The arithmetic of continuous Z-numbers
In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z=(A, B), as an ordered pair of continuous fuzzy numbers A and B. The first describes a linguistic value, and the second one is the associated reliability. Unfortunate...
Uloženo v:
| Vydáno v: | Information sciences Ročník 373; s. 441 - 460 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Elsevier Inc
10.12.2016
|
| Témata: | |
| ISSN: | 0020-0255, 1872-6291 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z=(A, B), as an ordered pair of continuous fuzzy numbers A and B. The first describes a linguistic value, and the second one is the associated reliability. Unfortunately, up to day there is no works devoted to arithmetic of continuous Z-numbers in existence. An original formulation of operations over continuous Z-numbers proposed by Zadeh includes complex non-linear variational problems. We propose an alternative approach which has a better computational complexity and accuracy tradeoff. The proposed approach is based on linear programming and other simple optimization problems. We developed basic arithmetic operations such as addition, subtraction, multiplication and division, and some algebraic operations as maximum, minimum, square and square root of continuous Z-numbers. Vast compendium of examples shows validity of the suggested approach. |
|---|---|
| AbstractList | In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z =(A, B), as an ordered pair of continuous fuzzy numbers A and B. The first describes a linguistic value, and the second one is the associated reliability. Unfortunately, up to day there is no works devoted to arithmetic of continuous Z-numbers in existence. An original formulation of operations over continuous Z-numbers proposed by Zadeh includes complex non-linear variational problems. We propose an alternative approach which has a better computational complexity and accuracy tradeoff. The proposed approach is based on linear programming and other simple optimization problems. We developed basic arithmetic operations such as addition, subtraction, multiplication and division, and some algebraic operations as maximum, minimum, square and square root of continuous Z-numbers. Vast compendium of examples shows validity of the suggested approach. |
| Author | Aliev, R.A. Zeinalova, L.M. Huseynov, O.H. |
| Author_xml | – sequence: 1 givenname: R.A. surname: Aliev fullname: Aliev, R.A. email: raliev@asoa.edu.az organization: Joint MBA Program, Azerbaijan State Oil and Industry University, Azerbaijan, 20 Azadlig Ave., AZ1010 Baku, Azerbaijan; Georgia State University, USA; Department of Computer Engineering, Near East University, Lefkosa, North Cyprus – sequence: 2 givenname: O.H. surname: Huseynov fullname: Huseynov, O.H. email: oleg_huseynov@yahoo.com organization: Department of Computer Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan – sequence: 3 givenname: L.M. surname: Zeinalova fullname: Zeinalova, L.M. email: zeynalova-69@mail.ru organization: Department of Computer Engineering, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan |
| BookMark | eNp9kD1PwzAQhi1UJNrCD2DLhFgS_BF_REyo4kuqxFIWFst1LqqrxCm2g8S_x1WZGFjubnif092zQDM_ekDomuCKYCLu9pXzsaJ5rLCqsFRnaE6UpKWgDZmhOcYUl5hyfoEWMe4xxrUUYo5uNjsoTHBpN0Bythi7wo4-OT-NUyw-Sj8NWwjxEp13po9w9duX6P3pcbN6Kddvz6-rh3VpGcOpZJYZorbQtJbaRnKGJTvW2hBpZd22reKMmwYo7WrBgdaKGm4FN8R2RBi2RLenvYcwfk4Qkx5ctND3xkM-SBNVc8XqRsgclaeoDWOMATptXTLJ5euDcb0mWB_N6L3OZvTRjMZKZzOZJH_IQ3CDCd__MvcnBvL3Xw6CjtaBt9C6ADbpdnT_0D-cWnxn |
