Bipolar Fuzzy Knowledge-Based Accuracy Measure With Applications in Medical Diagnosis, Pattern Detection and Cluster Analysis

Abstract The fuzzy set theory has several types of extensions. Bipolar fuzzy sets are fuzzy set extensions that have been developed by several researchers and applied in various settings. The satisfaction levels of a property and its counter-property define the membership degrees in bipolar fuzzy sets. These sets are useful in expert systems and decision-making, because they provide a refined representation of uncertainty by enabling both positive and negative membership degrees to exist simultaneously. This paper deals with calculating the knowledge passed by a bipolar fuzzy set; a knowledge-measure in the bipolar fuzzy framework is proposed here. Its validity is examined together with its mathematical characteristics and its performance is assessed with different examples. In addition, novel dissimilarity, similarity and accuracy measures are derived from the proposed measure in the bipolar fuzzy framework. The basic properties of the derived measures are outlined and their validity is evaluated. The proposed accuracy measure based on a new approach is discussed for solving cluster analysis issues. Furthermore, a case study about air pollution in different regions of the world in the year 2022 is examined. The proposed approach uses the information gathered from this investigation to generate clusters. In addition, medical diagnosis and pattern detection issues are addressed using the proposed measures in the bipolar fuzzy framework.