A Brief Analysis and Interpretation on Arithmetic Operations of Fuzzy Numbers

Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many ap...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Results in control and optimization Ročník 13; s. 100312
Hlavní autoři: Mukherjee, Asesh Kumar, Gazi, Kamal Hossain, Salahshour, Soheil, Ghosh, Arijit, Mondal, Sankar Prasad
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.12.2023
Elsevier
Témata:
Arithmetic operations of fuzzy numbers
Fuzzy sets
Triangular fuzzy number
α–cut set
α–cut set
Fuzzy sets
Arithmetic operations of fuzzy numbers
Triangular fuzzy number
ISSN:2666-7207, 2666-7207
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Abstract Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many approaches, such as the α−cut technique, extension principle, vertex method, etc., to execute arithmetic operations on fuzzy numbers. In this study we perform details analysis and interpretation on arithmetic operations based on the α−cut method in a new way.
AbstractList Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for every element in the set. There are several strategies for arithmetic operations on fuzzy numbers. Previous studies show that there are many approaches, such as the α−cut technique, extension principle, vertex method, etc., to execute arithmetic operations on fuzzy numbers. In this study we perform details analysis and interpretation on arithmetic operations based on the α−cut method in a new way.
ArticleNumber 100312
Author Ghosh, Arijit
Mukherjee, Asesh Kumar
Gazi, Kamal Hossain
Salahshour, Soheil
Mondal, Sankar Prasad
Author_xml – sequence: 1
  givenname: Asesh Kumar
  surname: Mukherjee
  fullname: Mukherjee, Asesh Kumar
  organization: Department of Mathematics, Haringhata Mahavidyalaya, Subarnapur, Nadia741249, West Bengal, India
– sequence: 2
  givenname: Kamal Hossain
  orcidid: 0000-0001-7179-984X
  surname: Gazi
  fullname: Gazi, Kamal Hossain
  email: kamalhossain.gazi@makautwb.ac.in
  organization: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, West Bengal, India
– sequence: 3
  givenname: Soheil
  surname: Salahshour
  fullname: Salahshour, Soheil
  organization: Faculty of Engineering and Natural Sciences, Istanbul Okan University, Istanbul, Turkey
– sequence: 4
  givenname: Arijit
  surname: Ghosh
  fullname: Ghosh, Arijit
  organization: Department of Mathematics, St. Xavier's College (Autonomous), Kolkata 700016, India
– sequence: 5
  givenname: Sankar Prasad
  orcidid: 0000-0003-4690-2598
  surname: Mondal
  fullname: Mondal, Sankar Prasad
  organization: Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata 741249, West Bengal, India
BookMark eNp9kF1LwzAUhoNMcM79Aa_yBzrz0aYNeFOH08F0N3od0vREU7Z2JJ2w_XqzVcQrISHhhffhnOcajdquBYRuKZlRQsVdM_POdDNGGI8B4ZRdoDETQiQ5I_noz_8KTUNoCCGsoDTeMXop8YN3YHHZ6s0huIB1W-Nl24Pfeeh177oWx1N6139uoXcGr3fgz3nAncWL_fF4wK_7bQU-3KBLqzcBpj_vBL0vHt_mz8lq_bScl6vEcEH7pOA1B1alqaWpLeqKygxMZUFakmUZqRjJilSwVMiskiKrC2MYtxK4MMSYIuMTtBy4dacbtfNuq_1Bddqpc9D5D6V9nHUDSkdDtJa5rWQEcloUkaUtBylTW-c0stjAMr4LwYP95VGiTn5Vo05-1cmvGvzG0v1QgrjllwOvgnHQGqidB9PHMdx_9W-9o4RS
Cites_doi 10.3390/buildings13010152
10.1016/j.autcon.2023.104858
10.1504/IJMOR.2013.057491
10.5121/ijfls.2013.3302
10.1016/j.fss.2010.09.016
10.5899/2016/ojids-00004
10.1002/mma.7228
10.14445/22315373/IJMTT-V66I12P505
10.1002/mma.7305
10.1080/03081078608934952
10.1080/00207727808941724
10.1016/S0020-7373(83)80038-8
10.9734/ARJOM/2017/31578
10.4304/jsw.4.4.331-338
10.1016/j.fss.2014.05.005
10.3390/sym12040572
10.1016/0165-0114(94)90097-3
10.1007/s00500-021-05909-9
10.3390/sym11020248
10.1016/j.engappai.2019.06.003
10.1051/ro/2023025
10.1016/S0198-9715(02)00069-8
10.1108/JQME-10-2022-0062
10.1007/s12597-014-0194-1
10.1504/IJMOR.2013.050512
10.5121/ijfls.2017.7103
10.1016/S0165-0114(99)00053-6
10.1016/j.asoc.2023.110213
10.1007/978-3-319-59614-3_1
10.1016/S0019-9958(65)90241-X
10.1016/j.engappai.2022.105747
10.1109/ACCESS.2022.3205305
10.1007/s00521-015-2110-x
10.1016/j.ijpe.2012.02.009
10.3390/info8020051
10.1016/j.apm.2012.01.036
10.1016/0020-0255(75)90017-1
10.1007/s40815-022-01425-6
10.1007/BF02977589
10.1007/978-3-7908-1870-3_2
10.3390/axioms12030277
10.3390/systems11050231
10.1016/j.ins.2013.06.055
10.1007/s40096-018-0242-8
10.1016/S0165-0114(86)80034-3
10.1109/TFUZZ.2006.889755
10.1016/j.ins.2015.07.045
10.1002/malq.19760220120
10.1007/s12065-007-0001-5
10.1109/TFUZZ.2003.822678
ContentType Journal Article
Copyright 2023 The Author(s)
Copyright_xml – notice: 2023 The Author(s)
DBID 6I.
AAFTH
AAYXX
CITATION
DOA
DOI 10.1016/j.rico.2023.100312
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
CrossRef
DOAJ Directory of Open Access Journals
DatabaseTitle CrossRef
DatabaseTitleList

Database_xml – sequence: 1
  dbid: DOA
  name: DOAJ Directory of Open Access Journals
  url: https://www.doaj.org/
  sourceTypes: Open Website
DeliveryMethod fulltext_linktorsrc
Discipline Engineering
EISSN 2666-7207
ExternalDocumentID oai_doaj_org_article_a0161d97fb92463188c23af3e994fd71
10_1016_j_rico_2023_100312
S2666720723001145
GroupedDBID 0R~
6I.
AAEDW
AAFTH
AALRI
AAXUO
ADVLN
AFJKZ
AITUG
AKRWK
ALMA_UNASSIGNED_HOLDINGS
AMRAJ
EBS
FDB
GROUPED_DOAJ
M~E
OK1
ROL
AAYWO
AAYXX
ACVFH
ADCNI
AEUPX
AFPUW
AIGII
AKBMS
AKYEP
APXCP
CITATION
ID FETCH-LOGICAL-c361t-83d3e2b44f14f8db195ecbfe9f05550b20584624695b965d8cc23f9e36c0cc853
IEDL.DBID DOA
ISICitedReferencesCount 18
ISICitedReferencesURI http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001208993700001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D
ISSN 2666-7207
IngestDate Fri Oct 03 12:45:53 EDT 2025
Sat Nov 29 02:35:28 EST 2025
Sat Nov 16 15:57:10 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Keywords α–cut set
Fuzzy sets
Arithmetic operations of fuzzy numbers
Triangular fuzzy number
Language English
License This is an open access article under the CC BY license.
