On quasi-metric aggregation functions and fixed point theorems

The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was exten...

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Vydané v:	Fuzzy sets and systems Ročník 228; s. 88 - 104
Hlavní autori:	Martín, J., Mayor, G., Valero, O.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Elsevier B.V 01.10.2013
Predmet:	Agglomeration Aggregation function Asymmetry Asymptotic complexity analysis Complexity Computation Denotational semantics Fixed points (mathematics) Homogeneous function Mathematical analysis Mathematical models Metric Projective [formula omitted]-contraction Projective contraction Quasi-metric Recursive Theorems Projective contraction Denotational semantics Homogeneous function Metric Asymptotic complexity analysis Quasi-metric Aggregation function Projective Φ-contraction
ISSN:	0165-0114, 1872-6801
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Abstract	The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci.180 (2010) 803–812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective Φ-contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification.
AbstractList	The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. BorsASHk and J. DoboA! [On a product of metric spaces, Math. Slovaca31 (1981) 193a205]. Motivated by the utility of quasi-metrics in Computer Science, the BorsASHk and DoboA! study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci.180 (2010) 803a812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective IBBIBB-contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification. The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric spaces, Math. Slovaca31 (1981) 193–205]. Motivated by the utility of quasi-metrics in Computer Science, the Borsík and Doboš study was extended to the quasi-metric context in such a way that a general description of how to combine through a function a family of quasi-metrics in order to obtain a single one as output was provided by G. Mayor and O. Valero [Aggregation of asymmetric distances in Computer Science, Inform. Sci.180 (2010) 803–812]. In this paper, inspired by the fact that fixed point theory provides an efficient tool in many fields of applied sciences, we have proved fixed point theorems for a new type of contractions, that we have called projective Φ-contractions, defined between quasi-metric spaces that have been obtained via the so-called quasi-metric aggregation functions. Moreover, we show that the new fixed point results are useful to discuss, on the one hand, the complexity of a collection of recursive programs whose running times of computing hold a coupled system of recurrence equations and, on the other hand, to analyze simultaneously the complexity and the correctness of recursive algorithms that perform a computation by means of a recursive denotational specification.
Author	Mayor, G. Martín, J. Valero, O.
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References	H.P.A. Künzi, Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology, Kluwer Academic Publishers, vol. 3, 2001, pp. 853–968. J. Llull-Chavarría, O. Valero, An Application of Generalized Complexity Spaces to Denotational Semantics via the Domain of Words, Lecture Notes in Computer Science, vol. 5457, 2009, pp. 530–541. Mesiar, Pap (bib27) 2008; 178 Tirado, Valero (bib41) 2009; 49 de Bakker (bib2) 1996; 806 Romaguera, Tirado (bib37) 2011; 376 Matthews (bib22) 1994; 728 Schellekens (bib42) 1995; 1 Mayor, Valero (bib26) 2010; 180 Bolton, Gader, Wilson (bib4) 2008; 16 Boxer, Miler (bib28) 2005 Matthews (bib23) 1995; 151 Pradera, Trillas (bib30) 2002; 31 Romaguera, Schellekens, Valero (bib36) 2011; 88 Seda (bib40) 1999; 24 Fora (bib12) 1982; 99 Martín, Mayor, Valero (bib24) 2011; 54 M.D. Atkinson, The complexity