Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values

Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example...
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Autor*in:	Piegat, Andrzej [verfasserIn] Plucinski, Marcin

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Schlagwörter:	Interval arithmetic Interval-precisiation arithmetic Granular computing Interval equations Computing with words

Anmerkung:	© the authors 2015

Übergeordnetes Werk:	Enthalten in: International journal of computational intelligence systems - Paris : Atlantis Press, 2008, 8(2015), 6 vom: Jan., Seite 1192-1209
Übergeordnetes Werk:	volume:8 ; year:2015 ; number:6 ; month:01 ; pages:1192-1209

Links:	Volltext

DOI / URN:	10.1080/18756891.2015.1113756

Katalog-ID:	SPR054191777

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520			\|a Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples.
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allfields	10.1080/18756891.2015.1113756 doi (DE-627)SPR054191777 (SPR)18756891.2015.1113756-e DE-627 ger DE-627 rakwb eng Piegat, Andrzej verfasserin aut Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © the authors 2015 Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213 Plucinski, Marcin aut Enthalten in International journal of computational intelligence systems Paris : Atlantis Press, 2008 8(2015), 6 vom: Jan., Seite 1192-1209 (DE-627)777781514 (DE-600)2754752-8 1875-6883 nnns volume:8 year:2015 number:6 month:01 pages:1192-1209 https://dx.doi.org/10.1080/18756891.2015.1113756 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2015 6 01 1192-1209
spelling	10.1080/18756891.2015.1113756 doi (DE-627)SPR054191777 (SPR)18756891.2015.1113756-e DE-627 ger DE-627 rakwb eng Piegat, Andrzej verfasserin aut Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © the authors 2015 Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213 Plucinski, Marcin aut Enthalten in International journal of computational intelligence systems Paris : Atlantis Press, 2008 8(2015), 6 vom: Jan., Seite 1192-1209 (DE-627)777781514 (DE-600)2754752-8 1875-6883 nnns volume:8 year:2015 number:6 month:01 pages:1192-1209 https://dx.doi.org/10.1080/18756891.2015.1113756 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2015 6 01 1192-1209
allfields_unstemmed	10.1080/18756891.2015.1113756 doi (DE-627)SPR054191777 (SPR)18756891.2015.1113756-e DE-627 ger DE-627 rakwb eng Piegat, Andrzej verfasserin aut Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © the authors 2015 Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213 Plucinski, Marcin aut Enthalten in International journal of computational intelligence systems Paris : Atlantis Press, 2008 8(2015), 6 vom: Jan., Seite 1192-1209 (DE-627)777781514 (DE-600)2754752-8 1875-6883 nnns volume:8 year:2015 number:6 month:01 pages:1192-1209 https://dx.doi.org/10.1080/18756891.2015.1113756 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2015 6 01 1192-1209
allfieldsGer	10.1080/18756891.2015.1113756 doi (DE-627)SPR054191777 (SPR)18756891.2015.1113756-e DE-627 ger DE-627 rakwb eng Piegat, Andrzej verfasserin aut Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © the authors 2015 Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213 Plucinski, Marcin aut Enthalten in International journal of computational intelligence systems Paris : Atlantis Press, 2008 8(2015), 6 vom: Jan., Seite 1192-1209 (DE-627)777781514 (DE-600)2754752-8 1875-6883 nnns volume:8 year:2015 number:6 month:01 pages:1192-1209 https://dx.doi.org/10.1080/18756891.2015.1113756 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2015 6 01 1192-1209
allfieldsSound	10.1080/18756891.2015.1113756 doi (DE-627)SPR054191777 (SPR)18756891.2015.1113756-e DE-627 ger DE-627 rakwb eng Piegat, Andrzej verfasserin aut Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © the authors 2015 Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213 Plucinski, Marcin aut Enthalten in International journal of computational intelligence systems Paris : Atlantis Press, 2008 8(2015), 6 vom: Jan., Seite 1192-1209 (DE-627)777781514 (DE-600)2754752-8 1875-6883 nnns volume:8 year:2015 number:6 month:01 pages:1192-1209 https://dx.doi.org/10.1080/18756891.2015.1113756 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 8 2015 6 01 1192-1209
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source	Enthalten in International journal of computational intelligence systems 8(2015), 6 vom: Jan., Seite 1192-1209 volume:8 year:2015 number:6 month:01 pages:1192-1209
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author	Piegat, Andrzej
spellingShingle	Piegat, Andrzej misc Interval arithmetic misc Interval-precisiation arithmetic misc Granular computing misc Interval equations misc Computing with words Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values
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topic_title	Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values Interval arithmetic (dpeaa)DE-He213 Interval-precisiation arithmetic (dpeaa)DE-He213 Granular computing (dpeaa)DE-He213 Interval equations (dpeaa)DE-He213 Computing with words (dpeaa)DE-He213
topic	misc Interval arithmetic misc Interval-precisiation arithmetic misc Granular computing misc Interval equations misc Computing with words
topic_unstemmed	misc Interval arithmetic misc Interval-precisiation arithmetic misc Granular computing misc Interval equations misc Computing with words
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title	Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values
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title_sort	some advantages of the rdm-arithmetic of intervally-precisiated values
title_auth	Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values
abstract	Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. © the authors 2015
abstractGer	Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. © the authors 2015
abstract_unstemmed	Abstract Moore’s interval arithmetic always provides the same results of arithmetic operations, e.g. [1,3]+ [5,9] = [6,12]. But in real life problems, the operation result can be different, e.g. equal to [4,7]. Therefore, real problems require more advanced arithmetic. The paper presents (on example of the division) an arithmetic of intervally-precisiated values (IPV-arithmetic) and its main advantages. Thanks to it, it is possible to process different tasks that people solve intuitively. The most important advantages are: existence of inverse elements of addition and multiplication, holding the distributivity law and the cancellation law of multiplication, possibility of achieving not only the solution span [x,̄x] but also the full, multidimensional solution and its cardinality distribution without using Monte Carlo method, possibility of achieving unique and complete solution sets of equations with unknowns, possibility of calculations with uncorrelated IPVs, possibility of calculations with fully correlated and partly correlated IPVs, possibility of uncertainty decreasing of original data items occurring in problems. All these advantages are illustrated and visualised by examples. © the authors 2015
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title_short	Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values
url	https://dx.doi.org/10.1080/18756891.2015.1113756
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score	7.401639

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Some Advantages of the RDM-arithmetic of Intervally-Precisiated Values

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