Complete Ranking of Intuitionistic Fuzzy Numbers

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.

Abstract

Fuzzy number was introduced by Dubois and Prade [10] to handle imprecise numerical quantities. Later it was generalized to intuitionistic fuzzy number by Burillo et al. [5]. Ranking intuitionistic fuzzy numbers plays an important role in decision making and information systems. All over the world many researchers have proposed different score functions for ranking intuitionistic fuzzy numbers but unfortunately every method produces some anti-intuitive results in certain places. A complete ranking on the entire class of fuzzy numbers have been achieved by W. Wang, Z. Wang [22] using upper dense sequence defined in $(0,1]$. But a complete ranking on the set of all intuitionistic fuzzy number remains an open problem till today. Complete ranking on the class of intuitionistic fuzzy interval number was done by Geetha et al. [13]. In this paper, total ordering on the entire class of intuitionistic fuzzy number (IFN) using upper lower dense sequence is proposed and compared with existing techniques using illustrative examples. This new total ordering on intuitionistic fuzzy numbers (IFNs) generalizes the total ordering defined in W. Wang, Z. Wang [22] for fuzzy numbers (FNs).

Keywords:

• Upper lower dense sequence
• Total order relation
• Intuitionistic fuzzy number
• Intuitionistic fuzzy interval number
• Trapezoidal intuitionistic fuzzy number
• Lexicography

Notes

Peer review under responsibility of Fuzzy Information and Engineering Branch of the Operations Research Society of China.