AHPtä

AHPtä is a methodological extension of the Analytic Hierarchy Process (AHP) intended for multi-criteria decision analysis in contexts where judgments are both uncertain and time-dependent. It preserves the basic AHP structure—decomposing a decision goal into criteria and alternatives and deriving priority weights through pairwise comparisons—while adding two key features: fuzzy representation of judgments and temporal weighting to reflect evolving preferences.

Methodologically, AHPtä uses triangular fuzzy numbers to express the subjective judgments in pairwise comparisons, allowing decision-makers to capture uncertainty and partial knowledge. These fuzzy judgments are aggregated to obtain fuzzy priority vectors, which are then defuzzified through a chosen method to yield crisp priority scores. A distinctive aspect is the incorporation of a time-decay or time-accumulation mechanism. Each judgment is assigned a temporal weight that can reflect recency or the reliability of information over time. The framework combines past and present judgments to produce a current priority vector, enabling the analysis to adapt as new information becomes available.

Consistency assessment in AHPtäextends the traditional consistency checks to the fuzzy domain, providing a measure of how coherent the fuzzy judgments are within the evolving matrix. Sensitivity analyses can examine how changes in the time-decay parameter and fuzziness affect the resulting rankings.

Applications of AHPtä span project selection, supplier evaluation, policy analysis, and risk assessment in dynamic environments where preferences and data quality shift over time. Advantages include better handling of uncertainty and evolving priorities; limitations involve additional parameter choices, increased computational complexity, and a greater data requirement for reliable fuzzy judgments. See also Analytic Hierarchy Process, fuzzy AHP, and dynamic decision analysis.