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c361t-83d3e2b44f14f8db195ecbfe9f05550b20584624695b965d8cc23f9e36c0cc853
ORCID 0000-0003-4690-2598
0000-0001-7179-984X
OpenAccessLink https://doaj.org/article/a0161d97fb92463188c23af3e994fd71
ParticipantIDs doaj_primary_oai_doaj_org_article_a0161d97fb92463188c23af3e994fd71
crossref_primary_10_1016_j_rico_2023_100312
elsevier_sciencedirect_doi_10_1016_j_rico_2023_100312
PublicationCentury 2000
PublicationDate December 2023
2023-12-00
2023-12-01
PublicationDateYYYYMMDD 2023-12-01
PublicationDate_xml – month: 12
  year: 2023
  text: December 2023
PublicationDecade 2020
PublicationTitle Results in control and optimization
PublicationYear 2023
Publisher Elsevier B.V
Elsevier
Publisher_xml – name: Elsevier B.V
– name: Elsevier
References Zadeh (bib0001) 1965; 8
Riera, Torrens (bib0029) 2015; 264
Arfina, Ali (bib0064) 2020; 66
Parvathi, Malathi (bib0052) 2012; 1
Wu (bib0066) 2023; 12
Chakraborty, Jana, Roy (bib0017) 2015; 52
Tamilarasi, Paulraj (bib0065) 2020
Yager (bib0010) 2013
Garibaldi, Ozen (bib0008) 2007; 15
Rama, Rosario (bib0063) 2019; 10
Momena, Mandal, Gazi, Giri, Mondal (bib0031) 2023; 11
Klir, Yuan (bib0080) 1996; 32
Casasnovas, Riera (bib0027) 2011; 167
Seikh, Nayak, Pal (bib0035) 2013; 5
Grattan-Guinness (bib0003) 1976; 22
Sahayasudha, Vijayalakshmi (bib0059) 2017; 7
Smarandache (bib0007) 1999
Voxman (bib0025) 2001; 118
Alshammari, Al-Smadi, Arqub, Hashim, Alias (bib0039) 2020; 12
Abu Arqub, Singh, Maayah, Alhodaly (bib0041) 2023; 46
Fateminia, Fayek (bib0071) 2023; 151
Hanss (bib0051) 1999
Mondal, Mandal (bib0014) 2017; 2
Vanitha (bib0062) 2018; 9
Raj, Sivaraman, Vishnukumar (bib0070) 2023; 25
Wang, Shi, Xie, Shi (bib0037) 2016; 326
Alzahrani, Ghorui, Gazi, Giri, Ghosh, Mondal (bib0046) 2023; 13
Liu, Phinn (bib0047) 2003; 27
Ranjbar, Miri, Effati (bib0024) 2022; 19
Abu Arqub, Singh, Alhodaly (bib0040) 2023; 46
Khajuria (bib0067) 2023
Dutta, Boruah, Ali (bib0072) 2011; 2
Yager (bib0005) 1986; 13
Gani, Assarudeen (bib0020) 2012; 6
Abbasi, F. (2016). The fuzzy arithmetic operations of transmission average on pseudo-pentagonal fuzzy numbers.
Jana (bib0016) 2016; 18
Weckenmann, Schwan (bib0074) 2001; 6
Jezewski, Czabanski, Leski, Prokopowicz, Czerniak, Mikołajewski, Apiecionek (bib0075) 2017; 356
Thiripurasundari, K., Latha, K., & Valli, D. (2019). A Study on Arithmetic Operations of Type-2 Triangular Mixed Fuzzy Numbers.
Abu Arqub (bib0036) 2017; 28
Atanassov, Stoeva (bib0004) 1986; 20
Herrera (bib0048) 2008; 1
Rajarajeswari, Sudha, Karthika (bib0053) 2013; 3
Chameau, Alteschaeffl, Michael, Yao (bib0050) 1983; 19
Tudu, Gazi, Rahaman, Mondal, Chatterjee, Alam (bib0078) 2023; 25
Massanet, Riera, Torrens, Herrera-Viedma (bib0028) 2014; 258
Mahapatra, Roy (bib0033) 2013; 7
Sudha, Gokilamani (bib0073) 2017; 7
Dubois, Prade (bib0013) 1978; 9
Chakraborty, Mondal, Alam, Ahmadian, Senu, De, Salahshour (bib0032) 2019; 11
Gündoğdu, Kahraman (bib0011) 2019; 85
Deschrijver, Cornelis, Kerre (bib0021) 2004; 12
Yeganehmanesh, Amirfakhrian, Grzegorzewski (bib0030) 2018; 12
Xiao, Xia, Gong, Li (bib0077) 2012; 36
Pathinathan, Santhoshkumar (bib0061) 2018; 7
Gao, Zhang, Cao (bib0022) 2009; 4
Liu, Fu, Wang, Gao, Li, Peng, Chen (bib0049) 2022; 10
Atanassov, Atanassov (bib0006) 1999
Shaw, Roy (bib0018) 2013; 5
Vahidi, Rezvani (bib0054) 2013; 2013
Aydın, Kutlu Gündoğdu (bib0012) 2021
Chandrasekaran, Tamilmani (bib0055) 2015; 2
Gazi, Mondal, Chatterjee, Ghorui, Ghosh, De (bib0045) 2023; 57
Wang, Zheng (bib0068) 2023; 467
Ayağ, Özdemir (bib0076) 2012; 140
Si, Das, Kar (bib0042) 2023; 27
Minj, Pathinathan (bib0038) 2018; 9
Shaocheng (bib0079) 1994; 66
Singh, Gor, Gazi, Mukherjee, Mahata, Mondal (bib0015) 2023
Naveena, N. R., & RajNumar, A. A New Reverse Order Pentadecagonal, Nanogonal and Decagonal Fuzzy Number with Arithmetic Operations. Int J Rec Tech Eng (IJRTE) ISSN, 2277-3878.