| CitedBy_id | crossref_primary_10_1631_FITEE_1700434 crossref_primary_10_1007_s12559_018_9556_y crossref_primary_10_1016_j_engappai_2019_08_005 crossref_primary_10_1016_j_ins_2023_119886 crossref_primary_10_1016_j_procs_2017_11_306 crossref_primary_10_1016_j_eswa_2021_115387 crossref_primary_10_3233_JIFS_212954 crossref_primary_10_1016_j_engappai_2024_109484 crossref_primary_10_3233_JIFS_235304 crossref_primary_10_1109_TFUZZ_2018_2868496 crossref_primary_10_1109_TFUZZ_2021_3094657 crossref_primary_10_1007_s40747_020_00204_w crossref_primary_10_1016_j_asoc_2018_10_026 crossref_primary_10_1007_s40815_019_00674_2 crossref_primary_10_1016_j_ins_2020_10_038 crossref_primary_10_1016_j_ins_2022_03_049 crossref_primary_10_1109_TFUZZ_2019_2908131 crossref_primary_10_1109_TFUZZ_2019_2923948 crossref_primary_10_1007_s12652_019_01228_y crossref_primary_10_1109_ACCESS_2020_2979060 crossref_primary_10_1016_j_ins_2021_08_077 crossref_primary_10_1002_int_22642 crossref_primary_10_1016_j_eswa_2020_113218 crossref_primary_10_1016_j_ijar_2023_108977 crossref_primary_10_1109_TFUZZ_2019_2918999 crossref_primary_10_1007_s40815_020_00819_8 crossref_primary_10_1109_TFUZZ_2018_2816909 crossref_primary_10_3390_math12101443 crossref_primary_10_1088_1742_6596_1703_1_012010 crossref_primary_10_1016_j_engappai_2021_104437 crossref_primary_10_1016_j_ins_2022_07_171 crossref_primary_10_1016_j_cie_2020_106517 crossref_primary_10_1016_j_ins_2020_05_106 crossref_primary_10_1016_j_ins_2022_04_031 crossref_primary_10_1080_16168658_2018_1509517 crossref_primary_10_1016_j_jii_2025_100805 crossref_primary_10_3233_JIFS_212116 crossref_primary_10_1016_j_asoc_2023_110168 crossref_primary_10_1016_j_eswa_2022_117369 crossref_primary_10_26417_ejef_v3i3_p47_55 crossref_primary_10_1109_TFUZZ_2018_2816581 crossref_primary_10_1109_ACCESS_2019_2912922 crossref_primary_10_1007_s40314_020_01167_x crossref_primary_10_1016_j_cie_2020_106430 crossref_primary_10_1109_TFUZZ_2022_3170208 crossref_primary_10_1109_TFUZZ_2021_3138649 crossref_primary_10_1371_journal_pone_0227307 crossref_primary_10_1016_j_ins_2024_121703 crossref_primary_10_1109_TIM_2022_3193185 crossref_primary_10_1016_j_ins_2023_119987 crossref_primary_10_1109_ACCESS_2020_2994508 crossref_primary_10_1016_j_ins_2024_121707 crossref_primary_10_1007_s40314_025_03432_3 crossref_primary_10_1007_s40747_021_00523_6 crossref_primary_10_3233_JIFS_223025 crossref_primary_10_1007_s40747_025_01786_z crossref_primary_10_3390_math12193091 crossref_primary_10_1016_j_procs_2017_11_204 crossref_primary_10_1016_j_procs_2017_11_205 crossref_primary_10_1016_j_procs_2017_11_249 crossref_primary_10_1002_int_22050 crossref_primary_10_1007_s12652_019_01251_z crossref_primary_10_1016_j_asoc_2023_111196 crossref_primary_10_1007_s00500_020_04914_8 crossref_primary_10_3390_math11173750 crossref_primary_10_1007_s10489_024_05765_8 crossref_primary_10_1016_j_ins_2024_121791 crossref_primary_10_1016_j_ins_2024_120100 crossref_primary_10_1109_TFUZZ_2022_3191359 crossref_primary_10_1051_e3sconf_202342006022 crossref_primary_10_1109_TII_2024_3397392 crossref_primary_10_1109_TFUZZ_2019_2930935 crossref_primary_10_1016_j_ins_2023_119799 crossref_primary_10_3233_JIFS_18927 crossref_primary_10_1016_j_ins_2023_119477 crossref_primary_10_1051_e3sconf_202343105015 crossref_primary_10_1108_K_07_2024_1837 crossref_primary_10_1088_1757_899X_919_5_052041 crossref_primary_10_1155_2019_1545263 crossref_primary_10_1016_j_ins_2021_11_016 crossref_primary_10_1007_s00500_020_05087_0 crossref_primary_10_1016_j_engappai_2021_104618 crossref_primary_10_1016_j_cie_2019_02_011 crossref_primary_10_1016_j_asoc_2018_02_001 crossref_primary_10_1007_s10668_019_00464_8 crossref_primary_10_3233_JIFS_190300 crossref_primary_10_1016_j_ins_2019_05_090 crossref_primary_10_1109_TCYB_2025_3545195 crossref_primary_10_1007_s40815_022_01297_w crossref_primary_10_1155_2020_8407830 crossref_primary_10_3389_fenvs_2023_1137689 crossref_primary_10_1016_j_amc_2017_12_006 crossref_primary_10_1007_s10489_021_02435_x crossref_primary_10_1016_j_apenergy_2024_124616 crossref_primary_10_1016_j_ins_2022_01_024 crossref_primary_10_1080_01605682_2020_1759382 |
