Fuzzy Entropy Measures in Decision-Making Systems
Summary
The concept of fuzzy entropy has emerged as a cornerstone in quantifying uncertainty and vagueness within decision-making systems. Originating in classical fuzzy set theory, fuzzy entropy provides a scalar measure of the spread or fuzziness of membership functions. Over the past decade, extensions to intuitionistic fuzzy sets have introduced a complementary non-membership degree and a hesitation margin, enriching the representation of incomplete knowledge. Pythagorean fuzzy sets further generalise these ideas, allowing for greater flexibility in modelling complex uncertainties by relaxing constraints on membership and non-membership norms. Neutrosophic sets expand the framework to include indeterminacy as a distinct component. Across these formalisms, entropy measures serve a dual role: they inform the assignment of criterion weights and support the ranking of alternatives in multi-attribute decision-making and group decision-making contexts. The mathematical development of entropy measures has followed both distance-based and axiomatic approaches, ensuring properties such as monotonicity, boundary conditions and additivity are satisfied. Practical applications span supplier evaluation, sustainable blockchain product assessment, project prioritisation and threat analysis in cybersecurity. By translating imprecise judgements into quantitative indices, fuzzy entropy measures enhance both the rigour and transparency of real-world decision processes, facilitating more nuanced risk assessment and resource allocation on a global scale.
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Fuzzy Entropy Measures in Decision-Making Systems publication trend
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Technical terms
Fuzzy entropy: A scalar quantification of the fuzziness or uncertainty within a fuzzy set.
Intuitionistic fuzzy set: A fuzzy set extension characterised by membership, non-membership and hesitation degrees.
Pythagorean fuzzy set: A generalisation of intuitionistic fuzzy sets permitting greater combined uncertainty under a squared-sum constraint.
Multi-attribute decision making (MADM): A methodology for ranking or selecting alternatives based on multiple evaluation criteria.
Distance-based measure: An entropy or knowledge index derived from a metric distance between fuzzy sets or between a set and its complement.
References
- An intuitionistic fuzzy entropy approach for supplier selection. Complex & Intelligent Systems (2021).
- Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making. Entropy (2021).
- A Novel Decision-Making Model with Pythagorean Fuzzy Linguistic Information Measures and Its Application to a Sustainable Blockchain Product Assessment Problem. Sustainability (2019).
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