of algorithms, in: Computing Tomorrow: Future Research Directions in Computer Science, Cambridge University Press, New York, 1996, pp. 1–20. de Bakker, de Vink (bib3) 1998; 85 Doboš (bib10) 1995; 13 García-Raffi, Romaguera, Schellekens (bib14) 2008; 348 J. Martín, G. Mayor, O. Valero, A fixed point theorem for asymmetric distances via aggregation functions, in: Proceedings of the 6th International Summer School on Aggregation Operators, 2011, pp. 217–222. Borsík, Doboš (bib6) 1981; 31 Grabisch, Marichal, Mesiar, Pap (bib16) 2009 A. Pradera, E. Trillas, E. Castiñeira, On distances aggregation, in: Proceedings of the Information Processing and Management of Uncertainty in Knowledge-based Systems International Conference, 2000, pp. 693–700. Brassard, Bratley (bib5) 1988 A. Pradera, E. Trillas, E. Castiñeira, On the aggregation of some classes of fuzzy relations, in: Technologies for Constructing Intelligent Systems, Springer-Verlag, 2002, pp. 125–147. C.A. Gunter, D.S. Scott, Semantic domains, in: Handbook of Theoretical Computer Science, North Holland, vol. B, 1990, pp. 633–674. Herburt, Moszyńska (bib17) 1995; 62 Romaguera, Schellekens (bib35) 1999; 98 Recasens (bib33) 2010 Espínola, Kirk (bib11) 2001; 5 Romaguera, Sapena, Tirado (bib34) 2007; 154 Jaggi, Dass (bib19) 1974; 7 Saminger, Mesiar, Bodenhofer (bib38) 2002; 10 Casasnovas, Valero (bib8) 2008; 15 García-Raffi, Romaguera, Sánchez-Pérez (bib13) 2003; 74 Castro-Company, Romaguera, Tirado (bib9) 2012; 399 Romaguera, Tirado, Valero (bib29) 2012; 89 Yager (bib43) 2010; 18 Seda (bib39) 1997; 29 Casasnovas, Rosselló (bib7) 2005; 152 Hitzler, Seda (bib18) 2010; 53 Fora (10.1016/j.fss.2012.08.009_bib12) 1982; 99 Tirado (10.1016/j.fss.2012.08.009_bib41) 2009; 49 10.1016/j.fss.2012.08.009_bib20 Castro-Company (10.1016/j.fss.2012.08.009_bib9) 2012; 399 10.1016/j.fss.2012.08.009_bib21 Doboš (10.1016/j.fss.2012.08.009_bib10) 1995; 13 Martín (10.1016/j.fss.2012.08.009_bib24) 2011; 54 Boxer (10.1016/j.fss.2012.08.009_bib28) 2005 Romaguera (10.1016/j.fss.2012.08.009_bib29) 2012; 89 Romaguera (10.1016/j.fss.2012.08.009_bib35) 1999; 98 Romaguera (10.1016/j.fss.2012.08.009_bib34) 2007; 154 Yager (10.1016/j.fss.2012.08.009_bib43) 2010; 18 Brassard (10.1016/j.fss.2012.08.009_bib5) 1988 García-Raffi (10.1016/j.fss.2012.08.009_bib13) 2003; 74 Hitzler (10.1016/j.fss.2012.08.009_bib18) 2010; 53 Matthews (10.1016/j.fss.2012.08.009_bib22) 1994; 728 Casasnovas (10.1016/j.fss.2012.08.009_bib7) 2005; 152 10.1016/j.fss.2012.08.009_bib25 García-Raffi (10.1016/j.fss.2012.08.009_bib14) 2008; 348 Recasens (10.1016/j.fss.2012.08.009_bib33) 2010 Mesiar (10.1016/j.fss.2012.08.009_bib27) 2008; 178 Mayor (10.1016/j.fss.2012.08.009_bib26) 2010; 180 Seda (10.1016/j.fss.2012.08.009_bib39) 1997; 29 Matthews (10.1016/j.fss.2012.08.009_bib23) 1995; 151 Jaggi (10.1016/j.fss.2012.08.009_bib19) 1974; 7 Espínola (10.1016/j.fss.2012.08.009_bib11) 2001; 5 10.1016/j.fss.2012.08.009_bib31 de Bakker (10.1016/j.fss.2012.08.009_bib2) 1996; 806 Bolton (10.1016/j.fss.2012.08.009_bib4) 2008; 16 10.1016/j.fss.2012.08.009_bib32 10.1016/j.fss.2012.08.009_bib1 Borsík (10.1016/j.fss.2012.08.009_bib6) 1981; 31 Romaguera (10.1016/j.fss.2012.08.009_bib37) 2011; 376 10.1016/j.fss.2012.08.009_bib15 Schellekens (10.1016/j.fss.2012.08.009_bib42) 1995; 1 Saminger (10.1016/j.fss.2012.08.009_bib38) 2002; 10 Casasnovas (10.1016/j.fss.2012.08.009_bib8) 2008; 15 de Bakker (10.1016/j.fss.2012.08.009_bib3) 1998; 85 Seda (10.1016/j.fss.2012.08.009_bib40) 1999; 24 Herburt (10.1016/j.fss.2012.08.009_bib17) 1995; 62 Romaguera (10.1016/j.fss.2012.08.009_bib36) 2011; 88 Grabisch (10.1016/j.fss.2012.08.009_bib16) 2009 Pradera (10.1016/j.fss.2012.08.009_bib30) 2002; 31
