# Conceptual Application of List Theory to Data Structures

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### "Conceptual Application of List Theo..." refers background in this paper

...(i) Insertion at the beginning: B-INSERT(15, A) = cons (15, A) = [15, 1, 5, 3, 1, 6, 8, 9] (ii) Insertion at the end: E-INSERT(15, A) = A ╫ [15] = [1, 5, 3, 1, 6, 8, 9] ╫ [15] = [1, 5, 3, 1, 6, 8, 9, 15] (iii) Insertion at any position: Suppose i = 4, and x = 15....

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...INSERT(15, 4, A) = take(4 - 1, A) ╫ [15] ╫ drop(4 -1, A) = take(3, A) ╫ [15] ╫ drop(3, A) = [1, 5, 3] ╫ [15] ╫ [1, 6, 8, 9] = [1, 5, 3, 15, 1, 6, 8, 9] (iv) To find the next and previous element at the position i = 4: NEXT( 4, A) = hd(take(5, A) – take (4, A))...

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...1: Consider the array of numbers A, given by A = [1, 5, 3, 1, 6, 8, 9]....

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...The concept of intuitionistic fuzzy sets introduced by Atanassov ([1]) is an extension of the notion of fuzzy sets and is a better model than fuzzy sets to model impreciseness in data....

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884 citations

### "Conceptual Application of List Theo..." refers background in this paper

...The new definition has much rigor than the earlier one used in computer science in general and functional programming ([2]) in particular....

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### "Conceptual Application of List Theo..." refers background or methods in this paper

...The concepts of fuzzy sets and fuzzy bags were introduced and studied by Zadeh [11] and Yager [10] respectively....

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...Similarly, the notion of a bag and its count function ([10]) are interchangeable concepts....

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...The concepts of fuzzy sets and fuzzy bags were introduced and studied by Zadeh [11] and Yager [10] respectively....

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### "Conceptual Application of List Theo..." refers background in this paper

...INSERT(15, 4, A) = take(4 - 1, A) ╫ [15] ╫ drop(4 -1, A) = take(3, A) ╫ [15] ╫ drop(3, A) = [1, 5, 3] ╫ [15] ╫ [1, 6, 8, 9] = [1, 5, 3, 15, 1, 6, 8, 9] (iv) To find the next and previous element at the position i = 4: NEXT( 4, A) = hd(take(5, A) – take (4, A))...

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...This could be realized by Tripathy, Ghosh and Jena ([3]), where they introduced the notion of position function for lists....

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...1: Consider the array of numbers A, given by A = [1, 5, 3, 1, 6, 8, 9]....

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...= hd([1, 5, 3, 1, 6] – [1, 5, 3, 1]) = hd([6]) = 6 PREVIOUS(4, A) = hd(take(3, A) – take (2, A)) = hd([1, 5, 3] – [1, 5]) = hd([3]) = 3...

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...: Advances in Computing and Information Technology, AISC 177, pp.551-560. springerlink.com © Springer-Verlag Berlin Heidelberg 2012 (bag) through its count function, Tripathy, Ghosh and Jena introduced the concept of position function to define lists....

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