2009
DOI: 10.1016/j.cam.2008.09.013
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Quicksort algorithm: Application of a fixed point theorem in intuitionistic fuzzy quasi-metric spaces at a domain of words

Abstract: Dedicated to Prof. M.R. Mokhtarzadeh MSC: 47H10 54E50 Keywords: Domain of words Quicksort algorithms Intuitionistic fuzzy metric spaces Completeness Fixed point theorem a b s t r a c tIn this paper, we apply an intuitionistic fuzzy quasi-metric version of a fixed point theorem, to obtain the existence of solution for a recurrence equation associated with the analysis of Quicksort algorithms.

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Cited by 42 publications
(22 citation statements)
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“…Due to the increasing complexity of real life problems, intuitionistic fuzzy set is very suitable for representing fuzzy information under complicated and uncertain settings as an extension of traditional fuzzy set. Intuitionistic fuzzy set theory has been deeply discussed by many scholars since the notations appearance and applied in various fields, such as decision-making [2][3][4][5][6][7], supplier selection [8][9][10], pattern recognition [11][12][13][14], medical diagnosis [15,16], and artificial intelligence [17,18].…”
Section: Introductionmentioning
confidence: 99%
“…Due to the increasing complexity of real life problems, intuitionistic fuzzy set is very suitable for representing fuzzy information under complicated and uncertain settings as an extension of traditional fuzzy set. Intuitionistic fuzzy set theory has been deeply discussed by many scholars since the notations appearance and applied in various fields, such as decision-making [2][3][4][5][6][7], supplier selection [8][9][10], pattern recognition [11][12][13][14], medical diagnosis [15,16], and artificial intelligence [17,18].…”
Section: Introductionmentioning
confidence: 99%
“…Several researchers have applied fuzzy theory to the well-known results in many fields, for example, quantum physics [20], nonlinear dynamical systems [21], population dynamics [22], computer programming [23], fixed point theorem [24][25][26][27], fuzzy stability problems [28][29][30], statistical convergence [31][32][33][34], functional equation [35], approximation theory [36], nonlinear equation [37,38] and many others.…”
Section: Introductionmentioning
confidence: 99%
“…In fact the fuzzy theory has become an area of active research for the last 40 years. It has wide range applications in the field of science and engineering, e.g., population dynamics [1], chaos control [8], computer programming [9], nonlinear dynamical systems [10], fuzzy physics [13], fuzzy topology [22], etc. Recently fuzzy topology proves to be a very useful tool to deal with such situation where the use of classical theories breaks down.…”
Section: Introductionmentioning
confidence: 99%