Relations on neutrosophic soft set and their application in decision making

Neutrosophic soft sets are a mathematical model put forward to overcome uncertainty with the contribution of a parameterization tool and neutrosophic logic by considering of information a falsity membership function, an indeterminacy membership function and a truth membership function. This set theory which is a very successful mathematical model, especially as it handles information in three different aspects, was first introduced to the literature by Maji (Ann Fuzzy Math Inf 5(1):157-168, 2013) and later modified by Deli and Broumi (J Intell Fuzzy Syst 28(5):2233-2241, 2015). In this way, they aimed to use neutrosophic soft sets more effectively for uncertainty problems encountered in most real life problems. Relations are a method preferred by researchers to explain the correspondences between objects. In this paper, neutrosophic soft relationships are discuss and define by referring to the theory of neutrosophic soft set proposed by Deli and Broumi (Ann Fuzzy Math Inf 9:169-182, 2015). Then, we present the concepts of composition, inverse of neutrosophic soft relations and functions along with some related properties and theorems. Moreover, the equivalence classes and equivalence relations of soft relations are given with support from real life examples and some of their properties are analyzed. Finally, we propose an algorithm to be used in expressing the correspondence between objects in solving uncertainty problems by using the soft relationship defined and an example is given to show how this algorithm can be applied for uncertainty problems.