| Cites_doi | 10.1016/j.eswa.2013.03.020 10.1016/j.ins.2013.06.003 10.1016/j.ins.2011.02.022 10.1007/s12652-012-0137-8 10.1016/j.asoc.2011.04.005 10.1002/int.21521 10.1016/j.ins.2007.05.001 10.1016/S0167-9473(02)00234-7 10.1137/110839680 10.1016/0888-613X(90)90022-T 10.1016/j.ins.2014.08.024 10.1016/j.csda.2006.04.029 10.1016/j.fss.2009.06.009 10.1002/int.21709 10.1016/S0019-9958(65)90241-X 10.3233/FI-2013-831 10.1016/0022-247X(68)90078-4 10.1016/j.ins.2010.09.020 10.1016/j.tcs.2012.12.034 10.1109/FUZZ-IEEE.2014.6891827 |
| ContentType | Journal Article |
| Copyright | 2016 Elsevier Inc. |
| Copyright_xml | – notice: 2016 Elsevier Inc. |
| DBID | AAYXX CITATION 7SC 8FD JQ2 L7M L~C L~D |
| DOI | 10.1016/j.ins.2016.08.078 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Technology Research Database ProQuest Computer Science Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Computer and Information Systems Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Advanced Technologies Database with Aerospace ProQuest Computer Science Collection Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Computer and Information Systems Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Engineering Library & Information Science |
| EISSN | 1872-6291 |
| EndPage | 460 |
| ExternalDocumentID | 10_1016_j_ins_2016_08_078 S0020025516306600 |
| GroupedDBID | --K --M --Z -~X .DC .~1 0R~ 1B1 1RT 1~. 1~5 4.4 457 4G. 5GY 5VS 7-5 71M 8P~ 9JN 9JO AAAKF AABNK AACTN AAEDT AAEDW AAIAV AAIKJ AAKOC AALRI AAOAW AAQFI AARIN AAXUO AAYFN ABAOU ABBOA ABFNM ABJNI ABMAC ABUCO ABYKQ ACAZW ACDAQ ACGFS ACRLP ACZNC ADBBV ADEZE ADGUI ADTZH AEBSH AECPX AEKER AENEX AFKWA AFTJW AGHFR AGUBO AGYEJ AHHHB AHJVU AHZHX AIALX AIEXJ AIGVJ AIKHN AITUG AJBFU AJOXV ALMA_UNASSIGNED_HOLDINGS AMFUW AMRAJ AOUOD APLSM ARUGR AXJTR BJAXD BKOJK BLXMC CS3 DU5 EBS EFJIC EFLBG EJD EO8 EO9 EP2 EP3 F5P FDB FIRID FNPLU FYGXN G-Q GBLVA GBOLZ HAMUX IHE J1W JJJVA KOM LG9 LY1 M41 MHUIS MO0 MS~ N9A O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q38 RIG ROL RPZ SDF SDG SDP SES SPC SPCBC SSB SSD SST SSV SSW SSZ T5K TN5 TWZ WH7 XPP ZMT ~02 ~G- 1OL 29I 77I 9DU AAAKG AAQXK AATTM AAXKI AAYWO AAYXX ABEFU ABWVN ABXDB ACLOT ACNNM ACRPL ACVFH ADCNI ADJOM ADMUD ADNMO ADVLN AEIPS AEUPX AFFNX AFJKZ AFPUW AGQPQ AIGII AIIUN AKBMS AKRWK AKYEP ANKPU APXCP ASPBG AVWKF AZFZN CITATION EFKBS FEDTE FGOYB HLZ HVGLF HZ~ H~9 R2- SBC SDS SEW UHS WUQ YYP ZY4 ~HD 7SC 8FD JQ2 L7M L~C L~D |
| ID | FETCH-LOGICAL-c330t-3c3a18be9dc2c975307375304a17c74ddd8535a9e22f465e2482a5c65a1cf16a3 |
| ISICitedReferencesCount | 123 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000385470400026&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 0020-0255 |
| IngestDate | Sat Sep 27 23:17:44 EDT 2025 Sat Nov 29 06:25:01 EST 2025 Tue Nov 18 22:12:03 EST 2025 Fri Feb 23 02:33:55 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | A continuous fuzzy number Convolution Arithmetic operations A random variable A probability measure Z-number |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c330t-3c3a18be9dc2c975307375304a17c74ddd8535a9e22f465e2482a5c65a1cf16a3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| PQID | 1845834967 |
| PQPubID | 23500 |
| PageCount | 20 |
| ParticipantIDs | proquest_miscellaneous_1845834967 crossref_citationtrail_10_1016_j_ins_2016_08_078 crossref_primary_10_1016_j_ins_2016_08_078 elsevier_sciencedirect_doi_10_1016_j_ins_2016_08_078 |
| PublicationCentury | 2000 |
| PublicationDate | 2016-12-10 |
| PublicationDateYYYYMMDD | 2016-12-10 |
| PublicationDate_xml | – month: 12 year: 2016 text: 2016-12-10 day: 10 |
| PublicationDecade | 2010 |
| PublicationTitle | Information sciences |
| PublicationYear | 2016 |
| Publisher | Elsevier Inc |
| Publisher_xml | – name: Elsevier Inc |
