Abstract
The intuitionistic fuzzy sets (IFSs) introduced by Atanassov are widely applied in all areas such as data analysis, artificial intelligence, decision support systems in modelling problems with incomplete and imprecise information due to their better accuracy. More precisely, trapezoidal intuitionis tic fuzzy numbers (TraIFNs) are able to model incomplete and imprecise information based on qualitative in nature. Many researchers have proposed different ranking methods on TraIFNs, but none of them has covered the entire class of TraIFNs and also almost all the methods have disadvantage that they ranked two different IFNs as the same at some point of time. In this paper, a complete ranking on the class of TraIFNs using axiomatic set of total ordering on some special subclasses of TraIFN based on different score functions and an algorithm for making decisions from information system with incomplete trapezoidal information using proposed ordering, have been studied and also the significance of our proposed method over existing methods is shown by comparing the proposed method with existing methods.
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