An Evidence-Derived Interval-Valued Fermatean Fuzzy MEREC-CRADIS Framework for Bread Wheat Cultivar Prioritisation under Water-Deficit and Saline-Soil Conditions

Abstract

This study develops an interval-valued Fermatean fuzzy (IVFF) MEREC-CRADIS framework and demonstrates it using cultivar-by-environment measurements reported in a published two-season field study. Six Egyptian bread wheat cultivars are compared using six criteria derived solely from measurements reported in the source study: spike density, 1000-kernel weight and grain yield under water-deficit and saline-soil conditions. All primary inputs were derived from the published field study; no newly elicited or author-constructed ratings entered the analysis. Published means, genotype-by-environment least significant differences and between-season yield variation are converted to admissible IVFF numbers through a deterministic uncertainty-envelope rule. A parameterised powered-endpoint Minkowski family is defined, and for every fixed α≥1, the function Dα is proved to be a bounded metric on the set of interval-valued Fermatean fuzzy numbers; its relationship to established Fermatean distances is stated explicitly. MEREC derives objective criterion weights from the positive-shifted score matrix, and CRADIS ranks the cultivars by their weighted distances from observed positive and negative references. Giza 171 ranks first, followed by Sakha 95 and Misr 3. Same-input IVFF-TOPSIS and weighted-score benchmarks reproduce the same order (Spearman ρ=1.0), the order is unchanged for α∈{1,2,3,5}, and every leave-one-out analysis preserves the relative order of the remaining cultivars. In 5,000 reproducible triangular uncertainty replications, Giza 171 ranks first in 83.1% and Sakha 95 in 16.9%, with a mean Spearman correlation of 0.953 against the baseline. These analyses assess internal concordance and uncertainty sensitivity; they do not provide independent agronomic validation. The framework should be recalibrated with local multi-environment data before making a field recommendation.