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

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 article we introduce the notion of I-Cauchy sequence and I-convergent sequence in probabilistic n-normed space. The concept of I*-Cauchy sequence and I*-convergence in probabilistic n-normed space are also introduced and some of their properties related to these notions have been established.

I -convergence in probabilistic n -normed space

To obtain the group properties of fuzzy quantities, Mares introduced an equivalence relation between fuzzy quantities. However, the Mares's method used to prove his main theorems demands to limit the investigation to fuzzy quantities with finite support. In this paper, we discuss the properties of symmetric fuzzy numbers, show an equivalent characterization of convex fuzzy sets, and present a way to construct a symmetric convex fuzzy set with a convex fuzzy set. Based on these results, we restrict ourselves to fuzzy numbers and prove Mares's results without the limitation to fuzzy numbers with finite support using the refined equivalence relation due to Hong and Do. Our results prove one of Mares's open questions in the literature.

Symmetric fuzzy numbers and additive equivalence of fuzzy numbers

In this article we have introduced the concept of lacunary bounded variation sequence of fuzzy real numbers. We have verified some properties like solid, symmetric, convergence free etc. and also proved some inclusion results.

Achyutananda Baruah

Papers

Nörlund and Riesz mean of sequences of fuzzy real numbers