Du, Fan, Wang, Wang, Qian, Zhu (bib0044) 2023; 139
Gohain, Chutia, Dutta (bib0043) 2023; 119
Zadeh (bib0002) 1975; 9
Torra (bib0009) 2010; 25
Shapique (bib0058) 2017; 2
Sudha, Anitha (bib0056) 2015; 112
Ye (bib0060) 2017; 8
Wang, Zhang, Cui (bib0026) 2008
Abbasi (bib0034) 2019; 11
Kumar, Singh (bib0069) 2023
Wang (10.1016/j.rico.2023.100312_bib0026) 2008
Gündoğdu (10.1016/j.rico.2023.100312_bib0011) 2019; 85
Si (10.1016/j.rico.2023.100312_bib0042) 2023; 27
Grattan-Guinness (10.1016/j.rico.2023.100312_bib0003) 1976; 22
Garibaldi (10.1016/j.rico.2023.100312_bib0008) 2007; 15
Liu (10.1016/j.rico.2023.100312_bib0049) 2022; 10
Yager (10.1016/j.rico.2023.100312_bib0005) 1986; 13
Liu (10.1016/j.rico.2023.100312_bib0047) 2003; 27
Arfina (10.1016/j.rico.2023.100312_bib0064) 2020; 66
Klir (10.1016/j.rico.2023.100312_bib0080) 1996; 32
Chameau (10.1016/j.rico.2023.100312_bib0050) 1983; 19
Minj (10.1016/j.rico.2023.100312_bib0038) 2018; 9
Aydın (10.1016/j.rico.2023.100312_bib0012) 2021
Jezewski (10.1016/j.rico.2023.100312_bib0075) 2017; 356
Wang (10.1016/j.rico.2023.100312_bib0037) 2016; 326
Zadeh (10.1016/j.rico.2023.100312_bib0001) 1965; 8
Gani (10.1016/j.rico.2023.100312_bib0020) 2012; 6
Gao (10.1016/j.rico.2023.100312_bib0022) 2009; 4
Du (10.1016/j.rico.2023.100312_bib0044) 2023; 139
Wang (10.1016/j.rico.2023.100312_bib0068) 2023; 467
Pathinathan (10.1016/j.rico.2023.100312_bib0061) 2018; 7
Shaocheng (10.1016/j.rico.2023.100312_bib0079) 1994; 66
Torra (10.1016/j.rico.2023.100312_bib0009) 2010; 25
Deschrijver (10.1016/j.rico.2023.100312_bib0021) 2004; 12
Tamilarasi (10.1016/j.rico.2023.100312_bib0065) 2020
Gazi (10.1016/j.rico.2023.100312_bib0045) 2023; 57
Casasnovas (10.1016/j.rico.2023.100312_bib0027) 2011; 167
Alzahrani (10.1016/j.rico.2023.100312_bib0046) 2023; 13
Jana (10.1016/j.rico.2023.100312_bib0016) 2016; 18
Sahayasudha (10.1016/j.rico.2023.100312_bib0059) 2017; 7
Vanitha (10.1016/j.rico.2023.100312_bib0062) 2018; 9
Abu Arqub (10.1016/j.rico.2023.100312_bib0040) 2023; 46
Gohain (10.1016/j.rico.2023.100312_bib0043) 2023; 119
Seikh (10.1016/j.rico.2023.100312_bib0035) 2013; 5
Rama (10.1016/j.rico.2023.100312_bib0063) 2019; 10
Herrera (10.1016/j.rico.2023.100312_bib0048) 2008; 1
Abu Arqub (10.1016/j.rico.2023.100312_bib0036) 2017; 28
Voxman (10.1016/j.rico.2023.100312_bib0025) 2001; 118
Vahidi (10.1016/j.rico.2023.100312_bib0054) 2013; 2013
Raj (10.1016/j.rico.2023.100312_bib0070) 2023; 25
Tudu (10.1016/j.rico.2023.100312_bib0078) 2023; 25
Shaw (10.1016/j.rico.2023.100312_bib0018) 2013; 5
Chandrasekaran (10.1016/j.rico.2023.100312_bib0055) 2015; 2
Weckenmann (10.1016/j.rico.2023.100312_bib0074) 2001; 6
Ayağ (10.1016/j.rico.2023.100312_bib0076) 2012; 140
Atanassov (10.1016/j.rico.2023.100312_bib0006) 1999
Dutta (10.1016/j.rico.2023.100312_bib0072) 2011; 2
Alshammari (10.1016/j.rico.2023.100312_bib0039) 2020; 12
Shapique (10.1016/j.rico.2023.100312_bib0058) 2017; 2
10.1016/j.rico.2023.100312_bib0023
Chakraborty (10.1016/j.rico.2023.100312_bib0017) 2015; 52
Hanss (10.1016/j.rico.2023.100312_bib0051) 1999
Khajuria (10.1016/j.rico.2023.100312_bib0067) 2023
Yeganehmanesh (10.1016/j.rico.2023.100312_bib0030) 2018; 12
Riera (10.1016/j.rico.2023.100312_bib0029) 2015; 264
Ranjbar (10.1016/j.rico.2023.100312_bib0024) 2022; 19
Sudha (10.1016/j.rico.2023.100312_bib0056) 2015; 112
Dubois (10.1016/j.rico.2023.100312_bib0013) 1978; 9
Massanet (10.1016/j.rico.2023.100312_bib0028) 2014; 258
Xiao (10.1016/j.rico.2023.100312_bib0077) 2012; 36
Zadeh (10.1016/j.rico.2023.100312_bib0002) 1975; 9
Abbasi (10.1016/j.rico.2023.100312_bib0034) 2019; 11
Abu Arqub (10.1016/j.rico.2023.100312_bib0041) 2023; 46
Kumar (10.1016/j.rico.2023.100312_bib0069) 2023
Yager (10.1016/j.rico.2023.100312_bib0010) 2013
Chakraborty (10.1016/j.rico.2023.100312_bib0032) 2019; 11
Ye (10.1016/j.rico.2023.100312_bib0060) 2017; 8
Singh (10.1016/j.rico.2023.100312_bib0015) 2023
Smarandache (10.1016/j.rico.2023.100312_bib0007) 1999
10.1016/j.rico.2023.100312_bib0019
10.1016/j.rico.2023.100312_bib0057
Sudha (10.1016/j.rico.2023.100312_bib0073) 2017; 7
Mahapatra (10.1016/j.rico.2023.100312_bib0033) 2013; 7
Rajarajeswari (10.1016/j.rico.2023.100312_bib0053) 2013; 3
Wu (10.1016/j.rico.2023.100312_bib0066) 2023; 12
Atanassov (10.1016/j.rico.2023.100312_bib0004) 1986; 20
Mondal (10.1016/j.rico.2023.100312_bib0014) 2017; 2
Parvathi (10.1016/j.rico.2023.100312_bib0052) 2012; 1
Fateminia (10.1016/j.rico.2023.100312_bib0071) 2023; 151
Momena (10.1016/j.rico.2023.100312_bib0031) 2023; 11
References_xml – volume: 467
  year: 2023
  ident: bib0068
  article-title: A class of fuzzy numbers induced by probability density functions and their arithmetic operations
  publication-title: Fuzz Set Syst
– volume: 5
  start-page: 55
  year: 2013
  end-page: 73
  ident: bib0018
  article-title: Trapezoidal Intuitionistic Fuzzy Number with some arithmetic operations and its application on reliability evaluation
  publication-title: Int J Math Oper Res
– volume: 139
  year: 2023
  ident: bib0044
  article-title: A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic
  publication-title: Appl Soft Comput
– year: 2023
  ident: bib0067
  article-title: Intuitionistic fuzzy fault tree analysis of PCBA using novel arithmetic operations
  publication-title: J Qual Maint Eng
– volume: 9
  start-page: 613
  year: 1978
  end-page: 626
  ident: bib0013
  article-title: Operations on fuzzy numbers
  publication-title: Int J Syst Sci
– volume: 12
  start-page: 45
  year: 2004
  end-page: 61
  ident: bib0021
  article-title: On the representation of intuitionistic fuzzy t-norms and t-conorms
  publication-title: IEEE Trans Fuzzy Syst
– volume: 2
  start-page: 1
  year: 2017
  end-page: 25
  ident: bib0058
  article-title: Arithmetic Operations on heptagonal fuzzy numbers
  publication-title: Asian Res J Math
– volume: 4
  start-page: 331
  year: 2009
  end-page: 338
  ident: bib0022
  article-title: Multiplication Operation on Fuzzy Numbers
  publication-title: J Softw
– volume: 57
  start-page: 571
  year: 2023
  end-page: 608
  ident: bib0045
  article-title: A new synergistic strategy for ranking restaurant locations: A decision-making approach based on the hexagonal fuzzy numbers
