Pethalakshmi, in Applied Soft Computing, 2009 Rough set theory is reliant upon a crisp dataset that is important information may be lost as a result of quantization. To avoid this information loss, Jensen and Shen reviewed semantics-preserving dimensionality reduction technique that preserved the ...
Atanassov et al. [50] considered another function called the non-membership function, which assures the non-belongingness of an element in the set, called intuitionistic fuzzy set in 1989. Application of IFS is Das et al. [51],
The algorithm is similar to crisp clustering, such as k-means clustering, in several aspects but incorporates fuzzy set concepts of partial memberships by allowing data points to belong to more than one cluster. This can be observed in the form of overlapping clusters. Additionally many crisp ...
From the overview of the discussion mentioned above, fuzzy logic has been put to its strength in this paper to design a robust data hiding scheme to model the vague nature asso- ciated with the features of an image. 3 Preliminaries The universal set can be described so that all elements ...
Renewable energy integration introduces grid instability due to variable and intermittent sources like solar and wind, impacting reliability. This paper provides a thorough discussion of recent advancements and emerging trends in grid-integrated wind ene
Given a fuzzy set defined on X and any number ␣ in [0, 1] the ␣-cut of A, denoted by A␣, is a crisp set that consists of all numbers of X whose member- ship grades in A are greater than or equal to ␣. This can be formally written as follows: A␣ ϭ ͕x...
a theory which relates to classes of objects without crisp, clearly defined boundaries. In such cases, membership in a set is a matter of degree. In this perspective, fuzzy logic in its narrow sense is a branch of FL. Even in its more narrow definition, fuzzy logic differs both in concep...
type-2 fuzzy set; intuitionistic type-2 fuzzy set; possibility and necessity operators; distance measure 1. Introduction Uncertainty is an intrinsic feature of information. In many scientific and industrial applications, we make decisions in an environment with different kinds of uncertainty. Currently,...
Step 5: Inference in a fuzzy model and final ranking: It can be easily observed that A j = a 1 j , a 2 j , … , a n j , j = 1 , 2 , … , m is a set of crisp number with respect to criteria C 1 , C 2 , … , C n which fulfills the following conditions: a 1...
Fuzzy set theory, introduced by Zadeh [1], expands upon classical set theory’s characteristic function with a membership function taking values in the closed interval [0,1]. Atanassov [2] later extended this concept to intuitionistic fuzzy sets (IFSs), which incorporate both membership and non...