This article introduces the notion of bipolar complex fuzzy soft set as a generalization of bipolar complex fuzzy set and soft set. Furthermore, this article contains elementary operations for bipolar complex fuzzy soft sets such as complement, union, intersection, extended intersection, and related properties. The OR and AND operations for bipolar complex fuzzy soft set are also initiated in this study. Moreover, this study contains the decision-making algorithm and real-life examples to display the success and usability of bipolar complex fuzzy soft sets. Finally, the comparative study of initiated notions with some prevailing ideas are also interpreted in this study.

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach.

On the basis of Hamacher operations, in this manuscript, we interpret bipolar complex fuzzy Hamacher weighted average (BCFHWA) operator, bipolar complex fuzzy Hamacher ordered weighted average (BCFHOWA) operator, bipolar complex fuzzy Hamacher hybrid average (BCFHHA) operator, bipolar complex fuzzy Hamacher weighted geometric (BCFHWG) operator, bipolar complex fuzzy Hamacher ordered weighted geometric (BCFHOWG) operator, and bipolar complex fuzzy Hamacher hybrid geometric (BCFHHG) operator. We present the features and particular cases of the above-mentioned operators. Subsequently, we use these operators for methods that can resolve bipolar complex fuzzy multiple attribute decision making (MADM) issues. We provide a numerical example to authenticate the interpreted methods. In the end, we compare our approach with existing methods in order to show its effectiveness and practicality.

A medical diagnosis is one the most efficient processes of determining a disease based on a person’s symptoms and signs. In recent days, due to the complexities of the same type of diseases, it is very difficult to diagnose a disease by using old methods and techniques. In this way, new and efficient medical diagnosis methods can help a lot in reaching an accurate conclusion, depending upon the timing and sequences of symptoms and medical history. The physician relies on other clues like medical tests and imaging tests. So, in this way, a list of possible diagnoses can be determined, which are referred to as different diagnoses. To handle these types of issues in this manuscript, additional information is identified, and possible disease is confirmed. Under the consideration of classical data, it is a very difficult task to deal with complex and asymmetric sorts of data. Fuzzy set theory has a wide range of applications, from engineering to the medical field. Different methods and techniques have been proposed to support the decision-making process in medical fields. Picture fuzzy soft sets are more generalized structures and efficient tools to formalize the information more decently and accurately. So, devoted from this notion, in this article based on picture fuzzy soft settings, we firstly have established some basic operational laws for picture fuzzy soft number; then based on these operational laws, we have developed some aggregation operators named as picture fuzzy soft prioritized average and geometric aggregation operators. In real-world problems, these operators can be useful in analyzing uncomfortable and asymmetric information. Furthermore, some basic properties of the introduced operators have been initiated and discussed briefly. Moreover, to show the effective use of this developed approach to medical diagnoses, we have proposed an algorithm, along with a descriptive example. Additionally, a comparative analysis of the proposed work shows the superiority and effectiveness of the introduced approach.