  publication-title: RAIRO-Oper Res
– volume: 112
  start-page: 14
  year: 2015
  end-page: 16
  ident: bib0056
  article-title: Solving a interval fuzzy linear programming problem using alpha-cut operation
  publication-title: Int J Comp Appl
– volume: 2
  start-page: 99
  year: 2011
  end-page: 107
  ident: bib0072
  article-title: Fuzzy Arithmetic with and without using α-cut method: A Comparative Study
  publication-title: Int J Latest Trend Comput
– volume: 7
  start-page: 92
  year: 2013
  end-page: 107
  ident: bib0033
  article-title: Intuitionistic fuzzy number and its arithmetic operation with application on system failure
  publication-title: J Uncert Syst
– volume: 13
  start-page: 152
  year: 2023
  ident: bib0046
  article-title: Optimal site selection for women university using neutrosophic multi-criteria decision making approach
  publication-title: Buildings
– volume: 2
  start-page: 110
  year: 2017
  end-page: 117
  ident: bib0014
  article-title: Pentagonal fuzzy number, its properties and application in fuzzy equation
  publication-title: Fut Comput Inform J
– year: 2020
  ident: bib0065
  article-title: Linear Programming Problems with Icosikaipentagonal Fuzzy Number
  publication-title: Int J Trend Sci Res Dev
– reference: Naveena, N. R., & RajNumar, A. A New Reverse Order Pentadecagonal, Nanogonal and Decagonal Fuzzy Number with Arithmetic Operations. Int J Rec Tech Eng (IJRTE) ISSN, 2277-3878.
– volume: 5
  start-page: 693
  year: 2013
  end-page: 708
  ident: bib0035
  article-title: Matrix games in intuitionistic fuzzy environment
  publication-title: Int J Math Oper Res
– volume: 52
  start-page: 431
  year: 2015
  end-page: 471
  ident: bib0017
  article-title: Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem
  publication-title: Opsearch
– volume: 25
  start-page: 33
  year: 2023
  end-page: 53
  ident: bib0078
  article-title: Type-2 fuzzy differential inclusion for solving type-2 fuzzy differential equation
  publication-title: Ann Fuzz Math Inform
– volume: 10
  start-page: 1466
  year: 2019
  end-page: 1475
  ident: bib0063
  article-title: Quadrant Fuzzy Number and its Arithmetic Operations
  publication-title: J Comp Math Sci
– volume: 66
  start-page: 301
  year: 1994
  end-page: 306
  ident: bib0079
  article-title: Interval number and fuzzy number linear programmings
  publication-title: Fuzz Set Syst
– volume: 12
  start-page: 572
  year: 2020
  ident: bib0039
  article-title: Residual series representation algorithm for solving fuzzy duffing oscillator equations
  publication-title: Symmetry
– volume: 151
  year: 2023
  ident: bib0071
  article-title: Hybrid fuzzy arithmetic-based model for determining contingency reserve
  publication-title: Autom Constr
– volume: 25
  start-page: 529
  year: 2010
  end-page: 539
  ident: bib0009
  article-title: Hesitant fuzzy sets
  publication-title: Int J Intell Syst
– volume: 326
  start-page: 258
  year: 2016
  end-page: 269
  ident: bib0037
  article-title: Two-dimensional discrete fuzzy numbers and applications
  publication-title: Inform Sci
– volume: 20
  start-page: 87
  year: 1986
  end-page: 96
  ident: bib0004
  article-title: Intuitionistic fuzzy sets
  publication-title: Fuzzy Sets Syst
– start-page: 139
  year: 1999
  end-page: 177
  ident: bib0006
  article-title: Interval valued intuitionistic fuzzy sets
  publication-title: Intuitionist Fuzzy Sets Theo Appl
– volume: 167
  start-page: 65
  year: 2011
  end-page: 81
  ident: bib0027
  article-title: Extension of discrete t-norms and t-conorms to discrete fuzzy numbers
  publication-title: Fuzz Set Syst
– volume: 12
  start-page: 277
  year: 2023
  ident: bib0066
  article-title: New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility
  publication-title: Axioms
– volume: 258
  start-page: 277
  year: 2014
  end-page: 290
  ident: bib0028
  article-title: A new linguistic computational model based on discrete fuzzy numbers for computing with words
  publication-title: Inform Sci
– volume: 8
  start-page: 51
  year: 2017
  ident: bib0060
  article-title: Subtraction and division operations of simplified neutrosophic sets
  publication-title: Information
– start-page: 812
  year: 2008
  end-page: 817
  ident: bib0026
  article-title: The discrete fuzzy numbers on a fixed set with finite support set
  publication-title: 2008 IEEE Conference on Cybernetics and Intelligent Systems
– start-page: 57
  year: 2013
  end-page: 61
  ident: bib0010
  article-title: Pythagorean fuzzy subsets
  publication-title: 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS)
– volume: 140
  start-page: 630
  year: 2012
  end-page: 636
  ident: bib0076
  article-title: Evaluating machine tool alternatives through modified TOPSIS and alpha-cut based fuzzy ANP
  publication-title: Int J Prod Econ
– volume: 9
  start-page: 43
  year: 1975
  end-page: 80
  ident: bib0002
  article-title: The concept of a linguistic variable and its application to approximate reasoning-III
  publication-title: Inform Sci
– volume: 11
  start-page: 231
  year: 2023
  ident: bib0031
  article-title: Prediagnosis of Disease Based on Symptoms by Generalized Dual Hesitant Hexagonal Fuzzy Multi-Criteria Decision-Making Techniques
  publication-title: Systems
– volume: 7
  start-page: 17
  year: 2017
  end-page: 26
  ident: bib0073
  article-title: An arithmetic operation on hexadecagonal fuzzy number
  publication-title: Int J Fuzz Log Syst
– volume: 28
  start-page: 1591
  year: 2017
  end-page: 1610
  ident: bib0036
  article-title: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations
  publication-title: Neural Comput Appl
– volume: 22
  start-page: 149
  year: 1976
  end-page: 160
  ident: bib0003
  article-title: Fuzzy membership mapped onto intervals and many-valued quantities
  publication-title: Math Logic Quart
– volume: 7
  start-page: 1018
  year: 2018
  end-page: 1021
  ident: bib0061
  article-title: Quadrilateral fuzzy number
  publication-title: Int J Eng Tech
– volume: 46
  start-page: 7807
  year: 2023
  end-page: 7834
  ident: bib0040
  article-title: Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations
  publication-title: Math Method Appl Sci
– volume: 13
  start-page: 23
