Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-192203 IOS Press 1 Detection and severity of tumor cells by graded decision-making methods under fuzzy N -soft model 1 2 3 Arooj Adeel a , Muhammad Akrama a , Naveed Yaqoob b and Wathek Chammam c,∗ 4 a Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan 5 b Department of Mathematics and Statistics, Riphah International University, I-14, Islamabad, Pakistan 6 c Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia 7 Abstract. The notion of fuzzy N-soft sets is a hybrid model, which is a more generalized framework than fuzzy soft sets. To investigate the objects of a reference set in medical field, which have uncertainties in data, can be correctly captured by proposed structures of novel decision-making methods, graded TOPSIS and graded ELECTRE-I methods, based on fuzzy N- soft sets (henceforth, (F, N)-soft sets). Both the proposed methods compute the decision-maker estimations in a more flexile and affluent way, as well as improve the reliability of the decisions, that depends on star ratings or grades for the purpose of the modelization of decision-making problems in medical field. We show the importance and feasibility of proposed methods by applying them on real life example in medical field having ambiguities, that can be accurately occupied by this framework. Finally, we discuss the comparison analysis of both the proposed decision-making methods. 8 9 10 11 12 13 14 15 Keywords: N-soft sets, (F, N)-soft sets, graded TOPSIS, graded ELECTRE-I, decision-making 16 1. Introduction 17 A number of problems existing in medical and 18 engineering fields involve ordered grades, vague- 19 ness and uncertainty. To deal with such type of 20 uncertainties, Fatimah et al. [15] introduced the N- 21 soft sets to enlarge the range of applications of the 22 theory that can be used to deal with the character- 23 istics, namely, soft set theory. They advanced their 24 concept to characterize the importance of ordered 25 grades in literally occurring problems. N-soft sets 26 capture the concept of a parameterized classifi- 27 cation of the objects of reference set that builds 28 upon the fixed number of ordered grades. However 29 instead of their crisp multinary description, Akram 30 ∗ Corresponding author. Wathek Chammamc, Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia. E-mail: w.chammam@mu.edu.sa. et al. [5] considered the possibility that parameterized 31 the characterization of the universe under fuzzy envi- 32 ronment. They combined the concept of fuzzy sets 33 with N-soft sets to introduce a novel hybrid model 34 known as (F, N)-soft sets. To combine the assump- 35 tions and assessments of numerous professionals into 36 an isolated input under fuzzy environment, Akram 37 et al. [6] proposed novel hybrid model, known as 38 hesitant N-soft sets (henceforth, HNSSs) with the 39 applications in decision-making and group decision- 40 making. They presented such a model to tackle the 41 ambiguities in knowledge concerning, which distinct 42 grades are assigned to objects, in the parameter- 43 izations by attributes under hesitant environment, 44 because they provide more flexibility for the direction 45 of the representation of decision-making problems. 46 In actual-world organizations and structures, usu- 47 ally we obverse actions and assignments in which 48 ISSN 1064-1246/20/$35.00 © 2020 – IOS Press and the authors. All rights reserved