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

Tahir Mahmood,Thammarat Panityakul,Dulyawit Prangchumpol,Zeeshan Ali

doi:10.32604/cmes.2022.017998

Tahir Mahmood, Thammarat Panityakul + Show 2 more

Open Access

https://doi.org/10.32604/cmes.2022.017998

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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.

Highlights

multi-attribute decisionmaking (MADM) is widely applied to real-world problems, but due to the complicated and inconsistent information acquired, the use of crisp sets in these contexts often has limitations
Liu et al [3] examined a viable weighted-based hybrid approach using intervalvalued intuitionistic FS (IFS); Garg et al [4] presented a similarity measure using right-angled triangles based on IFSs; Ejegwa et al [5] initiated a statistical correlation algorithm using IFSs; Xue et al [6] elaborated measure-based belief functions using IFSs; Aydin et al [7] explored interval-valued intuitionistic parameterized interval-valued intuitionistic fuzzy soft sets; Szmidt et al [8] proposed certain measures based on IFSs, and Ghosh et al [9] elaborated a fixed charge solid transportation problem based on IFSs
(2) To determine the relationship among any number of attributes, we develop the multi-valued complex neutrosophic uncertain linguistic Dombi normalized weighted Bonferroni mean (MVCNULDNWBM) operator and illustrate its important properties with some specific cases

Summary

Introduction

MADM is widely applied to real-world problems, but due to the complicated and inconsistent information acquired, the use of crisp sets in these contexts often has limitations. To resolve the problems which occur in certain issues, Zadeh [1] elaborated the principle of the fuzzy set (FS). FSs are more powerful and effective than crisp sets and can contain the truth grade (TG) belonging to the unit interval. FSs do not work effectively when an element can either belong or not belong to the set. To deal with these situations, the intuitionistic FS (IFS) was elaborated by Atanassov [2]. Liu et al [3] examined a viable weighted-based hybrid approach using intervalvalued IFSs; Garg et al [4] presented a similarity measure using right-angled triangles based on IFSs; Ejegwa et al [5] initiated a statistical correlation algorithm using IFSs; Xue et al [6] elaborated measure-based belief functions using IFSs; Aydin et al [7] explored interval-valued intuitionistic parameterized interval-valued intuitionistic fuzzy soft sets; Szmidt et al [8] proposed certain measures based on IFSs, and Ghosh et al [9] elaborated a fixed charge solid transportation problem based on IFSs

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