References_xml	– volume: 7 start-page: 592 year: 1974 end-page: 595 ident: bib19 article-title: On fixed point theorems for product of metric spaces publication-title: Indian J. Pure Appl. Math. – reference: J. Martín, G. Mayor, O. Valero, A fixed point theorem for asymmetric distances via aggregation functions, in: Proceedings of the 6th International Summer School on Aggregation Operators, 2011, pp. 217–222. – volume: 154 start-page: 2196 year: 2007 end-page: 2203 ident: bib34 article-title: The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words publication-title: Topology Appl. – volume: 53 start-page: 443 year: 2010 end-page: 464 ident: bib18 article-title: Generalized distance functions in the theory of computation publication-title: Comput. J. – volume: 99 start-page: 327 year: 1982 end-page: 335 ident: bib12 article-title: A fixed point theorem for product spaces publication-title: Pacific J. Math. – reference: H.P.A. Künzi, Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology, Kluwer Academic Publishers, vol. 3, 2001, pp. 853–968. – reference: J. Llull-Chavarría, O. Valero, An Application of Generalized Complexity Spaces to Denotational Semantics via the Domain of Words, Lecture Notes in Computer Science, vol. 5457, 2009, pp. 530–541. – volume: 89 start-page: 1728 year: 2012 end-page: 1741 ident: bib29 article-title: New results on mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces publication-title: Int. J. Comput. Math. – volume: 98 start-page: 311 year: 1999 end-page: 322 ident: bib35 article-title: Quasi-metric properties of complexity spaces publication-title: Topology Appl. – reference: M.D. Atkinson, The complexity of algorithms, in: Computing Tomorrow: Future Research Directions in Computer Science, Cambridge University Press, New York, 1996, pp. 1–20. – volume: 29 start-page: 97 year: 1997 end-page: 117 ident: bib39 article-title: Quasi-metrics and the semantics of logic programs publication-title: Fundam. Inf. – volume: 24 start-page: 223 year: 1999 end-page: 250 ident: bib40 article-title: Some issues concerning fixed points in computational logic publication-title: Topology Proc. – year: 2010 ident: bib33 article-title: Indistinguishability Operators – volume: 806 start-page: 11 year: 1996 end-page: 27 ident: bib2 article-title: A metric approach to control flow semantics publication-title: Ann. N. Y. Acad. Sci. – volume: 31 start-page: 193 year: 1981 end-page: 205 ident: bib6 article-title: On a product of metric spaces publication-title: Math. Slovaca – volume: 62 start-page: 121 year: 1995 end-page: 133 ident: bib17 article-title: On metric products publication-title: Colloq. Math. – volume: 151 start-page: 195 year: 1995 end-page: 205 ident: bib23 article-title: An extensional treatment of lazy data flow deadlok publication-title: Theoret. Comput. Sci. – volume: 49 start-page: 1852 year: 2009 end-page: 1868 ident: bib41 article-title: The average running time of an algorithm as a midpoint between fuzzy sets publication-title: Math. Comput. Model. – volume: 13 start-page: 129 year: 1995 end-page: 133 ident: bib10 article-title: A survey of metric preserving functions publication-title: Q & A Gen. Topology – volume: 348 start-page: 346 year: 2008 end-page: 355 ident: bib14 article-title: Applications of the complexity space to the general probabilistic divide and conquer algorithms publication-title: J. Math. Anal. Appl. – volume: 10 start-page: 11 year: 2002 end-page: 35 ident: bib38 article-title: Domination of aggregation operators and preservation of transitivity publication-title: Int. J. Uncertain. Fuzz. – year: 1988 ident: bib5 article-title: Algorithms – reference: C.A. Gunter, D.S. Scott, Semantic domains, in: Handbook of Theoretical Computer Science, North Holland, vol. B, 1990, pp. 633–674. – volume: 178 start-page: 3557 year: 2008 end-page: 3564 ident: bib27 article-title: