Analysis and application of Aczel-Alsina aggregation operators based on bipolar complex fuzzy information in multiple attribute decision making

Abstract

Bipolar complex fuzzy information is a new idea that can easily depict awkward and vague information in real life problems. The main theory of the bipolar complex fuzzy set is the fusion of two different theories, called bipolar fuzzy set and complex fuzzy set. The bipolar complex fuzzy set contained two different grades, called positive membership grade which is considered a positive aspect of the problem, and negative membership grade which is considered a negative aspect of the problem, both contain in a unit square of complex plane. The major analysis of this theory is to diagnose the interrelationship among any number of attributes. For this, we defined various Aczel-Alsina operational laws and proved their influential results. Further, by using the Aczel-Alsina operational laws and bipolar complex fuzzy information, we diagnosed the theory of bipolar complex fuzzy Aczel-Alsina weighted averaging (BCFAAWA), bipolar complex fuzzy Aczel-Alsina ordered weighted averaging (BCFAAOWA), and bipolar complex fuzzy Aczel-Alsina hybrid averaging (BCFAAHA) operators. To modify the influence of the explored work, we discussed various important results and some properties (Idempotency, Monotonicity, and Boundedness) of the proposed work. Additionally, we computed a multi-attribute decision-making rule under the presence of the initiated approaches and tried to justify it with the help of some examples. Finally, to evaluate the influence and dominancy of the diagnosed work, we compared our deliberated work with various prevailing approaches and also described their geometrical representations.