A Dynamic Circular Intuitionistic Fuzzy Soft Set Framework for Temporal Multi-Criteria Decision Making

Abstract

The circular intuitionistic fuzzy set (C-IFS) replaces each membership–non-membership points with a circle of radius r, encoding second-order uncertainty about the assessment itself. When assessments span several time periods, two forms of imprecision coexist: instability at a fixed instant and volatility across time. Existing circular intuitionistic fuzzy soft models capture the parameterised structure but not time; dynamic intuitionistic fuzzy models capture time but not the circular representation. We introduce the dynamic circular intuitionistic fuzzy soft set (DCIFSS), a time-indexed family of circular granules coupling both aspects through a temporally induced radius derived from the dispersion of the per-period centres. The weighted standard deviation is the primary radius rule, and we prove the sharp bound r^wsd ≤ D/√2 ≤ 1, where D is the diameter of the snapshot cloud. We define the DCIFWA and DCIFWG operators with a composite criterion-level radius, establish closure and algebraic properties, and characterise a risk-attitude score shown to be the Hurwicz optimism criterion adapted to circular intuitionistic fuzzy values. Since the score is affine in the risk attitude θ, ranking reversals follow in closed form. A trend-adjusted variant (TA-DCIFSS) separates deterministic trend from erraticism. On a synthetic benchmark, predictive validation against a held-out period shows the volatility-aware score improves rank prediction for noise-dominated series, while the trend-adjusted variant is best for trending series.