  year: 1986
  end-page: 37
  ident: bib0005
  article-title: On the theory of bags
  publication-title: Int J Gen Syst
– volume: 3
  start-page: 15
  year: 2013
  end-page: 26
  ident: bib0053
  article-title: A new operation on hexagonal fuzzy number
  publication-title: Int J Fuzz Log Syst
– volume: 15
  start-page: 16
  year: 2007
  end-page: 30
  ident: bib0008
  article-title: Uncertain fuzzy reasoning: a case study in modelling expert decision making
  publication-title: IEEE Trans Fuzzy Syst
– start-page: 462
  year: 1999
  end-page: 466
  ident: bib0051
  article-title: On the implementation of fuzzy arithmetical operations for engineering problems
  publication-title: 18th International Conference of the North American Fuzzy Information Processing Society-NAFIPS (Cat. No. 99TH8397)
– volume: 85
  start-page: 307
  year: 2019
  end-page: 323
  ident: bib0011
  article-title: A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets
  publication-title: Eng Appl Artif Intell
– volume: 12
  start-page: 41
  year: 2018
  end-page: 52
  ident: bib0030
  article-title: Fuzzy semi-numbers and a distance on them with a case study in medicine
  publication-title: Math Sci
– volume: 25
  start-page: 1069
  year: 2023
  end-page: 1076
  ident: bib0070
  article-title: A Novel Kind of Arithmetic Operations on Trapezoidal Fuzzy Numbers and Its Applications to Optimize the Transportation Cost
  publication-title: Int J Fuzzy Syst
– volume: 11
  start-page: 203
  year: 2019
  end-page: 212
  ident: bib0034
  article-title: New A rithmetic Operations on Developed Parabolic Fuzzy Numbers and Its Application
  publication-title: Int J Indust Math
– volume: 1
  start-page: 27
  year: 2008
  end-page: 46
  ident: bib0048
  article-title: Genetic fuzzy systems: taxonomy, current research trends and prospects
  publication-title: Evolut Intellig
– volume: 36
  start-page: 5844
  year: 2012
  end-page: 5855
  ident: bib0077
  article-title: The trapezoidal fuzzy soft set and its application in MCDM
  publication-title: Appl Math Modell
– volume: 46
  start-page: 7965
  year: 2023
  end-page: 7986
  ident: bib0041
  article-title: Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator
  publication-title: Math Method Appl Sci
– volume: 10
  start-page: 103349
  year: 2022
  end-page: 103363
  ident: bib0049
  article-title: Research on Cobot Action Decision-Making Method Based on Intuitionistic Fuzzy Set and Game Theory
  publication-title: IEEE Access
– volume: 9
  start-page: 650
  year: 2018
  end-page: 655
  ident: bib0062
  article-title: Fuzzy time series forecasting in enrollment by interval method
  publication-title: Int J Manage IT Eng
– start-page: 1
  year: 2023
  end-page: 16
  ident: bib0069
  article-title: Analysis of system reliability based on weakest t-norm arithmetic operations using Pythagorean fuzzy numbers
  publication-title: Int J Syst Assur Eng Manage
– volume: 66
  start-page: 28
  year: 2020
  end-page: 36
  ident: bib0064
  article-title: Alternative Arithmetic of Pentagonal Fuzzy Numbers
  publication-title: Int J Math Trend Tech
– year: 2023
  ident: bib0015
  article-title: Analysis and interpretation of Malaria disease model in crisp and fuzzy environment
  publication-title: Result Cont Optim
– volume: 356
  year: 2017
  ident: bib0075
  article-title: Introduction to Fuzzy Sets
  publication-title: Theory and Applications of Ordered Fuzzy Numbers
– volume: 19
  start-page: 97
  year: 2022
  end-page: 114
  ident: bib0024
  article-title: Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle
  publication-title: Iran J Fuzz Syst
– start-page: 1
  year: 1999
  end-page: 141
  ident: bib0007
  article-title: A unifying field in Logics: Neutrosophic Logic
  publication-title: Philosophy
– reference: Abbasi, F. (2016). The fuzzy arithmetic operations of transmission average on pseudo-pentagonal fuzzy numbers.
– volume: 32
  start-page: 207
  year: 1996
  end-page: 208
  ident: bib0080
  article-title: Fuzzy sets and fuzzy logic: theory and applications
  publication-title: Possib Theo Probab Theo
– volume: 2013
  start-page: 1
  year: 2013
  end-page: 8
  ident: bib0054
  article-title: Arithmetic operations on trapezoidal fuzzy numbers
  publication-title: J Nonlin Anal Appl
– start-page: 295
  year: 2021
  end-page: 322
  ident: bib0012
  article-title: Interval-valued spherical fuzzy MULTIMOORA method and its application to industry 4.0
  publication-title: Deci Mak Spher Fuzz Set Theo Appl
– volume: 119
  year: 2023
  ident: bib0043
  article-title: A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications
  publication-title: Eng Appl Artif Intell
– volume: 118
  start-page: 457
  year: 2001
  end-page: 466
  ident: bib0025
  article-title: Canonical representations of discrete fuzzy numbers
  publication-title: Fuzz Set Syst
– volume: 1
  start-page: 1
  year: 2012
  ident: bib0052
  article-title: Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers
  publication-title: A A
– volume: 11
  start-page: 248
  year: 2019
  ident: bib0032
  article-title: The pentagonal fuzzy number: its different representations, properties, ranking, defuzzification and application in game problems
  publication-title: Symmetry
– volume: 7
  start-page: 31
  year: 2017
  end-page: 48
  ident: bib0059
  article-title: An alpha-cut operation in a transportation problem using symmetric hexagonal fuzzy numbers
  publication-title: Int J Fuzz Log Syst
– volume: 8
  start-page: 338
  year: 1965
  end-page: 353
  ident: bib0001
  article-title: Fuzzy sets
  publication-title: Inform Control
– volume: 18
  start-page: 178
  year: 2016
  end-page: 189
  ident: bib0016
  article-title: Novel arithmetic operations on type-2 intuitionistic fuzzy and its applications to transportation problem
  publication-title: Pacif Sci Rev A Nat Sci Eng
– volume: 6
  start-page: 525
  year: 2012
  end-page: 532
  ident: bib0020
  article-title: A new operation on triangular fuzzy number for solving fuzzy linear programming problem
  publication-title: Appl Math Sci
– reference: Thiripurasundari, K., Latha, K., & Valli, D. (2019). A Study on Arithmetic Operations of Type-2 Triangular Mixed Fuzzy Numbers.