| References | Kaufmann, Gupta (bib0018) 1985 Tadayon, Tadayon (bib0030) 2012 Abu Aarqob, Shawagfeh, AbuGhneim (bib0001) 2008; 3 Bashar, Shirin (bib0008) 2005; 53 Springer (bib0029) 1979 Stefanini (bib0043) 2010; 161 Zhai, Mendel (bib0041) 2011; 181 Yager (bib0034) 2012; 27 Klir, Yuan (bib0020) 1995 J. Lorkowski, R.A. Aliev, and V. Kreinovich, Towards decision making under interval, set-valued, fuzzy, and z-number uncertainty: a fair price approach Aliev, Zeinalova (bib0005) 2014 Hanss (bib0045) 2005 Zadeh (bib0040) 2013; 248 Zadeh (bib0038) 1968; 23 Rohatgi (bib0042) 1976 Zadeh (bib0037) 2006; 51 Zadeh (bib0035) 2011; 181 Ruan (bib0027) 2010 Aliev, Alizadeh, Huseynov, Jabbarova (bib0003) 2015 Kang, Wei, Li, Deng (bib0017) 2012; 8 Castillo (bib0009) 2012 Glen, Leemis, Drew (bib0013) 2004; 44 Azadeh, Saberi, Atashbar, Chang, Pazhoheshfar (bib0006) 2013 Pal, Banerjee (bib0024) 2013; 488 Khorasani, Patel, Rahimi, Houle (bib0019) 2013; 4 Williamson (bib0032) 1989 L.A. Zadeh. Methods and systems for applications with Z-numbers, United States Patent, Patent No.: US 8,311,973 B1, Date of Patent: 2012. Sevastianov (bib0028) 2007; 177 Aliev, Huseynov (bib0004) 2014 Banerjee, Pal (bib0007) 2013; Volume 291 Castillo, Melin (bib0010) 2008 . Papoulis, Pillai (bib0026) 2002 Charles, Grinstead, Snell (bib0012) 1997 Hahn, Shapiro (bib0014) 1967 R.R. Yager, On a view of Zadeh's Z-numbers, Adv. Comput. Intell. Commun. Comput. Inf. Sci. 299(2012) 90–101. Mendel (bib0023) 2014 Jaroszewicz, Korzen (bib0015) 2012; 34 Bede (bib0044) 2013 Pal, Banerjee, Dutta, Sarma (bib0025) 2013; 124 Melin, Castillo (bib0022) 2013; 40 Castillo, Melin, Pedrycz (bib0011) 2011; 11 Kang, Wei, Li, Deng (bib0016) 2012; 9 Williamson, Downs (bib0031) 1990; 4 Zadeh (bib0036) 1965; 8 Aliev, Alizadeh, Huseynov (bib0002) 2015; 290 10.1016/j.ins.2016.08.078_bib0033 Charles (10.1016/j.ins.2016.08.078_bib0012) 1997 Tadayon (10.1016/j.ins.2016.08.078_bib0030) 2012 10.1016/j.ins.2016.08.078_bib0039 Khorasani (10.1016/j.ins.2016.08.078_bib0019) 2013; 4 Aliev (10.1016/j.ins.2016.08.078_bib0003) 2015 Castillo (10.1016/j.ins.2016.08.078_bib0011) 2011; 11 Klir (10.1016/j.ins.2016.08.078_bib0020) 1995 Zhai (10.1016/j.ins.2016.08.078_bib0041) 2011; 181 Springer (10.1016/j.ins.2016.08.078_bib0029) 1979 Jaroszewicz (10.1016/j.ins.2016.08.078_bib0015) 2012; 34 Banerjee (10.1016/j.ins.2016.08.078_bib0007) 2013; Volume 291 Williamson (10.1016/j.ins.2016.08.078_bib0031) 1990; 4 Yager (10.1016/j.ins.2016.08.078_bib0034) 2012; 27 Papoulis (10.1016/j.ins.2016.08.078_bib0026) 2002 Hanss (10.1016/j.ins.2016.08.078_bib0045) 2005 Kaufmann (10.1016/j.ins.2016.08.078_bib0018) 1985 Kang (10.1016/j.ins.2016.08.078_bib0016) 2012; 9 Bashar (10.1016/j.ins.2016.08.078_bib0008) 2005; 53 Williamson (10.1016/j.ins.2016.08.078_bib0032) 1989 Abu Aarqob (10.1016/j.ins.2016.08.078_bib0001) 2008; 3 Bede (10.1016/j.ins.2016.08.078_bib0044) 2013 10.1016/j.ins.2016.08.078_bib0021 Castillo (10.1016/j.ins.2016.08.078_bib0009) 2012 Melin (10.1016/j.ins.2016.08.078_bib0022) 2013; 40 Aliev (10.1016/j.ins.2016.08.078_bib0004) 2014 Zadeh (10.1016/j.ins.2016.08.078_bib0040) 2013; 248 Castillo (10.1016/j.ins.2016.08.078_bib0010) 2008 Pal (10.1016/j.ins.2016.08.078_bib0024) 2013; 488 Rohatgi (10.1016/j.ins.2016.08.078_bib0042) 1976 Zadeh (10.1016/j.ins.2016.08.078_bib0035) 2011; 181 Hahn (10.1016/j.ins.2016.08.078_bib0014) 1967 Glen (10.1016/j.ins.2016.08.078_bib0013) 2004; 44 Zadeh (10.1016/j.ins.2016.08.078_bib0037) 2006; 51 Kang (10.1016/j.ins.2016.08.078_bib0017) 2012; 8 Sevastianov (10.1016/j.ins.2016.08.078_bib0028) 2007; 177 Stefanini (10.1016/j.ins.2016.08.078_bib0043) 2010; 161 Azadeh (10.1016/j.ins.2016.08.078_bib0006) 2013 Pal (10.1016/j.ins.2016.08.078_bib0025) 2013; 124 Zadeh (10.1016/j.ins.2016.08.078_bib0036) 1965; 8 Mendel (10.1016/j.ins.2016.08.078_bib0023) 2014 Ruan (10.1016/j.ins.2016.08.078_bib0027) 2010 Zadeh (10.1016/j.ins.2016.08.078_bib0038) 1968; 23 Aliev (10.1016/j.ins.2016.08.078_bib0005) 2014 Aliev (10.1016/j.ins.2016.08.078_bib0002) 2015; 290 |
