Uncorrected Author Proof Journal of Intelligent & Fuzzy Systems xx (20xx) x–xx DOI:10.3233/JIFS-18818 IOS Press 1 Uncertain multiplicative linguistic soft sets and their application to group decision making 1 2 3 Srinivasan Vijayabalaji a,∗ and Adhimoolam Ramesh b 4 a Department of Mathematics, University College of Engineering, Panruti(A Constituent College of Anna Uni- versity, Chennai), Panruti-607106, Tamilnadu, India. 5 6 b Department of Mathematics, C. Abdul Hakeem College of Engineering and Technology, Melvisharm - 632509, Tamil Nadu, India. 7 8 Abstract. Interval valued linguistics preference relation is one of the model of simple uncertain linguistic preference structures (additive or multiplicative). It can be easily and conveniently used to express the experts evaluations over the considered alternatives in group decision making under uncertainty. The primary purpose of this paper is to define uncertain multiplicative linguistic soft set (UMLSS) and study some of its properties. Some basic algebraic operations such as the ’AND’ and ’OR’ operations are also introduced in UMLSS. Using multiplicative linguistic sets deviation operation [21] into ULMSS, we derive uncertain multiplicative virtual linguistic soft set (UMVLSS). Based on the UMVLSS, we introduce the generalized linguistic deviation operator. An approach based on virtual linguistic soft set deviation to rank the alternatives in the group decision making problem is also provided. Finally a numerical example is provided to justify the new approach and illustrate the validity of our approach to the selection of feasible candidate(s) in a software company problem. 9 10 11 12 13 14 15 16 17 Keywords: Soft set, uncertain multiplicative linguistic soft set , multiplicative virtual linguistic soft set, uncertain multiplica- tive virtual linguistic deviation. 18 19 1. Introduction 20 Most of the scientific data in the study of engi- 21 neering, economic, medical and social problems are 22 uncertain in nature rather than exact or crisp as in 23 the case with real world problems.Different Math- 24 ematical tools such as probability theory, theory of 25 evidence, vague set theory, fuzzy set theory and 26 its varients, rough set theory etc. are some of the 27 uncertainty theories used in the analysis of uncer- 28 tain data. Each of the theories mentioned above has 29 its own drawbacks and positive aspects. A common 30 deficiency of all these theories is their inadequacy 31 ∗ 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: svb@ucep.edu.in. in parameterization. To overcome this deficiency 32 Molodtsov(1999) [1] introduced the concept of soft 33 set theory, which is another mathematical tool to 34 study uncertainty using the parameterized family of 35 subsets of the universal set to represent uncertainty. 36 In recent years soft set theory has received more 37 attention in decision making problems. Some basic 38 operations on soft set was defined by Maji et al. [2, 3] 39 who also used soft sets in decision- making problems. 40 Many others [4–6, 8] studied the algebraic opera- 41 tions on soft sets. Roy et al. [3] gave an application 42 of soft set in group decision making problem for an 43 imprecise multi-observer data. 44 There are numerious real world problems and sit- 45 uations which cannot be adequately represented by 46 numerical data. Such problems can be better repre- 47 sented by linguistic descriptors. In otherwords, these 48 problem can be well assesed and analyzed with the 49 1064-1246/18/$35.00 © 2018 – IOS Press and the authors. All rights reserved