A Neutrosophic Functional-Analytic Model for Urban Sculpture Design Quality Evaluation

Abstract

Urban sculpture design must reconcile aesthetics, structural integrity, site context, public 
engagement, safety, and sustainability under evaluator disagreement and incomplete 
information. Classical and fuzzy methods compress ambiguity into single-valued scores, 
masking how much of a judgment is uncertain rather than negative. We propose a 
neutrosophic functional-analytic framework that models each criterion-level judgment as 
a triplet q=(T,I,F)capturing truth, indeterminacy, and falsity. On top of this informational 
primitive, we construct a neutrosophic inner-product module and an operator-based 
evaluation calculus: (i) a neutrosophic inner product returning triplets; (ii) a scalarization 
that yields well-defined seminorms/norms; (iii) bounded linear evaluation functionals for 
criteria; and (iv) a Quality Operator producing an institutional Neutrosophic Design 
Index (NDI). We prove consistency properties (monotonicity, boundedness, order
invariance) and deliver a worked numerical study evaluating three sculpture alternatives 
on six criteria. Results show the framework separates ambiguity from negativity, enabling 
targeted design refinement,e.g., decreasing I through clearer briefs or mock-ups, without 
conflating it with F. The approach is static, mathematically defined, computationally 
transparent, and directly applicable to urban design juries and public art programs. 

DOI: 10.5281/zenodo.16934664