| References_xml | – volume: 177 start-page: 4645 year: 2007 end-page: 4661 ident: bib0028 article-title: Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster–Shafer theory publication-title: Inf. Sci. – volume: 181 start-page: 2923 year: 2011 end-page: 2932 ident: bib0035 article-title: A note on Z-numbers publication-title: Inf. Sci. – volume: 4 start-page: 451 year: 2013 end-page: 470 ident: bib0019 article-title: An inference engine toolkit for computing with words publication-title: J. Ambient Intell. Human. Comput. – volume: 23 start-page: 421 year: 1968 end-page: 427 ident: bib0038 article-title: Probability measures of fuzzy events publication-title: J. Math. Anal. Appl. – year: 2012 ident: bib0009 article-title: Type-2 Fuzzy Logic in Intelligent Control Applications – volume: 44 start-page: 451 year: 2004 end-page: 464 ident: bib0013 article-title: Computing the distribution of the product of two continuous random variables publication-title: Comput. Stat. Data An. – year: 1979 ident: bib0029 article-title: The Algebra of Random Variables – volume: 181 start-page: 503 year: 2011 end-page: 518 ident: bib0041 article-title: Uncertainty measures for general type-2 fuzzy sets publication-title: Inf. Sci. – year: 2010 ident: bib0027 article-title: Computational Intelligence in Complex Decision Systems – reference: L.A. Zadeh. Methods and systems for applications with Z-numbers, United States Patent, Patent No.: US 8,311,973 B1, Date of Patent: 2012. – year: 2013 ident: bib0044 article-title: Mathematics of Fuzzy Sets and Fuzzy Logic – volume: 8 start-page: 2807 year: 2012 end-page: 2814 ident: bib0017 article-title: Decision making using Z-numbers under uncertain environment publication-title: J. Inf. Comput. Sci. – volume: 34 start-page: 1241 year: 2012 end-page: 1265 ident: bib0015 article-title: Arithmetic operations on independent random variables: a numerical approach publication-title: SIAM J. Sci. Comput. – year: 1985 ident: bib0018 article-title: Introduction to Fuzzy Arithmetic: Theory and Application – volume: 248 start-page: 1 year: 2013 end-page: 14 ident: bib0040 article-title: Toward a restriction-centered theory of truth and meaning (RCT) publication-title: Inf. Sci. – volume: 488 start-page: 2 year: 2013 end-page: 14 ident: bib0024 article-title: Context granulation and subjective-information quantification publication-title: Theor. Comput. Sci. – volume: 124 start-page: 197 year: 2013 end-page: 229 ident: bib0025 article-title: An insight into the Z-number approach to CWW publication-title: Fundamenta Informaticae – volume: Volume 291 start-page: 71 year: 2013 end-page: 88 ident: bib0007 article-title: The Z-number enigma: a study through an experiment publication-title: Soft Computing: State of the Art Theory and Novel Applications (Studies in Fuzziness and Soft Computing) – year: 2008 ident: bib0010 article-title: Type-2 Fuzzy Logic: Theory and Applications – volume: 27 start-page: 259 year: 2012 end-page: 278 ident: bib0034 article-title: On Z-valuations using Zadeh`s Z-numbers publication-title: Int. J. Intell. Syst. – volume: 40 start-page: 5413 year: 2013 end-page: 5423 ident: bib0022 article-title: A review on the applications of type-2 fuzzy logic in classification and pattern recognition publication-title: Expert Syst. Appl. – year: 1989 ident: bib0032 article-title: Probabilistic Arithmetic – reference: R.R. Yager, On a view of Zadeh's Z-numbers, Adv. Comput. Intell. Commun. Comput. Inf. Sci. 299(2012) 90–101. – year: 2005 ident: bib0045 article-title: Applied Fuzzy Arithmetic. An Introduction with Engineering Applications – volume: 3 start-page: 763 year: 2008 end-page: 776 ident: bib0001 article-title: Functions defined on fuzzy real numbers according to Zadeh's extension publication-title: Int. Math. Forum – year: 1995 ident: bib0020 article-title: Fuzzy Sets and Fuzzy Logic: Theory and Applications – volume: 8 start-page: 338 year: 1965 end-page: 353 ident: bib0036 article-title: Fuzzy sets publication-title: Inf. Control – volume: 11 start-page: 5590 year: 2011 end-page: 5601 ident: bib0011 article-title: Design of interval type-2 fuzzy models through optimal granularity allocation publication-title: Appl. Soft Comput. – year: 2015 ident: bib0003 article-title: Z-number based linear programming publication-title: