Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-200594 IOS Press 1 Sigmoid valued fuzzy soft set and its application to haze management 1 2 Srinivasan Vijayabalaji a,∗ , Parthasarathy Balaji b and Adhimoolam Ramesh c 3 a Department of Mathematics, University College of Engineering, Panruti (A Constituent College of Anna University, Chennai), Panruti-607106, Tamilnadu, India 4 5 b Department of Mathematics, MEASI Academy of Architecture, Chennai, Tamilnadu, India 6 c Department of Mathematics, C. Abdul Hakeem College of Engineering and Technology, Melvisharam, Tamilnadu, India 7 8 Abstract. The impetus of this paper is to broaden the structure of linguistic soft set (LSS) to a new domain namely sigmoid valued fuzzy soft set (SVFSS ). Some operating laws on SVFSS are also provided. Using the complement concept on SVFSS we define maximum rejection. This maximum rejection paves a way for defining a new similarity measure on SVFSS termed as maximum likely ratio (MLR). A new MCGDM algorithm for SVFSS is proposed using MLR. An illustrative example of haze equipment problem on sigmoid valued fuzzy soft set setting is also given. A comparative analysis of our approach with the existing approaches are also presented to justify our work. 9 10 11 12 13 14 Keywords: Sigmoid valued fuzzy soft set, maximum rejection, maximum likely ratio, generalized maximum likely ratio, weighted maximum likely ratio 15 16 1. Introduction 17 Multi-expert phenomenon is utilized in group 18 decision making process. Owing to ambiguity and 19 uncertainty, certain decision making processes are 20 difficult to handle. In the real world, the experts’ con- 21 fusion, limitations and even vague information causes 22 decision makers to struggle in giving exact figures 23 in order to express their views. Responding to the 24 linguistic setting decision problems can be achieved 25 using word computing (CW) [37]. The 2-tuple lin- 26 guistic fuzzy representation model (2-Tuple LFRM) 27 [32] is a special type of linguistic model used for 28 CW that provides a computation routine that con- 29 tains linguistic information which includes no loss of 30 ∗ Corresponding author. Srinivasan Vijayabalaji, Department of Mathematics, University College of Engineering, Panruti (A Con- stituent College of Anna University, Chennai), Panruti-607106, Tamilnadu, India. E-mail: balaji1977harshini@gmail.com. knowledge. Xu [34] extended the linguistic term set 31 (LTS) to uncertain LTS and provided specifications. 32 Numerical scale is the second key factor in deci- 33 sion making problems. Saaty’s 1-9 scale and [0, 34 1] scale are the two types of scales broadly used 35 in decision making situations. The 2-tuple linguis- 36 tic representation model (2-tuple LRM) is one such 37 type, the linguistic hierarchy-based model and the 38 numerical scale model [4] was built to pact with lin- 39 guistic decision-making problems. Dong et al. [5] 40 interrelated the 2-tuple linguistic model with hes- 41 istant unbalanced linguistic information. In dealing 42 with fuzzy preference relations, Zhou & Xu [40] 43 developed a new numerical scale for consistency 44 namely asymmetric sigmoid numerical scale (ASNS) 45 in hesistant fuzzy setting. This ASNS meets asym- 46 metry, through requirements of utility, volatility and 47 consistency. Ma & Xu [20] created the hyperbolic 48 scales based on intuitionistic multiplicative relation- 49 ships of choice and its implementation. Soft sets (SS), 50 ISSN 1064-1246/20/$35.00 © 2020 – IOS Press and the authors. All rights reserved