– volume: 9
  start-page: 1717
  year: 2018
  end-page: 1727
  ident: bib0038
  article-title: Totally symmetric type-2 triangular fuzzy numbers
  publication-title: J Comp Math Sci
– volume: 27
  start-page: 637
  year: 2003
  end-page: 658
  ident: bib0047
  article-title: Modelling urban development with cellular automata incorporating fuzzy-set approaches
  publication-title: Comp Environ Urb Syst
– volume: 264
  start-page: 121
  year: 2015
  end-page: 137
  ident: bib0029
  article-title: Using discrete fuzzy numbers in the aggregation of incomplete qualitative information
  publication-title: Fuzz Set Syst
– volume: 6
  start-page: 13
  year: 2001
  end-page: 18
  ident: bib0074
  article-title: Environmental life cycle assessment with support of fuzzy-sets
  publication-title: Int J Life Cycle Assess
– volume: 2
  year: 2015
  ident: bib0055
  article-title: Applications Of Fuzzy Number Mathematics
  publication-title: Int J Innov Sci Eng Tech
– volume: 27
  start-page: 3327
  year: 2023
  end-page: 3341
  ident: bib0042
  article-title: Picture fuzzy set-based decision-making approach using Dempster–Shafer theory of evidence and grey relation analysis and its application in COVID-19 medicine selection
  publication-title: Soft Comput
– volume: 19
  start-page: 9
  year: 1983
  end-page: 18
  ident: bib0050
  article-title: Potential applications of fuzzy sets in civil engineering
  publication-title: Int J Man Mach Stud
– volume: 13
  start-page: 152
  issue: 1
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0046
  article-title: Optimal site selection for women university using neutrosophic multi-criteria decision making approach
  publication-title: Buildings
  doi: 10.3390/buildings13010152
– volume: 151
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0071
  article-title: Hybrid fuzzy arithmetic-based model for determining contingency reserve
  publication-title: Autom Constr
  doi: 10.1016/j.autcon.2023.104858
– volume: 5
  start-page: 693
  issue: 6
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0035
  article-title: Matrix games in intuitionistic fuzzy environment
  publication-title: Int J Math Oper Res
  doi: 10.1504/IJMOR.2013.057491
– volume: 3
  start-page: 15
  issue: 3
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0053
  article-title: A new operation on hexagonal fuzzy number
  publication-title: Int J Fuzz Log Syst
  doi: 10.5121/ijfls.2013.3302
– volume: 2
  issue: 11
  year: 2015
  ident: 10.1016/j.rico.2023.100312_bib0055
  article-title: Applications Of Fuzzy Number Mathematics
  publication-title: Int J Innov Sci Eng Tech
– volume: 112
  start-page: 14
  issue: 10
  year: 2015
  ident: 10.1016/j.rico.2023.100312_bib0056
  article-title: Solving a interval fuzzy linear programming problem using alpha-cut operation
  publication-title: Int J Comp Appl
– volume: 167
  start-page: 65
  issue: 1
  year: 2011
  ident: 10.1016/j.rico.2023.100312_bib0027
  article-title: Extension of discrete t-norms and t-conorms to discrete fuzzy numbers
  publication-title: Fuzz Set Syst
  doi: 10.1016/j.fss.2010.09.016
– ident: 10.1016/j.rico.2023.100312_bib0057
  doi: 10.5899/2016/ojids-00004
– volume: 46
  start-page: 7807
  issue: 7
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0040
  article-title: Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations
  publication-title: Math Method Appl Sci
  doi: 10.1002/mma.7228
– volume: 66
  start-page: 28
  issue: 12
  year: 2020
  ident: 10.1016/j.rico.2023.100312_bib0064
  article-title: Alternative Arithmetic of Pentagonal Fuzzy Numbers
  publication-title: Int J Math Trend Tech
  doi: 10.14445/22315373/IJMTT-V66I12P505
– volume: 46
  start-page: 7965
  issue: 7
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0041
  article-title: Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator
  publication-title: Math Method Appl Sci
  doi: 10.1002/mma.7305
– volume: 7
  start-page: 1018
  issue: 4-10
  year: 2018
  ident: 10.1016/j.rico.2023.100312_bib0061
  article-title: Quadrilateral fuzzy number
  publication-title: Int J Eng Tech
– volume: 13
  start-page: 23
  issue: 1
  year: 1986
  ident: 10.1016/j.rico.2023.100312_bib0005
  article-title: On the theory of bags
  publication-title: Int J Gen Syst
  doi: 10.1080/03081078608934952
– volume: 10
  start-page: 1466
  issue: 7
  year: 2019
  ident: 10.1016/j.rico.2023.100312_bib0063
  article-title: Quadrant Fuzzy Number and its Arithmetic Operations
  publication-title: J Comp Math Sci
– volume: 9
  start-page: 613
  issue: 6
  year: 1978
  ident: 10.1016/j.rico.2023.100312_bib0013
  article-title: Operations on fuzzy numbers
  publication-title: Int J Syst Sci
  doi: 10.1080/00207727808941724
– volume: 19
  start-page: 9
  issue: 1
  year: 1983
  ident: 10.1016/j.rico.2023.100312_bib0050
  article-title: Potential applications of fuzzy sets in civil engineering
  publication-title: Int J Man Mach Stud
  doi: 10.1016/S0020-7373(83)80038-8
– start-page: 462
  year: 1999
  ident: 10.1016/j.rico.2023.100312_bib0051
  article-title: On the implementation of fuzzy arithmetical operations for engineering problems
– start-page: 812
  year: 2008
  ident: 10.1016/j.rico.2023.100312_bib0026
  article-title: The discrete fuzzy numbers on a fixed set with finite support set
– ident: 10.1016/j.rico.2023.100312_bib0019
– volume: 2
  start-page: 1
  issue: 5
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0058
  article-title: Arithmetic Operations on heptagonal fuzzy numbers
  publication-title: Asian Res J Math
  doi: 10.9734/ARJOM/2017/31578
– volume: 4
  start-page: 331
  issue: 4
  year: 2009
  ident: 10.1016/j.rico.2023.100312_bib0022
  article-title: Multiplication Operation on Fuzzy Numbers
  publication-title: J Softw
  doi: 10.4304/jsw.4.4.331-338
– volume: 6
  start-page: 525
  issue: 11
  year: 2012
  ident: 10.1016/j.rico.2023.100312_bib0020
  article-title: A new operation on triangular fuzzy number for solving fuzzy linear programming problem
  publication-title: Appl Math Sci
– volume: 264
  start-page: 121
  year: 2015
  ident: 10.1016/j.rico.2023.100312_bib0029
  article-title: Using discrete fuzzy numbers in the aggregation of incomplete qualitative information
  publication-title: Fuzz Set Syst
  doi: 10.1016/j.fss.2014.05.005
– volume: 12
  start-page: 572
  issue: 4
  year: 2020
  ident: 10.1016/j.rico.2023.100312_bib0039
  article-title: Residual series representation algorithm for solving fuzzy duffing oscillator equations
  publication-title: Symmetry
  doi: 10.3390/sym12040572
– volume: 66
  start-page: 301
  issue: 3
  year: 1994
  ident: 10.1016/j.rico.2023.100312_bib0079
  article-title: Interval number and fuzzy number linear programmings
  publication-title: Fuzz Set Syst
  doi: 10.1016/0165-0114(94)90097-3
– volume: 9
  start-page: 650
  issue: 1
  year: 2018
  ident: 10.1016/j.rico.2023.100312_bib0062