Int. J. Intell. Syst. – start-page: 141 year: 2013 end-page: 147 ident: bib0006 article-title: Z-AHP: a Z-number extension of fuzzy analytical hierarchy process publication-title: International Conference on Digital Ecosystems and Technologies (DEST) – year: 2014 ident: bib0004 article-title: Decision Theory with Imperfect Information – volume: 290 start-page: 134 year: 2015 end-page: 155 ident: bib0002 article-title: The arithmetic of discrete Z-numbers publication-title: Inf. Sci. – reference: . – year: 2012 ident: bib0030 article-title: Approximate Z-number evaluation based on categorical sets of probability distributions publication-title: Proc. 2nd World Conf. on Soft Computing, WConSC – year: 1967 ident: bib0014 article-title: Statistical Models in Engineering – volume: 161 start-page: 1564 year: 2010 end-page: 1584 ident: bib0043 article-title: A generalization of Hukuhara difference and division for interval and fuzzy arithmetic publication-title: Fuzzy Sets Syst. – reference: J. Lorkowski, R.A. Aliev, and V. Kreinovich, Towards decision making under interval, set-valued, fuzzy, and z-number uncertainty: a fair price approach, – volume: 51 start-page: 15 year: 2006 end-page: 46 ident: bib0037 article-title: Generalized theory of uncertainty (GTU) – principal concepts and ideas publication-title: Comput. Stat. Data Anal. – year: 2014 ident: bib0023 article-title: Type-2 Fuzzy Logic Control: Introduction to Theory and Application – volume: 4 start-page: 89 year: 1990 end-page: 158 ident: bib0031 article-title: Probabilistic arithmetic. I. numerical methods for calculating convolutions and dependency bounds publication-title: Int. J.Approx. Reason. – start-page: 233 year: 2014 end-page: 252 ident: bib0005 article-title: Decision making under Z-information publication-title: Human-Centric Decision-Making Models for Social Sciences (Studies in Computational Intelligence) – year: 1997 ident: bib0012 article-title: Introduction to Probability – year: 2002 ident: bib0026 article-title: Probability, Random Variables, and Stochastic Processes – volume: 53 start-page: 131 year: 2005 end-page: 140 ident: bib0008 article-title: Squares and square roots of continuous fuzzy numbers publication-title: Dhaka Univ. J. Sci. – volume: 9 start-page: 703 year: 2012 end-page: 709 ident: bib0016 article-title: A method of converting Z-number to classical fuzzy number publication-title: J. Inf. Comput. Sci. – year: 1976 ident: bib0042 article-title: An Introduction to Probability Theory Mathematical Statistics – volume: 40 start-page: 5413 issue: 13 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0022 article-title: A review on the applications of type-2 fuzzy logic in classification and pattern recognition publication-title: Expert Syst. Appl. doi: 10.1016/j.eswa.2013.03.020 – volume: 248 start-page: 1 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0040 article-title: Toward a restriction-centered theory of truth and meaning (RCT) publication-title: Inf. Sci. doi: 10.1016/j.ins.2013.06.003 – volume: 181 start-page: 2923 year: 2011 ident: 10.1016/j.ins.2016.08.078_bib0035 article-title: A note on Z-numbers publication-title: Inf. Sci. doi: 10.1016/j.ins.2011.02.022 – year: 1967 ident: 10.1016/j.ins.2016.08.078_bib0014 – ident: 10.1016/j.ins.2016.08.078_bib0033 – year: 2008 ident: 10.1016/j.ins.2016.08.078_bib0010 – year: 1997 ident: 10.1016/j.ins.2016.08.078_bib0012 – volume: 8 start-page: 2807 issue: 7 year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0017 article-title: Decision making using Z-numbers under uncertain environment publication-title: J. Inf. Comput. Sci. – year: 1995 ident: 10.1016/j.ins.2016.08.078_bib0020 – year: 2014 ident: 10.1016/j.ins.2016.08.078_bib0023 – volume: Volume 291 start-page: 71 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0007 article-title: The Z-number enigma: a study through an experiment – start-page: 233 year: 2014 ident: 10.1016/j.ins.2016.08.078_bib0005 article-title: