r-(i, j)-fuzzy regular semi open sets in smooth bitopological spaces
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In this paper, we introduce and study the concept of $r$-$(i, j)$-fuzzy regular semi open (closed) sets in smooth bitopological spaces. By using $r$-$(i, j)$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-$(i, j)$-fuzzy regular semi interior (closure) operator. Also, we introduce FP-regular semi continuous and FP-regular semi irresolute mappings. Moreover, we investigate the relationship among FP-regular semi continuous and FP-regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.
Abstract
In this paper, we introduce and study the concept of $r$-$(i, j)$-fuzzy regular semi open (closed) sets in smooth bitopological spaces. By using $r$-$(i, j)$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-$(i, j)$-fuzzy regular semi interior (closure) operator. Also, we introduce FP-regular semi continuous and FP-regular semi irresolute mappings. Moreover, we investigate the relationship among FP-regular semi continuous and FP-regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.
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