Aggregation of infinite sequences publication-title: Inf. Sci. – volume: 152 start-page: 139 year: 2005 end-page: 158 ident: bib7 article-title: Averaging fuzzy biopolymers publication-title: Fuzzy Set. Syst. – volume: 376 start-page: 732 year: 2011 end-page: 740 ident: bib37 article-title: The complexity probabilistic quasi-metric space publication-title: J. Math. Anal. Appl – volume: 1 start-page: 211 year: 1995 end-page: 232 ident: bib42 article-title: The Smyth completion publication-title: Electron. Notes Theor. Comput. Sci. – volume: 85 start-page: 35 year: 1998 end-page: 52 ident: bib3 article-title: Denotational models for programming languages publication-title: Topology Appl. – year: 2005 ident: bib28 article-title: Algorithms Sequential and Parallel – year: 2009 ident: bib16 article-title: Aggregation Functions – volume: 728 start-page: 183 year: 1994 end-page: 197 ident: bib22 article-title: Partial metric topology publication-title: Ann. N. Y. Acad. Sci. – volume: 54 start-page: 815 year: 2011 end-page: 827 ident: bib24 article-title: On aggregation of normed structures publication-title: Math. Comput. Model. – volume: 18 start-page: 57 year: 2010 end-page: 65 ident: bib43 article-title: Norms induced from OWA operators publication-title: IEEE Trans. Fuzzy Syst. – volume: 180 start-page: 803 year: 2010 end-page: 812 ident: bib26 article-title: Aggregation of asymmetric distances in computer science publication-title: Inf. Sci. – volume: 88 start-page: 1819 year: 2011 end-page: 1829 ident: bib36 article-title: The complexity space of partial functions publication-title: Int. J. Comput. Math. – volume: 399 start-page: 253 year: 2012 end-page: 268 ident: bib9 article-title: The Banach Contraction Principle on Fuzzy Quasi-Metric Spaces and on Product Complexity Spaces publication-title: Lecture Notes in Computer Science – volume: 31 start-page: 41 year: 2002 end-page: 51 ident: bib30 article-title: A note on pseudometrics aggregation publication-title: Int. J. Gen. Syst. – reference: A. Pradera, E. Trillas, E. Castiñeira, On distances aggregation, in: Proceedings of the Information Processing and Management of Uncertainty in Knowledge-based Systems International Conference, 2000, pp. 693–700. – volume: 5 start-page: 405 year: 2001 end-page: 416 ident: bib11 article-title: Fixed points and approximate fixed points in product spaces publication-title: Taiwan J. Math. – volume: 16 start-page: 1107 year: 2008 end-page: 1110 ident: bib4 article-title: Discrete Choquet integral as a distance metric publication-title: IEEE Trans. Fuzzy Syst. – volume: 15 start-page: 251 year: 2008 end-page: 261 ident: bib8 article-title: A connection between computer science and fuzzy theory:midpoints and running time of computing publication-title: Mathware Soft Comput. – reference: A. Pradera, E. Trillas, E. Castiñeira, On the aggregation of some classes of fuzzy relations, in: Technologies for Constructing Intelligent Systems, Springer-Verlag, 2002, pp. 125–147. – volume: 74 start-page: 39 year: 2003 end-page: 50 ident: bib13 article-title: The supremum asymmetric norm on sequence algebras publication-title: Electron. Notes Theor. Comput. Sci. – volume: 89 start-page: 1728 year: 2012 ident: 10.1016/j.fss.2012.08.009_bib29 article-title: New results on mathematical foundations of asymptotic complexity analysis of algorithms via complexity spaces publication-title: Int. J. Comput. Math. doi: 10.1080/00207160.2012.659246 – ident: 10.1016/j.fss.2012.08.009_bib31 doi: 10.1007/978-3-7908-1796-6_10 – volume: 806 start-page: 11 year: 1996 ident: 10.1016/j.fss.2012.08.009_bib2 article-title: A metric approach to control flow semantics publication-title: Ann. N. Y. Acad. Sci. doi: 10.1111/j.1749-6632.1996.tb49156.x – volume: 348 start-page: 346 year: 2008 ident: 