Open Access

ARTICLE

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Tahir Mahmood¹, Zeeshan Ali¹, Dulyawit Prangchumpol^2,*, Thammarat Panityakul³

1 Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan
2 Department of Information Technology, Faculty of Science and Technology, Suan Sunandha Rajabhat University, Bangkok, 10300, Thailand
3 Division of Computational Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla, 90110, Thailand

* Corresponding Author: Dulyawit Prangchumpol. Email:

(This article belongs to the Special Issue: Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences: Theory, Models, and Applications (ANPSESTMA))

Computer Modeling in Engineering & Sciences 2022, 130(3), 1587-1623. https://doi.org/10.32604/cmes.2022.017998

Received 22 June 2021; Accepted 24 September 2021; Issue published 30 December 2021

Abstract

Although fuzzy set concepts have evolved, neutrosophic sets are attracting more attention due to the greater power of the structure of neutrosophic sets. The ability to account for components that are true, false or neither true nor false is useful in the resolution of real-life problems. However, simultaneous variations render neutrosophic sets unsuitable in specific circumstances. To enable the management of these sorts of issues, we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multi-valued complex neutrosophic uncertain linguistic sets. Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth, abstinence, and falsity, and uncertain linguistic terms, which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval. Some important Dombi laws are elaborated along with Bonferroni mean operators, which offer a flexible general structure with modifiable factors. Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics. To determine relationships among any number of attributes, we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases. By using these laws, we can deploy the multi-attribute decision-making (MADM) technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets. To determine the power and flexibility of the elaborated approach, we resolve some numerical examples based on the proposed operator. Finally, the work is validated with the help of comparative analysis, a discussion of its advantages, and geometric expressions of the elaborated theories.

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