On λ¯-Statistically Convergent Double Sequences of Fuzzy Numbers

We study the notion of λ¯-statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations

On I_2​​ -convergence and I_2​​ -convergence of double sequences in fuzzy normed spaces

In this paper first, we investigate some properties of I2-convergence in fuzzy normed spaces. After, we study some relationships between I_2-convergence and I*_2-convergence of double sequences in fuzzy normed spaces

I_2-Cauchy double sequences of fuzzy numbers

In this paper, we introduce the concepts of I2-Cauchy, I∗2-Cauchy double sequence of fuzzy numbers and study their some properties and relations, where I2 denotes the ideal of subsets of N × N

On I_2-Cauchy double sequences in fuzzy normed spaces

In this paper, we investigate relationship between I_2-convergence and I_2-Cauchy double sequences in fuzzy normed spaces. After, we introduce the concepts of I*_2-Cauchy double sequences and study relationships between I_2-Cauchy and I*_2-Cauchy double sequences in fuzzy normed spaces

Spatial Metric Space for Pattern Recognition Problems

The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is generalized based on a novel divided difference operator. The proposed operator is used over a two-dimensional sequence of bounded variation, and it generalizes metric space with the introduction of a multivalued metric space called spatial metric space. The environment considered for the study is a two-dimensional Atanassov intuitionistic fuzzy set (AIFS) under the assumption that membership and non-membership components are its independent variables. The weighted distance measure is proposed as a spatial distance measure in the spatial metric space. The spatial distance measure consists of three branches. In the first branch, there is a domination of membership values, non-membership values dominate the second branch, and the third branch is equidominant. The domination of membership and non-membership values are not in the form of weights in the proposed spatial distance measure, and hence it is a measure independent of weights. The proposed spatial metric space is mathematically studied, and as an implication, the spatial similarity measure is multivalued in nature. The spatial similarity measure can recognize a maximum of three patterns simultaneously. The spatial similarity measure is tested for the pattern recognition problems and the obtained classification results are compared with some other existing similarity measures to show its potency. This study connects the double sequence to the application domain via a divided difference operator for the first time while proposing a novel divided difference operator-based spatial metric space.Comment: 2