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From Crisp to Fuzzy: A Comparative Review of Statistical and Fuzzy Approaches to Problem Solving |
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PP: 647-658 |
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doi:10.18576/amis/190313
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Author(s) |
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N. Yogeesh,
Suleiman Ibrahim Mohammad,
N. Raja,
R. Chetana,
P. William,
Asokan Vasudevan,
Badrea Al Qraini,
Muhammad Turki Alshurideh,
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Abstract |
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| In this research we investigate the collaborative aspects of statistical and fuzzy approaches to solve different types of problems. These methods do not involve statistical methods of hypothesis testing (which rely on strictly quantitative measures like mean, variance and regression to represent the role of randomness and variability in sample populations). Unlike crisp logic, which is binary and assumes a clear distinction between true and false, fuzzy logic allows for degrees of truth, providing a more nuanced approach to reasoning in situations where classical logic fails to capture the complexity of the problem. These hybrid statistical-fuzzy methodologies unite the analytical power of statistical methods with the descriptive capacity of fuzzy systems. In this work, a case study comparing the statistical and fuzzy methods for risk assessment in ten projects is presented. For numerical risk scores, statistical metrics such as mean, variance, and standard deviation were computed, while for qualitative risk levels, fuzzy logic employed membership functions and defuzzification to evaluate risk. These findings illustrate how fuzzy approaches augment those evaluations with additional qualitative consideration, yielding a defuzzified risk score that sits alongside causal statistics. These hybrid methods, including fuzzy regression and fuzzy statistical analysis, extend problem-solving capability, offering enriched insights and wider applications. Challenges still exist despite their benefits, including computational complexity, interpretability, and standardization. The implementation of both uncertainty handling techniques captures the nature of the world around us and especially non-linear real-life problems.
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