In the present study, we discuss the concept of internal cubic bipolar fuzzy (ICBF) sets and external cubic bipolar fuzzy (ECBF) sets. We also discuss some properties of ICBF-sets and ECBF-sets under both P-Order and R-Order. We present examples and counterexamples to support our concepts. Furthermore, we see the importance of ICBF-sets and EBCF-sets in multiple attribute decision making. We proposed two cubic bipolar fuzzy ordered weighted geometric aggregation operators, including, P-CBFOWG operator and R-CBFOWG operator to aggregate cubic bipolar fuzzy information with both perspectives, i.e., ICBF data and ECBF data. Finally, we present a multiple attribute decision making problem to examine the useability and capability of these operators and a comparison between ICBF information and ECBF information. Keywords Internal cubic bipolar fuzzy sets • External cubic bipolar fuzzy sets • Properties of ICBF-sets and ECBF-sets • P-CBFOWG and R-CBFOWG operators • Multiple attribute decision making Mathematics Subject Classification 90B50 • 03E72 Definition 2.5 (Riaz and Tehrim 2019b) Let [J ] be the cumulation of all closed subintervals of [−1, 1]. An interval-valued bipolar fuzzy set (IVBFS) is of the form K = { ς, {M P K (ς), M N K (ς)} } where M P K (ς) : V → [0, 1] and M N K (ς) : V → [−1, 0] are interval-valued positive and negative membership degrees of ς ∈ V. An interval-valued bipolar fuzzy element (IVBFE) can be written as K
Bipolar disorder is a neurological disorder that consists of two main factors, i.e. mania and depression. There are two main drawbacks in clinical diagnosis of the bipolar disorder. First, bipolar disorder is mostly wrongly diagnosed as unipolar depression in clinical diagnosis. This is, because in clinical diagnosis, the first factor is often neglected due to its approach toward positivity. Consequently, the element of bipolarity vanishes and the disease becomes worse. Second, the types of bipolar disorder are mostly misdiagnosed due to similar symptoms. To overcome these problems, the bipolar fuzzy soft set (BFS-set) and bipolar fuzzy soft mappings (BFS-mappings) are useful to tackle bipolarity and to construct a strong mathematical modeling process to diagnose this disease correctly. This technique is extensive but simple as compared to existing medical diagnosis methods. A chart (relation between different types and symptoms of bipolar disorder) is provided which contains different ranges over the interval [Formula: see text]. A process of BFS-mappings is also provided to obtain correct diagnosis and to suggest the best treatment. Lastly, a generalized BFS-mapping is introduced which is helpful to keep patient’s improvement record. The case study indicates the reliability, efficiency and capability of the achieved theoretical results. Further, it reveals that the connection of soft set with bipolar fuzzy set is fruitful to construct a connection between symptoms which minimize the complexity of the case study.
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