TLDR: This research introduces improved distance measures and a score function for Cognitive Fuzzy Sets (CFS), which are used to model complex expert assessments. The paper proposes the improved cognitive fuzzy Minkowski (CF-IM) distance and cognitive fuzzy Hausdorff (CF-H) distance, then combines them into a Cognitive Fuzzy Combined (CF-C) distance to balance information utilization and anti-perturbation ability. This new framework is applied to lung cancer pain evaluation, demonstrating its reliability and advantages in reconciling subjective patient reports with nurse assessments, especially when dealing with uncertainty or ‘confused’ judgments.
In the complex world of decision-making, especially when relying on expert opinions, understanding and quantifying subjective assessments is crucial. Researchers Lisheng Jiang, Tianyu Zhang, Shiyu Yan, and Ran Fang have introduced a novel approach using Cognitive Fuzzy Sets (CFS) to enhance the accuracy of these evaluations, with a significant application in assessing lung cancer pain. Their work, detailed in their paper, addresses a critical gap in how we measure the ‘distance’ between these fuzzy assessments.
Cognitive Fuzzy Sets are a powerful tool for experts to express their nuanced judgments, particularly when dealing with both positive and negative aspects of an alternative. For instance, an expert might rate an alternative as ‘0.5 good’ and ‘0.3 not good’. Traditional fuzzy sets struggle with such dual information, and even intuitionistic fuzzy sets have limitations when the sum of ‘good’ and ‘not good’ exceeds one, indicating a level of confusion or overlap in judgment. CFS, however, elegantly captures this ‘joint degree’ of membership and non-membership, providing a more interpretable and less information-losing model.
A key challenge in applying CFS to practical problems is accurately measuring the ‘distance’ between different cognitive fuzzy sets. Previous methods, like the Minkowski distance for CFS, overlooked a crucial element: the hesitancy degree. This oversight could lead to inaccurate comparisons, as demonstrated by examples where two different fuzzy sets appeared equidistant from a reference point, despite one being intuitively closer when hesitancy was considered.
To overcome this, the researchers proposed two new distance measures: the improved cognitive fuzzy Minkowski (CF-IM) distance and the cognitive fuzzy Hausdorff (CF-H) distance. The CF-IM distance enhances the original Minkowski distance by incorporating the hesitancy degree, thus utilizing more information. The CF-H distance, inspired by the practical Hausdorff distance, offers strong anti-perturbation ability, meaning it’s less affected by small errors or ‘noise’ in the expert’s assessment.
Recognizing that each new distance measure has its unique strengths – CF-IM for high information utilization and CF-H for robust anti-perturbation – the team developed the Cognitive Fuzzy Combined (CF-C) distance. This innovative distance measure linearly combines the CF-IM and CF-H distances, allowing for a balance between information utilization and resistance to perturbations. A ‘balance parameter’ (λ) can be adjusted to prioritize one aspect over the other, offering flexibility in different application scenarios.
Building on the CF-C distance, a combined-distance-based score function was introduced. This function allows for a clear comparison between different cognitive fuzzy numbers. By measuring how far a given CFS is from an ‘ideal best’ CFS (representing perfect positive information) and an ‘ideal worst’ CFS (representing perfect negative information), the function assigns a score between 0 and 1. A higher score indicates a better performance or a more positive assessment.
The practical utility of this new methodology was vividly demonstrated through its application in lung cancer pain evaluation. Pain assessment is inherently subjective, involving both the patient’s self-reported experience (using scales like the National Comprehensive Cancer Network’s impact list) and objective observations by healthcare professionals, such as nurses (using face pain scales). The challenge arises because patients might conceal pain due to stigma, or nurses might have varying levels of experience, leading to confused or overlapping assessments. The CFS framework, particularly the joint degree, is ideal for modeling this ‘confused level’ in a nurse’s assessment.
In a case study, the method was used to reconcile a patient’s subjective pain score with a nurse’s assessment, expressed as a CFN. By minimizing the gap between these two evaluations, the model could determine the ‘joint degree’ (j) – representing the nurse’s confused level – that best aligns the assessments. This helps identify situations where further investigation might be needed, such as when a patient is concealing pain or a nurse’s assessment is highly uncertain.
Sensitivity and comparison analyses confirmed the reliability and advantages of the proposed method. It was found that the CF-C distance-based score function provides more stable and reliable results compared to older methods that ignore hesitancy. For the specific application of lung cancer pain evaluation, the research suggests that using a parameter value of p=2 in the distance calculation is optimal for achieving the smallest gap between patient and nurse evaluations, further enhancing the method’s practical recommendations.
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This research significantly enriches the theory of Cognitive Fuzzy Sets by providing robust distance measures and a practical score function. Its application in lung cancer pain evaluation highlights its potential to improve decision-making in healthcare and other fields where complex, subjective expert assessments are common. For more details, you can refer to the full research paper here.
