"and"- and "or"-operations for "double", "triple", etc. fuzzy sets

• Main Authors: Hung T. Nguyen, Vladik Kreinovich, Olga Kosheleva
• Format: Conference Proceeding
• Published: 2018
• Online Access: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84912529656&origin=inward; http://cmuir.cmu.ac.th/jspui/handle/6653943832/45750
• Institution: Chiang Mai University

© 2014 IEEE. In the traditional fuzzy logic, the expert's degree of confidence d(A & B) in a complex statement A & B (or A V B) is uniquely determined by his/her degrees of confidence d(A) and d(B) in the statements A and B, as f & (d(A), d(B)) for an appropriate 'and'-operation (t-norm). In practice, for the same degrees d(A) and d(B), we may have different degrees d(A & B) depending on the relation between A and B. The best way to take this relation into account is to explicitly elicit the corresponding degrees d(A & B) and d(A V B), i.e., to come up with a 'double' fuzzy set. If we only elicit information about pairs of statements, then we still need to estimate, e.g., the degree d(A & B & C) based on the known values d(A), d(B), d(C), d(A & B), d(A & C), and d(B & C). In this paper, we explain how to produce such 'and'-operations for 'double' fuzzy sets - and how to produce similar 'or'-operations.