10.1016/j.fss.2012.08.009_bib14 article-title: Applications of the complexity space to the general probabilistic divide and conquer algorithms publication-title: J. Math. Anal. Appl. doi: 10.1016/j.jmaa.2008.07.026 – ident: 10.1016/j.fss.2012.08.009_bib25 – volume: 10 start-page: 11 year: 2002 ident: 10.1016/j.fss.2012.08.009_bib38 article-title: Domination of aggregation operators and preservation of transitivity publication-title: Int. J. Uncertain. Fuzz. doi: 10.1142/S0218488502001806 – volume: 74 start-page: 39 year: 2003 ident: 10.1016/j.fss.2012.08.009_bib13 article-title: The supremum asymmetric norm on sequence algebras publication-title: Electron. Notes Theor. Comput. Sci. doi: 10.1016/S1571-0661(04)80764-3 – volume: 728 start-page: 183 year: 1994 ident: 10.1016/j.fss.2012.08.009_bib22 article-title: Partial metric topology publication-title: Ann. N. Y. Acad. Sci. doi: 10.1111/j.1749-6632.1994.tb44144.x – volume: 54 start-page: 815 year: 2011 ident: 10.1016/j.fss.2012.08.009_bib24 article-title: On aggregation of normed structures publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2011.03.030 – volume: 7 start-page: 592 year: 1974 ident: 10.1016/j.fss.2012.08.009_bib19 article-title: On fixed point theorems for product of metric spaces publication-title: Indian J. Pure Appl. Math. – volume: 53 start-page: 443 year: 2010 ident: 10.1016/j.fss.2012.08.009_bib18 article-title: Generalized distance functions in the theory of computation publication-title: Comput. J. doi: 10.1093/comjnl/bxm108 – volume: 13 start-page: 129 year: 1995 ident: 10.1016/j.fss.2012.08.009_bib10 article-title: A survey of metric preserving functions publication-title: Q & A Gen. Topology – volume: 49 start-page: 1852 year: 2009 ident: 10.1016/j.fss.2012.08.009_bib41 article-title: The average running time of an algorithm as a midpoint between fuzzy sets publication-title: Math. Comput. Model. doi: 10.1016/j.mcm.2008.08.003 – volume: 178 start-page: 3557 year: 2008 ident: 10.1016/j.fss.2012.08.009_bib27 article-title: Aggregation of infinite sequences publication-title: Inf. Sci. doi: 10.1016/j.ins.2008.05.020 – year: 1988 ident: 10.1016/j.fss.2012.08.009_bib5 – volume: 376 start-page: 732 year: 2011 ident: 10.1016/j.fss.2012.08.009_bib37 article-title: The complexity probabilistic quasi-metric space publication-title: J. Math. Anal. Appl doi: 10.1016/j.jmaa.2010.11.056 – ident: 10.1016/j.fss.2012.08.009_bib15 doi: 10.1016/B978-0-444-88074-1.50017-2 – volume: 1 start-page: 211 year: 1995 ident: 10.1016/j.fss.2012.08.009_bib42 article-title: The Smyth completion publication-title: Electron. Notes Theor. Comput. Sci. doi: 10.1016/S1571-0661(04)00029-5 – volume: 31 start-page: 193 year: 1981 ident: 10.1016/j.fss.2012.08.009_bib6 article-title: On a product of metric spaces publication-title: Math. Slovaca – volume: 85 start-page: 35 year: 1998 ident: 10.1016/j.fss.2012.08.009_bib3 article-title: Denotational models for programming languages publication-title: Topology Appl. doi: 10.1016/S0166-8641(97)00140-5 – ident: 10.1016/j.fss.2012.08.009_bib1 doi: 10.1017/CBO9780511605611.002 – volume: 154 start-page: 2196 year: 2007 ident: 10.1016/j.fss.2012.08.009_bib34 article-title: The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words publication-title: Topology Appl. doi: 10.1016/j.topol.2006.09.018 – ident: 10.1016/j.fss.2012.08.009_bib32 – volume: 24 start-page: 223 year: 1999 ident: 10.1016/j.fss.2012.08.009_bib40 article-title: Some issues concerning fixed points in computational logic publication-title: Topology Proc. – volume: 16 start-page: 1107 year: 2008 ident: 10.1016/j.fss.2012.08.009_bib4 article-title: Discrete Choquet integral as a distance metric publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2008.924347 – volume: 151 start-page: 