Improved Correlation Coefficients of Quadripartitioned Single-Valued Neutrosophic Sets and Interval-Quadripartitioned Neutrosophic Sets

1. Introduction

Fuzzy sets were introduced by Zadeh (1965) which allows the membership function valued in the interval [0,1] and also it is an extension of classical set theory. Fuzzy set helps to deal the concept of uncertainty, vagueness and imprecision which is not possible in the cantorian set. As an extension of Zadeh’s fuzzy set theory intuitionstic fuzzy set(IFS) was introduced by Atanassov (1986) which consists of degree of membership and degree of non membership and lies in the interval of [0,1]. IFS theory widely used in the areas of logic programming, decision making problems, medical diagnosis etc.

Smarandache (1995) introduced the concept of Neutrosophic set which provides the knowledge of neutral thought by introducing the new factor called indeterminacy in the set. Therefore neutrosophic set was framed and it includes the components of truth membership function(T), indeterminacy membership function(I), and falsity membership function(F) respectively. Neutrosophic sets deals with non standard interval of ]^‑0,1⁺[. Since neutrosophic set deals the indeterminacy effectively it plays an vital role in many applications areas include information technology, decision support system, relational database systems, medical diagnosis, multicriteria decision making problems etc.,

To process the incomplete information or imperfect knowledge to vagueness a new mathematical approach i.e., Rough set was introduced by Pawlak (1991) and it is in terms of a pair of sets include the lower and upper approximations of the original set. A new hybrid model of neutrosophic rough set was introduced by Broumi(2014) by combining the concept of neutrosophic set with rough set. To deal the real world problems, Wang (2010) introduced the concept of single valued neutrosophic sets(SVNS) which is also known as an extension of initutionstic fuzzy sets and it became a very new hot research topic now. Chatterjee.,et al(2016) proposed the concept of Quadripartitioned single valued neutrosophic sets (QSVNS) which is based on Belnap’s four valued logic and Smarandache’s four numerical valued logic. In (QSVNS) indeterminacy is splitted into two functions known as ‘Contradicition’ (both true and false) and ‘Unknown’ (neither true nor false) so that QSVNS has four components T,C,U,F which also lies in the non standard unit interval ]^‑0,1⁺[. Further, K Mohana and M Mohanasundari (2018) defined a new hybrid model of Quadripartitioned Single Valued Neutrosophic Rough Sets.

Neutrosophic set has a tremendous applications in various field and many researchers focused in solving real world problems by applying suitable method like similarity measure, correlation coefficient to some important notions of neutrosophic logic, neutrosophic measure, neutrosophic integral, single valued neutrosophic set(SVNS), Quadripartitioned Single Valued Neutrosophic set(QSVNS) etc., In our day-to-day life making correct decision is a challenging task when it involves complex issues like uncertainity, complexity, High risk consequences, alternatives etc., For that multi criteria decision making helps in solving the real world problems including information systems, software engineering, Decision analysis, Economics, Personnel selection, Medical diagnosis, IoT based enterprises for making decisions correctly by analyzing the problem with suitable method. Many methods are available in solving a multi -criteria decision making problems particularly TOPSIS is one of the effective method because of its very good computational efficiency and simplicity.