New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple at
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ORIGINAL ARTICLE
New ranking method for normal intuitionistic sets under crisp, interval environments and its applications to multiple attribute decision making process Harish Garg1 Received: 13 December 2019 / Accepted: 28 April 2020 © The Author(s) 2020
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 intervalvalued 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. Keywords Multiple attribute decision-making · Interval-valued set · Normal distribution functions · Normal intuitionistic fuzzy set · Score function
Introduction Multiple attribute decision making (MADM) belongs to the process of getting optimal alternatives in complicated situations via synthetically assessing the values of multiple criteria of all alternatives given by a group of domain experts [1,2]. In this process, there are two crucial tasks. The first one is to call the environment where the consequences of different criteria are measured adequately, while the second task is to aggregate the related information. However, in any case, because of the lack of learning and other factors, it is greatly troublesome- if not difficult express the data. Originally, the data which accesses the alternatives is ordinarily taken as a crisp number. However, in many cases, it is difficult for a person to opt for a suitable one due to the presence of sev-
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Harish Garg [email protected] http://sites.google.com/site/harishg58iitr/ School of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab 147004, India
eral kinds of uncertainties in the data, which may occur due to a lack of knowledge or human error. To access it completely, a theory of fuzzy set (FS) [3] and its extension such as intuitionistic fuzzy set (IFS) [4], cubic intuitionistic fuzzy set [5], interval-valued IFS (IVIFS) [6], linguistic intervalvalued IFS [1], are used by the researchers. In all these existing theories, an object is assessed in te
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