Measurement-theoretic justification of connectives in fuzzy set theory
Fuzzy Sets and Systems, cilt.76, sa.3, ss.289-307, 1995 (Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 76 Sayı: 3
- Basım Tarihi: 1995
- Doi Numarası: 10.1016/0165-0114(95)00067-4
- Dergi Adı: Fuzzy Sets and Systems
- Derginin Tarandığı İndeksler: Scopus
- Sayfa Sayıları: ss.289-307
- Anahtar Kelimeler: Measurement theory, Membership functions, Operators, Relations
- Boğaziçi Üniversitesi Adresli: Evet
Özet
The problem of representing intersection and union in fuzzy set theory is considered. There are various proposals in the literature to model these concepts. The possibility of using continuous triangular norms and conorms (including min and max) are taken up in a measurement-theoretic setting. The conditions are laid out to arrive at cardinal scales on which addition and multiplication are meaningful and critically discussed. These conditions must either be accepted on normative grounds or must be empirically verified before the modeling process in order to see which operations are meaningful. It is emphasized that the Archimedean axiom and the existence of natural bounds are crucial in arriving at ratio and absolute scale representations. © 1995.