Rank-Preserving Encryption for Cotangent Similarity using Complex Neutrosophic Sets

Abstract

We present a privacy-preserving pipeline for pairwise comparison of complex neutrosophic sets (CNS) that uses a rank-preserving (order-preserving) encryption to pairwise compare cotangent similarity (CotSM). We introduce a visual analysis method for paired target source relationships using rank-preserving encryption that maintains anonymity. On a 3x3 grid of targets (T1-T3) and sources  (S1-S3), we produce complementary views: (i) Cotangent Similarity (CotSM) Heatmaps and bar charts, all of which are encrypted; and (ii) Pearson-correlation Heatmaps and 3D surfaces, which are likewise encrypted. T1-S2 (i.e., max 0.4324 in Heatmaps; 0.6653 in bars) relationship is consistently the most significant in all CotSM perspectives, with T1 typically dominating and S2 the most convincing source. On the other hand, encrypted Pearson views had the highest T3 S3 value (normalized maximum 1.000), with T3 dominating and S3 having the biggest influence. The following is a summary of these findings: (1) Since the encryption maintains rank structure (maxima, minima, relative ranking), comparative
 interpretation is preserved even while veiled magnitudes in T1-S2 are encouraged; and (2) metric selection alters T3-S3 receives a high rank from Pearson’s emphasis on linear alignment, whereas T1-S2 receives a high rank from COTSM’s emphasis on similarity geometry. These hierarchies are only scaled or reformulated by normalization (01) and 3D surfaces. The final result is a secure, understandable pipeline
 that permits signal matching templates, model selection, and pattern recognition without revealing raw data. Strict data confidentiality is necessary, however this can be used directly in any scenario where any sensitive bi-paired connection needs to be examined, such as biological indications, user item affinities, or multi-sensors fusions.