AHSPR - Asymmetric Hesitant Fuzzy Sigmoid Preference Relations (Zhou-Xu 2016)

Hesitant fuzzy AHP-style method. Input is a pairwise hesitant fuzzy continuous preference term matrix (HFCPT) per criterion - NOT a standard decision matrix. An asymmetric sigmoid numerical scale (ASNS) parametrised by risk-appetite parameters h1 (preference) and h2 (non-preference) maps raw preference terms to [0,1] scores. Priority vectors are derived via the closed-form Approximate Translation Method (ATM, Theorem 2.5). Final ranking aggregates per-criterion priority vectors via hesitant fuzzy weighted operators.

Zhou, W., Xu, Z.2016doi:10.1016/j.ins.2016.04.003 ↗

Overview

AHSPR is suitable when investors cannot provide a numeric evaluation matrix but can compare alternatives pairwise using natural preference language. The ASNS translates risk appetite (conservative/neutral/aggressive) into different sigmoid curves, producing different rankings from the same pairwise input. Risk-averse investors (h2 >> h1) amplify non-preference differences; risk-seekers (h1 >> h2) amplify preferences.

Data: Hesitant Fuzzy
Weights: Derived internally, no weight source needed

Edge cases and pitfalls

Fitting h1, h2 from a single data point each is exact but sensitive - slight changes in S1/S2 values can significantly change the ASNS curve.
Tables 2.3-2.7 in the example share the same numerical values (repeated as an illustration), which is unlikely in practice - each criterion should have a distinct pairwise matrix.
The ATM may produce negative priority weights when preferences are highly inconsistent - always validate w_i > 0 before reporting results.
AHSPR is investor-specific: different h1/h2 values produce different rankings from identical pairwise data, which is a feature (personalized ranking), not a bug.

How to cite

Zhou, W.; Xu, Z. (2016). Asymmetric hesitant fuzzy sigmoid preference relations in the analytic hierarchy process. Information Sciences. https://doi.org/10.1016/j.ins.2016.04.003

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System ID, as it appears in reports and the API

AHSPR

AHSPR - Asymmetric Hesitant Fuzzy Sigmoid Preference Relations (Zhou-Xu 2016)

Overview

Data

Hesitant Fuzzy

Weights

Derived internally, no weight source needed

Edge cases and pitfalls

Fitting h1, h2 from a single data point each is exact but sensitive - slight changes in S1/S2 values can significantly change the ASNS curve.

Tables 2.3-2.7 in the example share the same numerical values (repeated as an illustration), which is unlikely in practice - each criterion should have a distinct pairwise matrix.

The ATM may produce negative priority weights when preferences are highly inconsistent - always validate w_i > 0 before reporting results.

AHSPR is investor-specific: different h1/h2 values produce different rankings from identical pairwise data, which is a feature (personalized ranking), not a bug.