Rajakumar Roopkumar

Bio: Rajakumar Roopkumar is an academic researcher. The author has contributed to research in topics: Fuzzy logic & Fuzzy subalgebra. The author has an hindex of 2, co-authored 3 publications receiving 7 citations.

Continuity of fuzzy proper functions on sostak's i-fuzzy topological spaces

Abstract: The relations among various types of continuity of fuzzy proper function on a fuzzy set and at fuzzy point belonging to the fuzzy set in the context of Sostak's I-fuzzy topological spaces are discussed. The projection maps are dened as fuzzy proper functions and their properties are proved.

Convolution theorems for fractional fourier cosine and sine transforms and their extensions to boehmians

Abstract: ∞ 0 |f(t)|p dt ) 1 p < ∞, is denoted by Lp+, where p = 1, 2. After the introduction of fractional Fourier transform [11], many integral transforms have been generalized as the corresponding fractional integral transforms. In particular, fractional Fourier cosine transform (frfct), fractional Fourier sine transform (frfst) and Fractional Hartley transform were defined and used extensively in signal processing. See [2, 16]. We now recall the definitions of frfct and frfst of f ∈ L+ from [2]. (F C (f))(u) = cα √

Some weaker forms of smooth fuzzy continuous functions

Abstract: In this paper we introduce various notions of continuous fuzzy proper functions by using the existing notions of fuzzy closure and fuzzy interior operators like Rτ -closure, Rτ -interior, etc., and present all possible relations among these types of continuities. Next, we introduce the concepts of α-quasi-coincidence, qα r -pre-neighborhood, qα r -pre-closure and qα r pre-continuous function in smooth fuzzy topological spaces and investigate the equivalent conditions of qα r pre-continuity.

Some results on fuzzy proper functions and connectedness in smooth fuzzy topological spaces

Abstract: In this paper, we introduce the notion of the $(\alpha ,\beta )$-weakly smooth fuzzy continuous proper function and discuss its properties. We also study several notions of connectedness in smooth fuzzy topological spaces and establish that the product of connected sets (spaces) is not connected in any sense, as well as investigate continuous images of smooth connected sets (spaces) under $(\alpha ,\beta )$-weakly smooth fuzzy continuous functions.

Quaternionic Fractional Fourier Transform for Boehmians

Abstract: We construct a Boehmian space of quaternion-valued functions by using the quaternionic fractional convolution. By applying the convolution theorem, the quaternionic fractional Fourier transform is extended to the case of Boehmians and its properties are established.

Convolution theorems for the linear canonical sine and cosine transform and its application

Abstract: For the denoising problem of odd and even signals, a multiplicative filter design method based on the convolution theorem of the linear canonical sine and cosine transform is proposed. Two kinds of convolution theorems associated with the linear canonical sine and cosine transform based on the existing linear canonical transform domain convolution theory are derived. Using this two convolution theorems, two kinds of the multiplicative filtering models of the band-limited signal are designed by choosing an appropriate filter function in linear canonical sine and cosine transform domain. And the complexity of these schemes is analyzed. The results indicate that these filtering models are particularly suitable for handling odd and even signals, and can effectively improve computational efficiency by reducing computational complexity.