MultiType/MultiRung Orthopair/Multilinguistic Fuzzy Set with Applications

Authors

https://doi.org/10.48314/anowa.v2i1.51

Abstract

A fuzzy set maps each element to a degree in [0, 1], representing partial membership and enabling reasoning and operations under vagueness. Type-n fuzzy sets nest memberships recursively: each value is a fuzzy set of order n − 1, capturing higher-order uncertainty and footprint variability. A q-rung orthopair fuzzy set assigns membership and nonmembership degrees satisfying µq + νq ≤ 1, modeling hesitation and generalizing intuitionistic and Pythagorean forms. A linguistic fuzzy set links verbal terms (with hedges) to membership functions over data, enabling interpretable, human-centric reasoning with calibrated semantics. In this paper, we study the MultiType, MultiRung Orthopair, and MultiLinguistic Fuzzy Sets, which extend the type, q-rung orthopair, and linguistic frameworks into multi-structured forms.

Keywords:

Fuzzy set, Neutrosophic set, Type-n fuzzy set, Q-rung orthopair fuzzy set, Linguistic fuzzy set

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Published

2026-03-05

Issue

Vol. 2 No. 1 (2026): Annals of Optimization With Applications (ANOWA)

Section

Articles

How to Cite

Fujita, T. (2026). MultiType/MultiRung Orthopair/Multilinguistic Fuzzy Set with Applications. Annals of Optimization With Applications, 2(1), 1-13. https://doi.org/10.48314/anowa.v2i1.51

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