In this paper we introduce the notion of γ-open sets and γ-continuous functions in fuzzy bitopological spaces. We examine some basic properties and prove some characterization theorems for the said functions. It is observed that every pairwise fuzzy γ-continuous functions is pairwise fuzzy precontinuous but the converse not true.

γ-Open sets and γ-continuous mappings in fuzzy bitopological spaces

Graphical abstractDisplay Omitted HighlightsThe proposed method is applied on UCI Machine Learning Repository datasets and its corresponding performance measures are obtained.The comparison of the proposed similarity measures with the existing results reveal that the accuracy obtained by the present technique provides better similarity rating.It is also observed that fixing the threshold values for the similarity measures is difficult due to the negative rating in some existing methodology.The above difficulty can be avoided by using this newly proposed technique, in which the similarity measures lies between 0 and 1.The similarity rating obtained by the suggested technique is compared with the class distribution data set and are analyzed.The proposed method exhibits more accuracy, sensitivity, ROC curves, AUC values and enhanced F-measure than the existing methods. In this paper, a new similarity measure and a weighted similarity measure on intuitionistic fuzzy soft sets (IFSSs) are proposed and some of their basic properties are discussed. Using the proposed similarity measure, a relation (?α) between two IFSSs are defined and it is found that the defined relation is not an equivalence relation. Further, the effectiveness of the proposed similarity measure is demonstrated in a numerical example with the help of measure of performance and measure of error. Moreover, medical diagnosis problems have been exhibited through a hypothetical case study by using this proposed similarity measure. Finally, the proposed method is applied to 10 different medical data sets from UCI Machine Learning Repository datasets and its similarity measures are calculated. The corresponding performance measures, like, accuracy, sensitivity, specificity, ROC curves, AUC values, and F-measures are obtained and it is compared with the existing methods. This shows that the proposed method exhibits more accuracy, sensitivity and enhanced F-measures than the existing methods.

A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis

In this paper, we present a new construction method for interval-valued fuzzy relations (interval-valued fuzzy images) from fuzzy relations (fuzzy images) by vicinity. This construction method is based on the concepts of triangular norm (t-norm) and triangular conorm (t-conorm). We analyze the effect of using different t-norms and t -conorms. Furthermore, we examine the influence of different sizes of the submatrix around each element of a fuzzy relation on the interval-valued fuzzy relation. Finally, we apply our construction method to image processing, and we compare the results of our approach with those obtained by means of other, i.e., fuzzy and nonfuzzy, techniques.

Construction of Interval-Valued Fuzzy Relations With Application to the Generation of Fuzzy Edge Images

Nörlund and Riesz mean of sequences of fuzzy real numbers

On lacunary statistical convergence of order α

In this paper we introduce the concept of lacunary statistical and lacunary strongly convergence of generalized difference sequence of fuzzy real numbers. We prove some inclusion relations and also study some of their properties.

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Lacunary Statically Convergent and Lacunary Strongly Convergent Generalized Difference Sequences of Fuzzy Real Numbers

In this paper we introduce the natation difference operator Δrn(m ≥ 0, an integer) for studying properties of some sequence spaces. We define the sequence spaces l ∞ F (Δm), cF(Δm), cF o(Δm) and investigate their properties like solid‐ness, convergence free, symmetricity, completeness.

/pdf/new-type-of-difference-sequence-spaces-of-fuzzy-real-numbers-lxert26tj1.pdf

New type of difference sequence spaces of fuzzy real numbers

In this paper, we introduce a new type of almost statistical convergence of generalized difference sequences of fuzzy numbers. We give the relations between the strongly almost Cesaro type convergence and almost statistical convergence in these spaces. Furthermore, we study some of their properties like completeness, solidity, symmetricity etc. We also give some inclusion relations related to these classes.

https://ijsts.shirazu.ac.ir/article_2065_84a95ddc8f117eb6738a5323311fd499.pdf

Achyutanada Baruah

Papers

Lacunary Statically Convergent and Lacunary Strongly Convergent Generalized Difference Sequences of Fuzzy Real Numbers

New type of difference sequence spaces of fuzzy real numbers

On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers