Spherical Fuzzy AHP Weighting with a Rank-Reversal-Free MARCOS Ranking for Occupational Risk Assessment in Underground Mining

Spherical fuzzy sets are the extension of ordinary fuzzy sets in which membership, non-membership, and hesitancy all vary freely. This independence matters for expert-driven risk assessment: it lets a judgement carry support, opposition, and hesitancy as three quantities that vary independently, which intuitionistic and Pythagorean representations cannot do because their hesitancy is a residual of the other two degrees. This paper uses spherical fuzzy AHP to weight risk criteria and shows that the recovered hesitancy varies systematically across criteria: across an illustrative assessment of ten underground mining operations, hesitancy is largest on likelihood and smallest on severity. That ordering is reproduced by the corresponding residual-hesitancy calculation, and it is therefore reported as a description of the pooled linguistic profile rather than as evidence of a representational advantage: under the scale adopted here, a single linguistic term fixes all three coordinates at once, so the hesitancy is scale-assigned rather than separately elicited. The weighted criteria are combined with the MARCOS method. Building on the recently established equivalence of MARCOS and the weighted-sum method, the single channel through which the alternative set can affect a ranking is identified and closed, yielding a fixed-anchor modification of MARCOS that is provably invariant to the addition or deletion of alternatives. The channel is localized exactly: a MARCOS ranking depends on the alternative set through the ideal row alone, and can reverse only when the alternative withdrawn is the sole holder of a column maximum. In a deletion experiment over 360 pairwise comparisons, the modified specification produces no reversals, against counts ranging from one to fifteen for the seven benchmark methods, with five for classical MARCOS. Spherical fuzzy weighting and a rank-reversal-resistant aggregation thus address the representation and the stability of expert risk judgements, respectively.