A Concise Comparative Analysis of Ambiguous Set Theory in Relation to Fuzzy, Intuitionistic Fuzzy, and Neutrosophic Sets
DOI:
https://doi.org/10.26740/vubeta.v3i3.46080Keywords:
Ambiguous set (AS), Fuzzy set (FS), Intuitionistic fuzzy set (IFS), Neutrosophic set (NS), UncertaintyAbstract
Uncertainty, vagueness, indeterminacy, and ambiguity are fundamental challenges in representing information arising from complex real-world environments, particularly when human perception and decision-making involve indistinct boundaries between truth and falsity. This article presents a conceptual review and comparative analysis of Ambiguous Set (AS) theory in relation to Fuzzy Set (FS), Intuitionistic Fuzzy Set (IFS), and Neutrosophic Set (NS). The objective is to clarify the structural and representational characteristics of AS and identify situations in which its formulation may provide additional flexibility for uncertainty modeling. The comparison considers the basic components, mathematical constraints, relationships among parameters, interpretation of uncertainty, and capability to represent human perception. FS represents uncertainty through a single membership degree, whereas IFS incorporates membership, non-membership, and hesitation. NS further introduces independently characterized truth, indeterminacy, and falsity components. In contrast, AS employs four interrelated components: true membership, false membership, true-ambiguous membership, and false-ambiguous membership, allowing partially true and partially false conditions to be explicitly represented. The reviewed literature indicates that AS has been explored in image processing, multi-criteria decision-making, ambiguous logic, mathematical modeling, complex analysis, and time-series applications. However, its additional parameters may increase computational and interpretational complexity. Therefore, AS should not be regarded as universally superior to FS, IFS, or NS; its suitability depends on the characteristics of the uncertainty and application context. This review provides a balanced assessment of the strengths, limitations, and potential applications of AS while identifying future research opportunities in machine learning, hybrid decision-making, temporal ambiguity modeling, cognitive artificial intelligence, optimization, and formal mathematical development.
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