Interval-valued intuitionistic quadripartitioned neutrosophic soft sets with T, F, C, and U as dependent neutrosophic components and their application in decision-making problem

Authors : Somen DEBNATH

Pages : 26-47

Doi:10.54187/jnrs.1031222

View : 17 | Download : 13

Publication Date : 2022-04-30

Article Type : Research Paper

Abstract :Molodtsov introduced a soft set insert ignore into journalissuearticles values(SS); to model uncertainty parametrically, and Chaterjee et al. proposed the notion of quadripartitioned neutrosophic set insert ignore into journalissuearticles values(QNS); by dividing indeterminacy into two independent components, namely contradiction insert ignore into journalissuearticles values(C); and unknown insert ignore into journalissuearticles values(U);. Afterwards, by combining the SS and QNS, a new concept known as quadripartitioned neutrosophic soft set insert ignore into journalissuearticles values(QNSS); is introduced. In relation to the concept of QNSS, another concept called interval-valued intuitionistic quadripartitioned neutrosophic soft set insert ignore into journalissuearticles values(in short IVIQNSS); is established to handle more complex indeterminate information parametrically with the restricted conditions. This paper aims to further generalize the existing soft models by introducing an IVIQNSS to explore another kind of imprecise knowledge. The IVIQNSS model can be viewed as a more flexible and powerful framework to encounter indeterminacy parametrically with T,F,C, and U as dependent interval quadripartitioned neutrosophic components where T,F,C,U⊆[0,1] such that sup⁡T+sup⁡F≤1, and sup⁡C+sup⁡U≤1. So, by using the IVIQNSS framework we are capable to address the indeterminate, inconsistent, and incomplete information more accurately. Different operations such as complement, AND, OR, union, intersection, etc. are defined on IVIQNSSs. Furthermore, an algorithm is constructed to solve decision-making insert ignore into journalissuearticles values(DM); problems based on IVIQNSS. Finally, an illustrative example is executed to validate the proposed study.
Keywords : Soft set, Neutrosophic soft sets, Interval valued intuitionistic neutrosophic soft sets, Quadripartitioned neutrosophic soft sets, Interval valued intuitionistic quadripartitioned neutrosophic soft sets