Fuzzy numbers and intuitionistic fuzzy numbers are introduced in the literature to model problems involving incomplete and imprecise numerical quantities. Researchers from all over the world have been working in ranking of intuitionistic fuzzy numbers since 1985, but till date there is no common methodology that rank any two arbitrary intuitionistic fuzzy numbers. In order to improve the familiar ranking methods, a new non-hesitance score function for the theory of interval-valued intuitionistic fuzzy sets is introduced and the necessity for defining a new non-hesitance score function is explained using illustrative examples. In this paper, a new multi-criteria decision-making algorithm is established for decision problems involving interval-valued intuitionistic fuzzy numbers. Further the practicality of the proposed method is shown by solving an interval-valued intuitionistic fuzzy MCDM problem. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approach.Keywords Intuitionistic fuzzy number · Interval-valued intuitionistic fuzzy number · Non-hesitance score · MCDM · IFMCDM
Modelling real life (industrial) problems using intuitionistic fuzzy numbers is inevitable in the present scenario due to their efficiency in solving problems and their accuracy in the results. Particularly, trapezoidal intuitionistic fuzzy numbers (TrIFNs) are widely used in describing impreciseness and incompleteness of a data. Any intuitionistic fuzzy decision-making problem requires the ranking procedure for intuitionistic fuzzy numbers. Ranking trapezoidal intuitionistic fuzzy numbers play an important role in problems involving incomplete and uncertain information. The available intuitionistic fuzzy decision-making methods cannot perform well in all types of problems, due to the partial ordering on the set of intuitionistic fuzzy numbers. In this paper, a new total ordering on the class of TrIFNs using eight different score functions, namely, imprecise score, nonvague score, incomplete score, accuracy score, spread score, nonaccuracy score, left area score, and right area score, is achieved and our proposed method is validated using illustrative examples. Significance of our proposed method with familiar existing methods is discussed.
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