Fuzzy Algebraic Structures and Decision-Making Methods
Summary
Fuzzy algebraic structures merge the graded membership concepts of fuzzy set theory with classical algebraic frameworks such as groups, rings and semirings. By allowing elements to belong to substructures to varying degrees, these models accommodate uncertainty, vagueness and multi-polar information in a rigorous mathematical setting. Central notions include fuzzy ideals, subsemirings and derivations, which capture the behaviour of algebraic operations under partial truth values. In parallel, decision-making methods built upon fuzzy algebra extend these theoretical advances into practical tools for multi-criteria and group choices. Hybrid approaches that combine fuzzy sets with soft rough sets, hesitant fuzzy sets or neutrosophic sets enable experts to express qualitative judgements, handle incomplete or contradictory data and derive preference rankings. Applications range from network reliability and supply-chain optimisation to medical diagnosis and environmental assessment, where the interplay between algebraic characterisations and computational procedures delivers both theoretical insight and solution-oriented algorithms.
Research from Nature Portfolio
Recent studies have advanced the theory of multi-polar fuzzy ideals within semiring contexts, introducing a hierarchy of m-polar fuzzy subsemirings, fuzzy ideals, generalized bi-ideals, bi-ideals and quasi-ideals. Key theorems characterise regularity and intra-regularity in semirings by properties of these fuzzy constructs, revealing new algebraic interrelations governed by multi-index membership values. Computational aspects receive particular emphasis, with constructive examples illustrating how m-polar fuzzy ideals can be employed to model complex multi-attribute information. This work refines the conceptual foundations of fuzzy algebra and demonstrates its capacity to address real-world problems where data exhibit multiple poles of uncertainty.
Fuzzy Algebraic Structures and Decision-Making Methods publication trend
The graph below shows the total number of articles in fuzzy algebraic structures and decision-making methods across all publications each year (not limited to Nature Index journals).
Technical terms
Fuzzy set: A set in which each element is assigned a membership degree between 0 and 1, representing partial inclusion rather than crisp belonging.
Semiring: An algebraic structure with two binary operations (addition and multiplication) satisfying associativity, distributivity and identity properties, generalising rings without requiring additive inverses.
m-Polar fuzzy set: A fuzzy set generalisation that permits multiple poles of membership, allowing elements to have several graded truth values reflecting multi-criteria or multi-agent information.
Ideal (in algebraic structures): A subset closed under certain operations and absorbing multiplication by elements of the parent structure, here extended to fuzzy membership contexts.
TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution): A multi-criteria decision-making method that ranks alternatives based on their distance from an ideal and an anti-ideal solution, adaptable to fuzzy and hesitant settings.
References
- An efficient approach to study multi-polar fuzzy ideals of semirings. Scientific Reports (2024).
- Fuzzy derivations of d-ideals of d-algebras and Cartesian product of Fuzzy derivation of d-ideals of d-algebras. Applied Artificial Intelligence (2022).
- A New Multi-Attribute Decision-Making Method Based on m-Polar Fuzzy Soft Rough Sets. Symmetry (2017).
- Group Decision-Making Based on m-Polar Fuzzy Linguistic TOPSIS Method. Symmetry (2019).
- m‐Polar Fuzzy Sets: An Extension of Bipolar Fuzzy Sets. The Scientific World JOURNAL (2014).
- Multi-Criteria Group Decision-Making Using an m-Polar Hesitant Fuzzy TOPSIS Approach. Symmetry (2019).
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