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T-norm
Schweizer-Sklar T-norm - Power-based parametric t-norm family
Parametric t-norm family - Schweizer-Sklar (power generator)
Schweizer, B., Sklar, A.1960doi:10.2140/pjm.1960.10.313 ↗
Overview
p=1 (Łukasiewicz) is most commonly used in recent q-ROFS MCDM papers. p<0 → more permissive (closer to min). p>1 → more restrictive. Report for p=-1,0,1 to show sensitivity.
- Output
- membership value, higher is better
- Data
- Intuitionistic Fuzzy, unit interval values
- Size
- 2+ alternatives
- Used for
- Q-ROFS MCDM, IFN MCDM, PFN MCDM
Fits when / Look elsewhere when
Fits when
- •Spans full range from min to drastic product
- •Well-studied mathematically
- •Includes Łukasiewicz as p=1 special case
Look elsewhere when
- •Crisp MCDM
Assumptions to verify
- IFN/q-ROFS membership constraint satisfied after aggregation
Limitations
- •p>0 can give zero output when x^p+y^p < 1
- •Less intuitive than Hamacher's rational form
Edge cases and pitfalls
Using p=0 directly - apply the product limit T=xy.
Confusing parameter p with the q-rung q in q-ROFS - they are different parameters.
Applying T_p for p>0 to small x,y where x^p+y^p-1 < 0 - result is 0 (clipped by max(0,...)).
Bu manifestin B.extensions bloğunda Wang ve ark. (2019) kaynağı (DOI 10.3233/JIFS-18607) GERİ ÇEKİLMİŞTİR (RETRACTED); kaynak olarak KULLANMAYIN.
Works with
How to cite
Schweizer, B.; Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics. https://doi.org/10.2140/pjm.1960.10.313
System ID, as it appears in reports and the API
TNORM-SCHWEIZER-SKLAR