International Journal of Computer Applications (0975 – 8887) Volume 177 – No. 38, February 2020 8 A Comprehensive Study of Intuitionistic Fuzzy Soft Matrices and its Applications in Selection of Laptop by using Score Function Muhammad Naveed Jafar Lahore Garrison University Lahore - 54000, Pakistan Ayisha Saeed Lahore Garrison University Lahore - 54000, Pakistan Mahnoor Waheed Lahore Garrison University Lahore - 54000, Pakistan Atiqa Shafiq Lahore Garrison University Lahore - 54000, Pakistan ABSTRACT This paper is being carried out to discuss Intuitionistic Fuzzy Soft Matrices and their operations have been described employing decisive issues by using Score Function of Intuitionistic Fuzzy soft matrices resulting in the efficiency of Intuitionistic Matrices over fuzzy matrices. Finally at the end we have presented a case study for the best selection of laptop. Keywords Intuitionistic Fuzzy Soft Matrices Score Function 1. INTRODUCTION Uncertainty is impreciseness and fuzziness in our daily lives. In real life, most of fields deals with imprecise and vague data set. Latterly, many theories have been presented to work on inconsistency, fuzziness and indefiniteness. Many theories have been established to deal with various kinds of inconsistency and fuzziness that is enclosed in a system. In this regard, the first theory which was presented is probability theory. In 1965 Zadeh introduced fuzzy soft sets and then IVF sets [2] and rough set theory [33] in later years which proved to be more accurate. In 1986, Intuitionistic Fuzzy soft sets are proposed by Atanassov. Later on Florentine presented the concept of Neutrosophic soft sets which give more precise information. Molodtsov [31] noticed that these theories have some intensive complications. Lack of configured mechanism of thesis is basically the main cause of these difficulties. Thereafter he established the concept of soft set theory dealing with various kinds of uncertainty and many other fascinating consequences of soft set theory have been attained by proposals of fuzzy sets, intuitionistic sets and etc. For instance, fuzzy soft set [26], rough soft set etc. These theories have been established and appropriate in various aspects of life for example on soft decision making [5], and the relation in intuitionistic fuzzy soft sets [13,32] etc. Many analysts put out various research papers on fuzzy and intuitionistic fuzzy soft matrices, and it is applicable in various real life disciplines [19, 21, 20, and 24]. Soft matrices and its issues in decision making was latterly presented by Cagman et al [6]. Fuzzy soft matrices [8] was also latterly presented by them. Intuitionistic fuzzy soft matrices and various products and characteristics of these products was explained by Chetia and Das. Moreover properties the concept of fuzzy soft matrices and four distinct products of intuitionistic fuzzy soft matrix and their implementation in medical field was presented by Saikia et al [35]. Further Broumi et al [4] deliberated fuzzy soft matrix and introduced some modified operations such as fuzzy soft complement matrix etc. Few years ago Mondal et al [28, 29, and 30] established intuitionistic and fuzzy soft matrices and its purpose in decision making problems established from 3 fundamental t-norm operators. In various real life disciplines [3, 32, and 34] matrices appear in many administrations. The researchers[18,19,20,36,38,41-44] observe in their study soft set and some relations with soft sets are the best tools for decision making, medical diagnosis, MCDM Problems. Basically the theory of intuitionistic fuzzy matrices and some operations on these matrices are defined and its implementation in decisive issue is our main intention. The extended portion is ordered as: Portion 2 describes fundamental description and symbolizations that are used in this paper. Portion 3 describes some redefined intuitionistic soft set, operations and comparison between fundamental definitions of intuitionistic soft set. Portion 4 contains the concept of intuitionistic fuzzy matrices and present their fundamental properties. Portion 5 describes 2 types of products defined on intuitionistic fuzzy matrices. Portion 6 explained soft decisive issues procedures established from Score Function of IS-Matrices. At the end in the last step conclusion is drawn. 2. PRELIMINARIES This portion describes some essential definitions and conclusions of Intuitionistic Set Theory, SMT [6] and SST [28] that helps in following analysis. DEFINITION. 1 Let Ʊ be a universal set and elements of this universal sets i.e. Ʊ can be represented by . An intuitionistic set in Ʊ can be regarded a truthiness function by and falseness function by Where and the real usual and unusual sets of [0, 1] and can be inscribed as follows: = The sum of and have no limit. Such that 0 ≤ Sup + Sup ≤ 2. DEFINITION. 2: [31] If a universal set is denoted as Ʊ and Ë indicates the parameters set or attributes with respect to Ʊ. Let be a set such that Ë. So that is a soft set with respect to the universal set Ʊ and can be described as a function and represented as given below: