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This chapter provides an overview of fuzzy measures and fuzzy integrals, measures of fuzziness, and their application in image
processing in the areas of region based segmentation, thresholding, and color retreieval. This chapter also introduces a fuzzy
color image retrieval method using a new type of membership function called beta membership func...
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... the present work, for calculating the precision and recall rates, the average of 20 precision/recall values have been taken. The query image is at the extreme top left of the figures in Figs. 2, 3, and 4. The color flag, color textured, and color logo images are ranked according similarity of colors present in the query image. As the query image is one of the images in the database, so the query image is the exact similar image. Other images are ranked according to the similarity in descending order. Table 1, 2, and 3 show the ...
Citations
... Other methods of generating fuzzy implications can be achieved using additive generating functions or by some initial implications [16][17][18][19][20][21][22]. Thus, fuzzy implications are useful in fuzzy relational equations and fuzzy mathematical morphology, fuzzy measures and image processing [23], data mining [24], and computing with words and fuzzy partitions. On the other hand, functions with two variables, named copulas, have attracted the interest of many researchers because they are used in many fields. ...
In this paper, we present two new classes of fuzzy negations. They are an extension of a well-known class of fuzzy negations, the Sugeno Class. We use it as a base for our work for the first two construction methods. The first method generates rational fuzzy negations, where we use a second-degree polynomial with two parameters. We investigate which of these two conditions must be satisfied to be a fuzzy negation. In the second method, we use an increasing function instead of the parameter δ of the Sugeno class. In this method, using an arbitrary increasing function with specific conditions, fuzzy negations are produced, not just rational ones. Moreover, we compare the equilibrium points of the produced fuzzy negation of the first method and the Sugeno class. We use the equilibrium point to present a novel method which produces strong fuzzy negations by using two decreasing functions which satisfy specific conditions. We also investigate the convexity of the new fuzzy negation. We give some conditions that coefficients of fuzzy negation of the first method must satisfy in order to be convex. We present some examples of the new fuzzy negations, and we use them to generate new non-symmetric fuzzy implications by using well-known production methods of non-symmetric fuzzy implications. We use convex fuzzy negations as decreasing functions to construct an Archimedean copula. Finally, we investigate the quadratic form of the copula and the conditions that the coefficients of the first method and the increasing function of the second method must satisfy in order to generate new copulas of this form.
... There are many types of capacities, one of which is the Sugeno measure [7]. The definition of the Sugeno measure is as follows. ...
The theory of Multi-Criteria Decision Making (MCDM) was introduced in the second half of the twentieth century and aids the decision maker to resolve problems when interacting criteria are involved and need to be evaluated. In this paper, we apply MCDM on the problem of the best drug for rheumatoid arthritis disease. Then, we solve the MCDM problem via-Sugeno measure and the Choquet integral to provide realistic values in the process of selecting the most appropriate drug. The approach confirms the proper interpretation of multi-criteria decision making in the drug ranking for rheumatoid arthritis.
... Analysis of the used fuzzy image processing schemes [1][2][3] shows that the used fuzzy representations of images, as well as the membership functions used to translate images into fuzzy forms, do not have a single mathematical basis. Used fuzzy signs and properties of images are built on the representation of images in the form of sets. ...
... This theory has the potential to address uncertainties associated with issues related to data extraction and their processing procedures. Therefore, the theory has been widely implemented in feature extraction and classification 45,46 . ...
A larger amount of sequence data in private and public databases produced by next-generation sequencing put new challenges due to limitation associated with the alignment-based method for sequence comparison. So, there is a high need for faster sequence analysis algorithms. In this study, we developed an alignment-free algorithm for faster sequence analysis. The novelty of our approach is the inclusion of fuzzy integral with Markov chain for sequence analysis in the alignment-free model. The method estimate the parameters of a Markov chain by considering the frequencies of occurrence of all possible nucleotide pairs from each DNA sequence. These estimated Markov chain parameters were used to calculate similarity among all pairwise combinations of DNA sequences based on a fuzzy integral algorithm. This matrix is used as an input for the neighbor program in the PHYLIP package for phylogenetic tree construction. Our method was tested on eight benchmark datasets and on in-house generated datasets (18 s rDNA sequences from 11 arbuscular mycorrhizal fungi (AMF) and 16 s rDNA sequences of 40 bacterial isolates from plant interior). The results indicate that the fuzzy integral algorithm is an efficient and feasible alignment-free method for sequence analysis on the genomic scale.
... This theory has capability to tackle uncertainties associated with issue related to the processing procedures and data extraction. Therefore, this theory has been extensively applied in pattern recognition 31 and classification. ...
Sequence comparison is an essential part of modern molecular biology research. In this study, we estimated the parameters of Markov chain by considering the frequencies of occurrence of the all possible amino acid pairs from each alignment-free protein sequence. These estimated Markov chain parameters were used to calculate similarity between two protein sequences based on a fuzzy integral algorithm. For validation, our result was compared with both alignment-based (ClustalW) and alignment-free methods on six benchmark datasets. The results indicate that our developed algorithm has a better clustering performance for protein sequence comparison.