Decision making under Z-information – year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0009 – volume: 4 start-page: 451 issue: 4 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0019 article-title: An inference engine toolkit for computing with words publication-title: J. Ambient Intell. Human. Comput. doi: 10.1007/s12652-012-0137-8 – volume: 11 start-page: 5590 issue: 8 year: 2011 ident: 10.1016/j.ins.2016.08.078_bib0011 article-title: Design of interval type-2 fuzzy models through optimal granularity allocation publication-title: Appl. Soft Comput. doi: 10.1016/j.asoc.2011.04.005 – year: 2014 ident: 10.1016/j.ins.2016.08.078_bib0004 – volume: 3 start-page: 763 issue: 16 year: 2008 ident: 10.1016/j.ins.2016.08.078_bib0001 article-title: Functions defined on fuzzy real numbers according to Zadeh's extension publication-title: Int. Math. Forum – volume: 53 start-page: 131 issue: 2 year: 2005 ident: 10.1016/j.ins.2016.08.078_bib0008 article-title: Squares and square roots of continuous fuzzy numbers publication-title: Dhaka Univ. J. Sci. – year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0030 article-title: Approximate Z-number evaluation based on categorical sets of probability distributions – year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0044 – volume: 27 start-page: 259 year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0034 article-title: On Z-valuations using Zadeh`s Z-numbers publication-title: Int. J. Intell. Syst. doi: 10.1002/int.21521 – volume: 177 start-page: 4645 issue: 21 year: 2007 ident: 10.1016/j.ins.2016.08.078_bib0028 article-title: Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster–Shafer theory publication-title: Inf. Sci. doi: 10.1016/j.ins.2007.05.001 – volume: 44 start-page: 451 year: 2004 ident: 10.1016/j.ins.2016.08.078_bib0013 article-title: Computing the distribution of the product of two continuous random variables publication-title: Comput. Stat. Data An. doi: 10.1016/S0167-9473(02)00234-7 – start-page: 141 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0006 article-title: Z-AHP: a Z-number extension of fuzzy analytical hierarchy process – year: 2010 ident: 10.1016/j.ins.2016.08.078_bib0027 – volume: 34 start-page: 1241 issue: 3 year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0015 article-title: Arithmetic operations on independent random variables: a numerical approach publication-title: SIAM J. Sci. Comput. doi: 10.1137/110839680 – volume: 4 start-page: 89 issue: 2 year: 1990 ident: 10.1016/j.ins.2016.08.078_bib0031 article-title: Probabilistic arithmetic. I. numerical methods for calculating convolutions and dependency bounds publication-title: Int. J.Approx. Reason. doi: 10.1016/0888-613X(90)90022-T – volume: 290 start-page: 134 year: 2015 ident: 10.1016/j.ins.2016.08.078_bib0002 article-title: The arithmetic of discrete Z-numbers publication-title: Inf. Sci. doi: 10.1016/j.ins.2014.08.024 – volume: 51 start-page: 15 year: 2006 ident: 10.1016/j.ins.2016.08.078_bib0037 article-title: Generalized theory of uncertainty (GTU) – principal concepts and ideas publication-title: Comput. Stat. Data Anal. doi: 10.1016/j.csda.2006.04.029 – year: 2002 ident: 10.1016/j.ins.2016.08.078_bib0026 – year: 1985 ident: 10.1016/j.ins.2016.08.078_bib0018 – volume: 161 start-page: 1564 issue: 11 year: 2010 ident: 10.1016/j.ins.2016.08.078_bib0043 article-title: A generalization of Hukuhara difference and division for interval and fuzzy arithmetic publication-title: Fuzzy Sets Syst. doi: 10.1016/j.fss.2009.06.009 – year: 2015 ident: 10.1016/j.ins.2016.08.078_bib0003 article-title: Z-number based linear programming publication-title: Int. J. Intell. Syst. doi: 10.1002/int.21709 – volume: 8 start-page: 338 year: 1965 ident: 10.1016/j.ins.2016.08.078_bib0036 article-title: Fuzzy sets publication-title: Inf. Control doi: 10.1016/S0019-9958(65)90241-X – volume: 9 start-page: 703 issue: 3 year: 2012 ident: 10.1016/j.ins.2016.08.078_bib0016 