Fuzzy sets, uncertainty, and information
Fuzzy sets, uncertainty, and information
A survey of thresholding techniques
Computer Vision, Graphics, and Image Processing
On strict preference relations
Fuzzy Sets and Systems - Special issue: Aggregation and best choices of imprecise opinions
Entropy, distance measure and similarity measure of fuzzy sets and their relations
Fuzzy Sets and Systems
A comparative assessment of measures of similarity of fuzzy values
Fuzzy Sets and Systems
An analysis of histogram-based thresholding algorithms
CVGIP: Graphical Models and Image Processing
A comparative study of similarity measures
Fuzzy Sets and Systems
Discrete distance operator on rectangular grids
Pattern Recognition Letters
Towards general measures of comparison of objects
Fuzzy Sets and Systems - Special issue dedicated to the memory of Professor Arnold Kaufmann
Subsethood measure: new definitions
Fuzzy Sets and Systems
Some notes on similarity measure and proximity measure
Fuzzy Sets and Systems
On global requirements for implication operators in fuzzy modus ponens
Fuzzy Sets and Systems - Special issue on fuzzy modeling and dynamics
Fuzzy Algorithms: With Applications to Image Processing and Pattern Recognition
Fuzzy Algorithms: With Applications to Image Processing and Pattern Recognition
Automorphisms, negations and implication operators
Fuzzy Sets and Systems - Implication operators
An association-based dissimilarity measure for categorical data
Pattern Recognition Letters
Sub-dominant theory in numerical taxonomy
Discrete Applied Mathematics - Special issue: Discrete mathematics & data mining II (DM & DM II)
Description-meet compatible multiway dissimilarities
Discrete Applied Mathematics
Semiautoduality in a restricted family of aggregation operators
Fuzzy Sets and Systems
Image thresholding using type II fuzzy sets
Pattern Recognition
Finite cut-based approximation of fuzzy sets and its evolutionary optimization
Fuzzy Sets and Systems
Extension of fuzzy logic operators defined on bounded lattices via retractions
Computers & Mathematics with Applications
Cosine similarity measures for intuitionistic fuzzy sets and their applications
Mathematical and Computer Modelling: An International Journal
Image segmentation using Atanassov's intuitionistic fuzzy sets
Expert Systems with Applications: An International Journal
Uncertainties with Atanassov's intuitionistic fuzzy sets: Fuzziness and lack of knowledge
Information Sciences: an International Journal
Rough set approach to incomplete numerical data
Information Sciences: an International Journal
Consensus measures constructed from aggregation functions and fuzzy implications
Knowledge-Based Systems
Information Sciences: an International Journal
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In this paper, we present the definition of restricted dissimilarity function. This definition arises from the concepts of dissimilarity and equivalence function. We analyze the relation there is between restricted dissimilarity functions, restricted equivalence functions (see [Bustince, H., Barrenechea, E., Pagola, M., 2006. Restricted equivalence functions. Fuzzy Sets Syst. 157, 2333-2346]) and normal E"N-functions. We present characterization theorems from implication operators and automorphisms. Next, by aggregating restricted dissimilarity functions in a special way, we construct distance measures of Liu, proximity measures of Fan et al. and fuzzy entropies. We also study diverse interrelations between the above-mentioned concepts. These interrelations enable us to prove that under certain conditions, the threshold of an image calculated with the algorithm of Huang and Wang [Huang, L.K., Wang, M.J., 1995. Image thresholding by minimizing the measure of fuzziness. Pattern Recognit. 28 (1), 41-51], with the methods of Forero [Forero, M.G., 2003. Fuzzy thresholding and histogram analysis. In: Nachtegael, M., Van der Weken, D., Van de Ville, D., Kerre, E.E. (Eds.), Fuzzy Filters for Image Processing. Springer, pp. 129-152] or with the algorithms developed in [Bustince, H., Barrenechea, E., Pagola, M., 2007. Image thresholding using restricted equivalence functions and maximizing the measures of similarity. Fuzzy Sets Syst. 158, 496-516] is always the same, that is, it remains invariant.