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Many industries are developing robust models, capable of analyzing huge and complex data by using machine learning (ML) while delivering faster and more accurate results on vast scales. ML is a subfield of artificial intelligence, which is broadly defined as the capability of a machine to imitate intelligent human behavior. ML tools enable organizations to swiftly identify profitable opportunities and potential risks. Besides these uses, ML also has a wide range of applications in our daily lives. So, the development in ML is most important in this age of digital system to solve more complex problems. In order to further develop ML and diminish the uncertainties to improve accuracy, an innovative concept of complex bipolar intuitionistic fuzzy sets (CBIFSs) is introduced in this article. Further, the Cartesian product of two CBIFSs is defined. Moreover, the complex bipolar intuitionistic fuzzy relations (CBIFRs) and their types with suitable examples are defined. In addition, some important results and properties are also presented. The proposed modeling techniques are used to study different ML factors and their interrelationship, so that the functionality of ML might be enhanced. Furthermore, the advantages and benefits of proposed methods are described by their side to side comparison with preexisting frameworks in the literature.

In the theory of fuzzy fixed point, many authors have been proved different contractive type fixed point results with different types of applications. In this paper, we establish some new fuzzy cone contractive type unique coupled fixed point theorems (FP-theorems) in fuzzy cone metric spaces (FCM-spaces) by using “the triangular property of fuzzy cone metric” and present illustrative examples to support our main work. In addition, we present a Lebesgue integral type mapping application to get the existence result of a unique coupled FP in FCM-spaces to validate our work.

In this paper, we study some coincidence point and common fixed point theorems in fuzzy metric spaces by using three-self-mappings. We prove the uniqueness of some coincidence point and common fixed point results by using the weak compatibility of three-self-mappings. In support of our results, we present some illustrative examples for the validation of our work. Our results extend and improve many results given in the literature. In addition, we present an application of fuzzy differential equations to support our work.