  article-title: Fuzzy time series forecasting in enrollment by interval method
  publication-title: Int J Manage IT Eng
– volume: 18
  start-page: 178
  issue: 3
  year: 2016
  ident: 10.1016/j.rico.2023.100312_bib0016
  article-title: Novel arithmetic operations on type-2 intuitionistic fuzzy and its applications to transportation problem
  publication-title: Pacif Sci Rev A Nat Sci Eng
– volume: 9
  start-page: 1717
  issue: 11
  year: 2018
  ident: 10.1016/j.rico.2023.100312_bib0038
  article-title: Totally symmetric type-2 triangular fuzzy numbers
  publication-title: J Comp Math Sci
– volume: 27
  start-page: 3327
  issue: 6
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0042
  article-title: Picture fuzzy set-based decision-making approach using Dempster–Shafer theory of evidence and grey relation analysis and its application in COVID-19 medicine selection
  publication-title: Soft Comput
  doi: 10.1007/s00500-021-05909-9
– volume: 11
  start-page: 248
  issue: 2
  year: 2019
  ident: 10.1016/j.rico.2023.100312_bib0032
  article-title: The pentagonal fuzzy number: its different representations, properties, ranking, defuzzification and application in game problems
  publication-title: Symmetry
  doi: 10.3390/sym11020248
– start-page: 1
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0069
  article-title: Analysis of system reliability based on weakest t-norm arithmetic operations using Pythagorean fuzzy numbers
  publication-title: Int J Syst Assur Eng Manage
– volume: 1
  start-page: 1
  year: 2012
  ident: 10.1016/j.rico.2023.100312_bib0052
  article-title: Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers
  publication-title: A A
– volume: 85
  start-page: 307
  year: 2019
  ident: 10.1016/j.rico.2023.100312_bib0011
  article-title: A novel fuzzy TOPSIS method using emerging interval-valued spherical fuzzy sets
  publication-title: Eng Appl Artif Intell
  doi: 10.1016/j.engappai.2019.06.003
– start-page: 295
  year: 2021
  ident: 10.1016/j.rico.2023.100312_bib0012
  article-title: Interval-valued spherical fuzzy MULTIMOORA method and its application to industry 4.0
  publication-title: Deci Mak Spher Fuzz Set Theo Appl
– volume: 57
  start-page: 571
  issue: 2
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0045
  article-title: A new synergistic strategy for ranking restaurant locations: A decision-making approach based on the hexagonal fuzzy numbers
  publication-title: RAIRO-Oper Res
  doi: 10.1051/ro/2023025
– volume: 25
  start-page: 33
  issue: 1
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0078
  article-title: Type-2 fuzzy differential inclusion for solving type-2 fuzzy differential equation
  publication-title: Ann Fuzz Math Inform
– volume: 27
  start-page: 637
  issue: 6
  year: 2003
  ident: 10.1016/j.rico.2023.100312_bib0047
  article-title: Modelling urban development with cellular automata incorporating fuzzy-set approaches
  publication-title: Comp Environ Urb Syst
  doi: 10.1016/S0198-9715(02)00069-8
– year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0067
  article-title: Intuitionistic fuzzy fault tree analysis of PCBA using novel arithmetic operations
  publication-title: J Qual Maint Eng
  doi: 10.1108/JQME-10-2022-0062
– year: 2020
  ident: 10.1016/j.rico.2023.100312_bib0065
  article-title: Linear Programming Problems with Icosikaipentagonal Fuzzy Number
  publication-title: Int J Trend Sci Res Dev
– volume: 52
  start-page: 431
  year: 2015
  ident: 10.1016/j.rico.2023.100312_bib0017
  article-title: Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem
  publication-title: Opsearch
  doi: 10.1007/s12597-014-0194-1
– volume: 5
  start-page: 55
  issue: 1
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0018
  article-title: Trapezoidal Intuitionistic Fuzzy Number with some arithmetic operations and its application on reliability evaluation
  publication-title: Int J Math Oper Res
  doi: 10.1504/IJMOR.2013.050512
– volume: 7
  start-page: 31
  issue: 1
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0059
  article-title: An alpha-cut operation in a transportation problem using symmetric hexagonal fuzzy numbers
  publication-title: Int J Fuzz Log Syst
  doi: 10.5121/ijfls.2017.7103
– volume: 2013
  start-page: 1
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0054
  article-title: Arithmetic operations on trapezoidal fuzzy numbers
  publication-title: J Nonlin Anal Appl
– volume: 32
  start-page: 207
  issue: 2
  year: 1996
  ident: 10.1016/j.rico.2023.100312_bib0080
  article-title: Fuzzy sets and fuzzy logic: theory and applications
  publication-title: Possib Theo Probab Theo
– volume: 118
  start-page: 457
  issue: 3
  year: 2001
  ident: 10.1016/j.rico.2023.100312_bib0025
  article-title: Canonical representations of discrete fuzzy numbers
  publication-title: Fuzz Set Syst
  doi: 10.1016/S0165-0114(99)00053-6
– volume: 139
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0044
  article-title: A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic
  publication-title: Appl Soft Comput
  doi: 10.1016/j.asoc.2023.110213
– volume: 356
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0075
  article-title: Introduction to Fuzzy Sets
  publication-title: Stud Fuzz Soft Comput
  doi: 10.1007/978-3-319-59614-3_1
– volume: 8
  start-page: 338
  issue: 3
  year: 1965
  ident: 10.1016/j.rico.2023.100312_bib0001
  article-title: Fuzzy sets
  publication-title: Inform Control
  doi: 10.1016/S0019-9958(65)90241-X
– volume: 119
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0043
  article-title: A distance measure for optimistic viewpoint of the information in interval-valued intuitionistic fuzzy sets and its applications
  publication-title: Eng Appl Artif Intell
  doi: 10.1016/j.engappai.2022.105747
– volume: 7
  start-page: 17
  issue: 1
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0073
  article-title: An arithmetic operation on hexadecagonal fuzzy number
  publication-title: Int J Fuzz Log Syst
– volume: 10
  start-page: 103349
  year: 2022
  ident: 10.1016/j.rico.2023.100312_bib0049
  article-title: Research on Cobot Action Decision-Making Method Based on Intuitionistic Fuzzy Set and Game Theory
  publication-title: IEEE Access
  doi: 10.1109/ACCESS.2022.3205305
– volume: 28
  start-page: 1591
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0036
  article-title: Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations
  publication-title: Neural Comput Appl
  doi: 10.1007/s00521-015-2110-x
– volume: 140
  start-page: 630
  issue: 2
  year: 2012
  ident: 10.1016/j.rico.2023.100312_bib0076
  article-title: Evaluating machine tool alternatives through modified TOPSIS and alpha-cut based fuzzy ANP
  publication-title: Int J Prod Econ
  doi: 10.1016/j.ijpe.2012.02.009
– start-page: 1
  year: 1999
  ident: 10.1016/j.rico.2023.100312_bib0007
