On Admissible Total Orders for Interval-valued Intuitionistic Fuzzy Membership Degrees

• Published in: Fuzzy information and engineering Vol. 8; no. 2; pp. 169 - 182
• Main Authors: Da Silva, I.A., Bedregal, B., Santiago, R.H.N.
• Format: Journal Article
• Language: English
• Published: Abingdon Elsevier B.V 01-06-2016; Taylor & Francis Group; Tsinghua University Press
• Subjects: Accuracy function; Admissible total orders; Decision making; Fuzzy logic; Interval-valued intuitionistic fuzzy sets; Linearity; Score function; Accuracy function; Admissible total orders; Interval-valued intuitionistic fuzzy sets; Score function
• ISSN: 1616-8658; 1616-8666
• DOI: 10.1016/j.fiae.2016.06.003

The linearity contained in the natural order of unit interval [0,1] plays an important role in many concepts and applications of fuzzy theory. Besides, it is very important in concepts like ordered weighted aggregation operators (OWA) and fuzzy decision making. However, this linearity is not inherited by most of fuzzy logics which extend the standard one. To recover the linearity for such frameworks it is required that its related partial order to be extended give rise to the notion of admissible order. In this paper, we study some admissible orders for the framework of interval-valued intuitionistic fuzzy logic.