Introduction to the MultiNeutrosophic Set

Authors

  • Florentin Smarandache University of New Mexico; Mathematics, Physics and Natural Sciences Division; 705 Gurley Ave., Gallup, NM 87301, United States of America

Abstract

In the real word, in most cases, everything (an attribute, event, proposition, theory, idea, person, object, action, etc.) is evaluated in general by many sources (called experts), not only one. The more sources evaluate a subject, the better accurate result (after fusioning all evaluations). That’s why, in this paper, we straightforwardly extend the Refined Neutrosophic Set to the MultiNeutrosophic Set, and we show that the last two are isomorphic. A MultiNeutrosophic Set is a Neutrosophic Set whose all elements’ degrees of truth/indeterminacy/falsehood are evaluated by many (Multi) sources.
Afterwards, we introduce a total order on the set of n-plets of the form (p, r, s), we build the operators on the (p, r, s)-plets, and show several applications of the MultiNeutrosophic Sets. Several particular cases of the MultiNeutrosophic Sets are presented: such as MultiFuzzy Set, MultiIntuitionistic Fuzzy Set, MultiPicture Fuzzy Set, and other Multi(Fuzzy Extension) Set.

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Published

2023-12-15

Issue

Section

SI#1,2024: Neutrosophical Advancements And Their Impact on Research

How to Cite

Florentin Smarandache. (2023). Introduction to the MultiNeutrosophic Set. Neutrosophic Sets and Systems, 61, 89-99. https://fs.unm.edu/nss8/index.php/111/article/view/3778

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