthcare facilities to deploy robots to improve patient care and outcomes. These include the surgical robot, Xenex Germ Zapping Robot, Therapeutic Robot, CyberKnife Robot, and Autonomous Mobile Robot. Four elements together with their associated weights are considered for each of the five medical robots including the controller features, programming software, safety codes, and experience with reputation. We can narrow down the many alternatives to the best option by comparing expert judgement with the criteria. In this case, the conclusions of these models are stronger and more closely related to the natural number \(\Psi \). Several models are under examination and we compare them with some proposed models to demonstrate their dependability and value.

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Authors and Affiliations

  1. Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai, 602105, India

    M. Palanikumar

  2. Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai, 600073, India

    K. Arulmozhi

  3. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Chiranjibe Jana & Madhumangal Pal

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  1. M. Palanikumar
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  2. K. Arulmozhi
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  3. Chiranjibe Jana
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  4. Madhumangal Pal
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Correspondence to Chiranjibe Jana.

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Palanikumar, M., Arulmozhi, K., Jana, C. et al. Multiple attribute decision-making Pythagorean vague normal operators and their applications for the medical robots process on surgical system. Comp. Appl. Math. 42, 287 (2023). https://doi.org/10.1007/s40314-023-02422-7

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