Similarity relations, fuzzy partitions, and fuzzy orderings
Fuzzy Sets and Systems - Special memorial volume on foundations of fuzzy reasoning
On the redundancy of fuzzy partitions
Fuzzy Sets and Systems - Special issue on methods for data analysis in classificatin and control
Fuzzy Sets and Systems
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
Fuzzy Models and Algorithms for Pattern Recognition and Image Processing
Foundations of Fuzzy Systems
A note on approximate equality versus the Poincaré paradox
Fuzzy Sets and Systems - Theme: Basic notions
On many-valued partitions and many-valued equivalence relations
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
A survey of fuzzy clustering algorithms for pattern recognition. I
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
A survey of fuzzy clustering algorithms for pattern recognition. II
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Differently implicational universal triple I method of (1, 2, 2) type
Computers & Mathematics with Applications
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This paper analyzes constraints in terms of fuzzy-logical concepts for transforming families of fuzzy sets in order to guarantee linguistically interpretable solutions of fine-tuned or optimized fuzzy systems, and further, to make the whole process of fine tuning a well-posed problem. For this purpose, transformations for fuzzy sets are introduced which are constructed by means of the compositional rule of inference. It is investigated under which conditions on these transformations various characteristics of fuzzy partitions and fuzzy sets, like redundancy, convexity and topological aspects remain invariant. It is argued that further restrictions like the compactness of the set of admissible transformations are required in order to make the process of fine tuning well-posed. As main result it is demonstrated that compactness of this function space endowed with the uniform norm can be characterized in terms of purely fuzzy-logical concepts, that is, by means of fuzzy equivalence relations.