Total Ordering on Generalized ‘n’ Gonal Linear Fuzzy Numbers

Abstract

Abstract Zadeh introduced fuzzy sets to study imprecision in real life after which many generalizations have been developed in literature. Fuzzy numbers is the major research area of study because of its needfulness for modeling qualitative and imprecise continuous transitions. Most of the time, data involved in multi-criteria decision making (MCDM) will be in the form of fuzzy numbers due to qualitative and continuous deforming criteria. Different methods of defining total ordering on the class of fuzzy numbers have important role in MCDM to find the preference order of alternatives. Many total ordering techniques for various types of piecewise linear fuzzy numbers such as triangular (3-sided), trapezoidal (4-sided), pentagonal (5-sided), hexagonal (6-sided) and so on are available in the literature. In this paper, a generalized ‘n’gonal linear fuzzy number (n-sided) as a generalization of triangular (3-sided), trapezoidal (4-sided), pentagonal (5-sided), hexagonal (6-sided) and so on is defined and a method of defining total ordering on the class of generalized ‘n’gonal linear fuzzy numbers (n-sided) which generalizes total ordering methods defined for triangular (3-sided), trapezoidal (4-sided), pentagonal (5-sided), hexagonal (6-sided) and so on in the literature has been proposed and analyzed. Further, a similarity measure on ‘n’ gonal linear fuzzy numbers using the proposed midpoint score function is also defined and the applicability of the proposed operations, total ordering method and similarity measure on ‘n’ gonal linear fuzzy numbers in MCDM is shown by comparing with some other methods in the literature.

Keywords

• Generalized ‘n’ gonal linear fuzzy number
• Total ordering
• Ranking of fuzzy numbers
• Ranking method