New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple attribute decision making process

Abstract

Abstract The aim of this paper is to present novel algorithms for solving the multiple attribute decision-making problems under the normal intuitionistic fuzzy set environment. Normal intuitionistic and interval-valued intuitionistic sets are the essential mechanisms for influencing the decision-making queries with anonymous and indeterminant data by engaging a degree of membership and non-membership of normal distribution data in quantitative terms. Holding these features in mind and united the idea of hesitation degree, this paper presents some improved score functions to rank the normal intuitionistic and interval-valued intuitionistic sets. The advantage of these proposed functions is to overwhelm the weakness of the existing functions and will aid to rank the given objects in a more consistent way. The numerous salient features of the proposed functions are studied. Later, we develop two new algorithms for interval-valued as well as crisp numbers based on the proposed functions to solve multiple attribute decision-making problems. The given approaches have been confirmed with numerical examples and the advantages, as well as comparative analysis, are furnished to shows its influence over existing approaches.

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