195 year: 1995 ident: 10.1016/j.fss.2012.08.009_bib23 article-title: An extensional treatment of lazy data flow deadlok publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(95)00051-W – year: 2005 ident: 10.1016/j.fss.2012.08.009_bib28 – ident: 10.1016/j.fss.2012.08.009_bib20 doi: 10.1007/978-94-017-0470-0_3 – volume: 98 start-page: 311 year: 1999 ident: 10.1016/j.fss.2012.08.009_bib35 article-title: Quasi-metric properties of complexity spaces publication-title: Topology Appl. doi: 10.1016/S0166-8641(98)00102-3 – volume: 152 start-page: 139 year: 2005 ident: 10.1016/j.fss.2012.08.009_bib7 article-title: Averaging fuzzy biopolymers publication-title: Fuzzy Set. Syst. doi: 10.1016/j.fss.2004.10.019 – volume: 99 start-page: 327 year: 1982 ident: 10.1016/j.fss.2012.08.009_bib12 article-title: A fixed point theorem for product spaces publication-title: Pacific J. Math. doi: 10.2140/pjm.1982.99.327 – volume: 31 start-page: 41 year: 2002 ident: 10.1016/j.fss.2012.08.009_bib30 article-title: A note on pseudometrics aggregation publication-title: Int. J. Gen. Syst. doi: 10.1080/03081070210320 – volume: 29 start-page: 97 year: 1997 ident: 10.1016/j.fss.2012.08.009_bib39 article-title: Quasi-metrics and the semantics of logic programs publication-title: Fundam. Inf. doi: 10.3233/FI-1997-291205 – volume: 15 start-page: 251 year: 2008 ident: 10.1016/j.fss.2012.08.009_bib8 article-title: A connection between computer science and fuzzy theory:midpoints and running time of computing publication-title: Mathware Soft Comput. – year: 2009 ident: 10.1016/j.fss.2012.08.009_bib16 – volume: 399 start-page: 253 year: 2012 ident: 10.1016/j.fss.2012.08.009_bib9 article-title: The Banach Contraction Principle on Fuzzy Quasi-Metric Spaces and on Product Complexity Spaces publication-title: Lecture Notes in Computer Science – volume: 180 start-page: 803 year: 2010 ident: 10.1016/j.fss.2012.08.009_bib26 article-title: Aggregation of asymmetric distances in computer science publication-title: Inf. Sci. doi: 10.1016/j.ins.2009.06.020 – year: 2010 ident: 10.1016/j.fss.2012.08.009_bib33 – volume: 5 start-page: 405 year: 2001 ident: 10.1016/j.fss.2012.08.009_bib11 article-title: Fixed points and approximate fixed points in product spaces publication-title: Taiwan J. Math. doi: 10.11650/twjm/1500407346 – ident: 10.1016/j.fss.2012.08.009_bib21 doi: 10.1007/978-3-642-00982-2_45 – volume: 88 start-page: 1819 year: 2011 ident: 10.1016/j.fss.2012.08.009_bib36 article-title: The complexity space of partial functions publication-title: Int. J. Comput. Math. doi: 10.1080/00207161003631885 – volume: 18 start-page: 57 year: 2010 ident: 10.1016/j.fss.2012.08.009_bib43 article-title: Norms induced from OWA operators publication-title: IEEE Trans. Fuzzy Syst. doi: 10.1109/TFUZZ.2009.2035812 – volume: 62 start-page: 121 year: 1995 ident: 10.1016/j.fss.2012.08.009_bib17 article-title: On metric products publication-title: Colloq. Math. doi: 10.4064/cm-62-1-121-133
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Snippet	The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. Borsík and J. Doboš [On a product of metric... The problem of how to merge, by means of a function, a family of metrics into a single one was studied deeply by J. BorsASHk and J. DoboA! [On a product of...
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SubjectTerms	Agglomeration Aggregation function Asymmetry Asymptotic complexity analysis Complexity Computation Denotational semantics Fixed points (mathematics) Homogeneous function Mathematical analysis Mathematical models Metric Projective [formula omitted]-contraction Projective contraction Quasi-metric Recursive Theorems
Title	On quasi-metric aggregation functions and fixed point theorems
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