Abstract
This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the parameter set and the opinions of all experts in one model, thus making it highly suitable for use in decision-making problems where the time factor plays a key role in determining the final decision. The complex neutrosophic soft expert set and complex neutrosophic soft expert relation are both defined. Utilizing the properties of CNSER introduced, an empirical study is conducted on the relationship between the variability of the currency exchange rate and Malaysian exports and the time frame (phase) of the interaction between these two variables. This study is supported further by an algorithm to determine the type and the degree of this relationship. A comparison between different existing relations and CNSER to show the ascendancy of our proposed CNSER is provided. Then, the notion of the inverse, complement and composition of CNSERs along with some related theorems and properties are introduced. Finally, we define the symmetry, transitivity and reflexivity of CNSERs, as well as the equivalence relation and equivalence classes on CNSESs. Some interesting properties are also obtained.
Highlights
Zadeh [1] introduced the concept of the fuzzy set to represent uncertain data, which is abounding in the real world, and it was extended by Atanassov [2] to the intuitionistic fuzzy set
We have established a novel structure for the relation between two complex neutrosophic soft expert sets, called the complex neutrosophic soft expert relation
We defined the concept of the complex neutrosophic soft expert set and the Cartesian product of two complex neutrosophic soft expert sets as a prerequisite to define the complex neutrosophic soft expert relation (CNSER)
Summary
Zadeh [1] introduced the concept of the fuzzy set to represent uncertain data, which is abounding in the real world, and it was extended by Atanassov [2] to the intuitionistic fuzzy set. The complex neutrosophic soft expert set (CNSES) is proposed to provide a more adequate parameterization tool that can represent the problem parameters in a more comprehensive and complete manner It has the added advantage of allowing the users to know the opinion of all the experts in a single model without the need for any additional cumbersome operations. The most significant shortcoming of these relations is their inability to capture information pertaining to the time frame of the interaction between the parameters, which is a very important component of most real-life situations Motivated by these studies, we introduce the complex neutrosophic soft expert relation (CNSER) for which the ranges of its membership functions are represented in terms of complex numbers, which give it the ability to represent the degree and the phase of the interaction between the elements of the CNSESs. CNSER is equipped with adequate parameterization and created with the opinions of all experts. We provide suggestions for further research in CNSERs
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