article-title: A method of converting Z-number to classical fuzzy number publication-title: J. Inf. Comput. Sci. – volume: 124 start-page: 197 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0025 article-title: An insight into the Z-number approach to CWW publication-title: Fundamenta Informaticae doi: 10.3233/FI-2013-831 – year: 1989 ident: 10.1016/j.ins.2016.08.078_bib0032 – ident: 10.1016/j.ins.2016.08.078_bib0039 – year: 1979 ident: 10.1016/j.ins.2016.08.078_bib0029 – year: 2005 ident: 10.1016/j.ins.2016.08.078_bib0045 – volume: 23 start-page: 421 issue: 2 year: 1968 ident: 10.1016/j.ins.2016.08.078_bib0038 article-title: Probability measures of fuzzy events publication-title: J. Math. Anal. Appl. doi: 10.1016/0022-247X(68)90078-4 – volume: 181 start-page: 503 issue: 3 year: 2011 ident: 10.1016/j.ins.2016.08.078_bib0041 article-title: Uncertainty measures for general type-2 fuzzy sets publication-title: Inf. Sci. doi: 10.1016/j.ins.2010.09.020 – volume: 488 start-page: 2 year: 2013 ident: 10.1016/j.ins.2016.08.078_bib0024 article-title: Context granulation and subjective-information quantification publication-title: Theor. Comput. Sci. doi: 10.1016/j.tcs.2012.12.034 – year: 1976 ident: 10.1016/j.ins.2016.08.078_bib0042 – ident: 10.1016/j.ins.2016.08.078_bib0021 doi: 10.1109/FUZZ-IEEE.2014.6891827 |
| SSID | ssj0004766 |
| Score | 2.5330143 |
| Snippet | In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z=(A, B), as an ordered... In order to deal with imprecision and partial reliability of real-world information, Prof. Zadeh suggested the concept of a Z-number Z =(A, B), as an ordered... |
| SourceID | proquest crossref elsevier |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 441 |
| SubjectTerms | A continuous fuzzy number A probability measure A random variable Algebra Arithmetic Arithmetic operations BASIC (programming language) Convolution Division Fuzzy systems Linguistics Nonlinearity Optimization Z-number |
| Title | The arithmetic of continuous Z-numbers |
| URI | https://dx.doi.org/10.1016/j.ins.2016.08.078 https://www.proquest.com/docview/1845834967 |
| Volume | 373 |
| WOSCitedRecordID | wos000385470400026&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVESC databaseName: Elsevier SD Freedom Collection Journals 2021 customDbUrl: eissn: 1872-6291 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0004766 issn: 0020-0255 databaseCode: AIEXJ dateStart: 19950101 isFulltext: true titleUrlDefault: https://www.sciencedirect.com providerName: Elsevier |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1baxQxFA669UEfRKti1UoE6YOQYXOZyeRxkUqVWn2osvQlZDIZatHZ0t0u9d97cpmLKxYVfAlD2JlZ8p05-ZKccz6EXjLjxQOsIUwyS0TBaqIqWpBcGiEdh0k-iPZ9PpRHR-V8rj4mmbtlkBOQbVteXanz_wo19AHYPnX2L-DuHwodcA2gQwuwQ_vHwMMCeHX6zecnxrBxLwdx6YNdT0iUAFmOSWlKSQqWkGbEnmnPgKOuAw7ZLBtsYOm-t4vQ_yE76PtPnNfYWqwDIT3M3mfjPQUalHhSdGnY6OqSXX6KxfTMkvglSJw6or8sJSMFi4JbnUPlko9cooiFrdLsKqJ6wC-OO-4hnMFqw9dQp0WoqxrFfTbqYfvj5bASAiYJfGk6vYm2mMxVOUFbs7f783dDWqyMR9Xd_-4OtUN438aLfkdLNibowDqO76G7abmAZxHm--iGa7fRnVERyW20m1JP8B4eAYmT036A9sAg8GAQeNHgwSBwbxAP0ac3-8evD0hSxyCW8-mKcMsNLSunasusT48GZ-1bYai0UtR1Dd9ZbpRjrBFF7pgomcltkRtqG1oY_ghN2kXrHiNspbJMVFVjbSOoa5QEkmsAqko1lOfVDpp2g6NtKh3vFUy-6i5G8EzDeGo_ntqrmspyB73qbzmPdVOu-7HoRlwnM4-EToN5XHfbiw4dDU7Rn3SZ1sHYaVr6cAChCvnk3x79FN0evotnaLK6uHS76JZdr74sL54nQ_sB4RGCtg |
| linkProvider | Elsevier |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=The+arithmetic+of+continuous+Z-numbers&rft.jtitle=Information+sciences&rft.au=Aliev%2C+R.A.&rft.au=Huseynov%2C+O.H.&rft.au=Zeinalova%2C+L.M.&rft.date=2016-12-10&rft.pub=Elsevier+Inc&rft.issn=0020-0255&rft.eissn=1872-6291&rft.volume=373&rft.spage=441&rft.epage=460&rft_id=info:doi/10.1016%2Fj.ins.2016.08.078&rft.externalDocID=S0020025516306600 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0020-0255&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0020-0255&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0020-0255&client=summon |