In this paper, a new method of ranking trapezoidal intuitionistic fuzzy numbers has been introduced based on the concept of value and ambiguity at different levels of decision‐making. The concept of decision levels α for the membership function and β for the non‐membership function called as the flexibility parameters have been introduced in ranking these types of fuzzy numbers. If the flexibility parameters α is close to maximum membership degree of the membership function and β close to minimum membership degree of non‐membership function, then a high‐level decision is made. Likewise, if the flexibility parameters α is close to minimum membership degree of membership function and β close to maximum membership degree of non‐membership function, then a low‐level decision is made. Again, if the flexibility parameters α and β lie between minimum membership degree of the membership function and maximum membership degree of the non‐membership function, then an intermediate decision is made. This phenomenon of the proposed method is an attractive feature as it allows the decision‐maker to make a choice on the levels of decision. Further, the rationality validation of the proposed method has been checked by proving some of the Wang and Kerre's reasonable properties on ordering fuzzy quantities.

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Decision-making under uncertainty is consistently an essential fear and the most challenging circle of exploration. To manage the uncertainty, the intuitionistic fuzzy set (IFS) assumes a critical part in taking care of the conditions wherein decision-makers furnish an alternative with a grade of membership and a nonmembership. Distance measures of IFSs are apparatuses used in different decision-making problems, such as medical investigation, pattern recognition, multicriteria decision-making, clustering problems, and other realworld problems. As such, various distance measures were developed by different researchers and applied to decision-making problems with situation-based deficiencies. Motivated by this, in this paper, a symmetric distance formula is being proposed for effectively determining the distance between the information held by IFSs. The distance formula involves membership degree, nonmembership degree, the difference of the minimum of the cross-evaluation factor, and the difference of the maximum of the cross-evaluation factor. Furthermore, it is being proved that the proposed distance formula follows all the axiomatic definitions of a distance measure.Numerical examples depict the efficiency of the proposed distance measure. Hence, this measure is being applied to practical problems of decision-making, pattern recognition, and clustering problems. This measure