IndetermSoft Sets: A Multi-Valued Framework for Modeling Indeterminacy in Decision Science

Takaaki Fujita; Ajoy Kanti Das; Suman Das

Authors

Takaaki Fujita Independent Researcher, Tokyo, Japan Author https://orcid.org/0009-0007-1509-2728
Ajoy Kanti Das Department of Mathematics, Tripura University, Agartala, Tripura, India Author https://orcid.org/0000-0002-9326-1677
Suman Das Department of Education (ITEP), NIT Agartala, Jirania, Tripura, India Author https://orcid.org/0000-0001-5682-9334

Keywords:

Soft Set, IndetermSoft Set, Double-valued IndetermSoft Set, Triple-valued IndetermSoft Set, Quadruple-valued IndetermSoft Set, Quintuple-valued IndetermSoft Set

Abstract

Soft sets are parameterized families of subsets of a universe, where each parameter selects elements relevant under a condition. This paper develops IndetermSoft sets, a class designed to treat indeterminacy explicitly through structured value slices. We define five variants: (i) single-valued, mapping each attribute value to one subset capturing undirected indeterminacy; (ii) double-valued, splitting into truth-leaning and falsity-leaning slices; (iii) triple-valued, adding a neutral slice; (iv) quadruple-valued, refining polarity by distinguishing strong and ordinary truth- and falsity-leanings; and (v) quintuple-valued, further introducing a central neutral band between the two strengths. These constructions yield a uniform framework for modeling ambiguous evidence, conflicts, and missing context.

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