  article-title: A unifying field in Logics: Neutrosophic Logic
  publication-title: Philosophy
– volume: 8
  start-page: 51
  issue: 2
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0060
  article-title: Subtraction and division operations of simplified neutrosophic sets
  publication-title: Information
  doi: 10.3390/info8020051
– volume: 36
  start-page: 5844
  issue: 12
  year: 2012
  ident: 10.1016/j.rico.2023.100312_bib0077
  article-title: The trapezoidal fuzzy soft set and its application in MCDM
  publication-title: Appl Math Modell
  doi: 10.1016/j.apm.2012.01.036
– volume: 9
  start-page: 43
  issue: 1
  year: 1975
  ident: 10.1016/j.rico.2023.100312_bib0002
  article-title: The concept of a linguistic variable and its application to approximate reasoning-III
  publication-title: Inform Sci
  doi: 10.1016/0020-0255(75)90017-1
– volume: 25
  start-page: 1069
  issue: 3
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0070
  article-title: A Novel Kind of Arithmetic Operations on Trapezoidal Fuzzy Numbers and Its Applications to Optimize the Transportation Cost
  publication-title: Int J Fuzzy Syst
  doi: 10.1007/s40815-022-01425-6
– volume: 6
  start-page: 13
  year: 2001
  ident: 10.1016/j.rico.2023.100312_bib0074
  article-title: Environmental life cycle assessment with support of fuzzy-sets
  publication-title: Int J Life Cycle Assess
  doi: 10.1007/BF02977589
– start-page: 57
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0010
  article-title: Pythagorean fuzzy subsets
– start-page: 139
  year: 1999
  ident: 10.1016/j.rico.2023.100312_bib0006
  article-title: Interval valued intuitionistic fuzzy sets
  publication-title: Intuitionist Fuzzy Sets Theo Appl
  doi: 10.1007/978-3-7908-1870-3_2
– volume: 2
  start-page: 110
  issue: 2
  year: 2017
  ident: 10.1016/j.rico.2023.100312_bib0014
  article-title: Pentagonal fuzzy number, its properties and application in fuzzy equation
  publication-title: Fut Comput Inform J
– volume: 12
  start-page: 277
  issue: 3
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0066
  article-title: New Arithmetic Operations of Non-Normal Fuzzy Sets Using Compatibility
  publication-title: Axioms
  doi: 10.3390/axioms12030277
– volume: 11
  start-page: 231
  issue: 5
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0031
  article-title: Prediagnosis of Disease Based on Symptoms by Generalized Dual Hesitant Hexagonal Fuzzy Multi-Criteria Decision-Making Techniques
  publication-title: Systems
  doi: 10.3390/systems11050231
– volume: 258
  start-page: 277
  year: 2014
  ident: 10.1016/j.rico.2023.100312_bib0028
  article-title: A new linguistic computational model based on discrete fuzzy numbers for computing with words
  publication-title: Inform Sci
  doi: 10.1016/j.ins.2013.06.055
– volume: 12
  start-page: 41
  year: 2018
  ident: 10.1016/j.rico.2023.100312_bib0030
  article-title: Fuzzy semi-numbers and a distance on them with a case study in medicine
  publication-title: Math Sci
  doi: 10.1007/s40096-018-0242-8
– volume: 20
  start-page: 87
  issue: 1
  year: 1986
  ident: 10.1016/j.rico.2023.100312_bib0004
  article-title: Intuitionistic fuzzy sets
  publication-title: Fuzzy Sets Syst
  doi: 10.1016/S0165-0114(86)80034-3
– ident: 10.1016/j.rico.2023.100312_bib0023
– volume: 7
  start-page: 92
  issue: 2
  year: 2013
  ident: 10.1016/j.rico.2023.100312_bib0033
  article-title: Intuitionistic fuzzy number and its arithmetic operation with application on system failure
  publication-title: J Uncert Syst
– volume: 467
  year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0068
  article-title: A class of fuzzy numbers induced by probability density functions and their arithmetic operations
  publication-title: Fuzz Set Syst
– volume: 11
  start-page: 203
  issue: 3
  year: 2019
  ident: 10.1016/j.rico.2023.100312_bib0034
  article-title: New A rithmetic Operations on Developed Parabolic Fuzzy Numbers and Its Application
  publication-title: Int J Indust Math
– year: 2023
  ident: 10.1016/j.rico.2023.100312_bib0015
  article-title: Analysis and interpretation of Malaria disease model in crisp and fuzzy environment
  publication-title: Result Cont Optim
– volume: 2
  start-page: 99
  issue: 1
  year: 2011
  ident: 10.1016/j.rico.2023.100312_bib0072
  article-title: Fuzzy Arithmetic with and without using α-cut method: A Comparative Study
  publication-title: Int J Latest Trend Comput
– volume: 15
  start-page: 16
  issue: 1
  year: 2007
  ident: 10.1016/j.rico.2023.100312_bib0008
  article-title: Uncertain fuzzy reasoning: a case study in modelling expert decision making
  publication-title: IEEE Trans Fuzzy Syst
  doi: 10.1109/TFUZZ.2006.889755
– volume: 25
  start-page: 529
  issue: 6
  year: 2010
  ident: 10.1016/j.rico.2023.100312_bib0009
  article-title: Hesitant fuzzy sets
  publication-title: Int J Intell Syst
– volume: 19
  start-page: 97
  issue: 1
  year: 2022
  ident: 10.1016/j.rico.2023.100312_bib0024
  article-title: Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle
  publication-title: Iran J Fuzz Syst
– volume: 326
  start-page: 258
  year: 2016
  ident: 10.1016/j.rico.2023.100312_bib0037
  article-title: Two-dimensional discrete fuzzy numbers and applications
  publication-title: Inform Sci
  doi: 10.1016/j.ins.2015.07.045
– volume: 22
  start-page: 149
  issue: 1
  year: 1976
  ident: 10.1016/j.rico.2023.100312_bib0003
  article-title: Fuzzy membership mapped onto intervals and many-valued quantities
  publication-title: Math Logic Quart
  doi: 10.1002/malq.19760220120
– volume: 1
  start-page: 27
  year: 2008
  ident: 10.1016/j.rico.2023.100312_bib0048
  article-title: Genetic fuzzy systems: taxonomy, current research trends and prospects
  publication-title: Evolut Intellig
  doi: 10.1007/s12065-007-0001-5
– volume: 12
  start-page: 45
  issue: 1
  year: 2004
  ident: 10.1016/j.rico.2023.100312_bib0021
  article-title: On the representation of intuitionistic fuzzy t-norms and t-conorms
  publication-title: IEEE Trans Fuzzy Syst
  doi: 10.1109/TFUZZ.2003.822678
SSID ssj0002811281
Score 2.3691094
Snippet Fuzzy set theory is a generalized form of crisp set theory where elements are binary inclusion forms. In fuzzy set, it differs with degree of membership for...
SourceID doaj
crossref
elsevier
SourceType Open Website
Index Database
Publisher
StartPage 100312
SubjectTerms Arithmetic operations of fuzzy numbers
Fuzzy sets
Triangular fuzzy number
α–cut set
Title A Brief Analysis and Interpretation on Arithmetic Operations of Fuzzy Numbers
URI https://dx.doi.org/10.1016/j.rico.2023.100312
https://doaj.org/article/a0161d97fb92463188c23af3e994fd71
Volume 13
WOSCitedRecordID wos001208993700001&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: PRVAON
  databaseName: DOAJ Directory of Open Access Journals
  customDbUrl:
  eissn: 2666-7207
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002811281
  issn: 2666-7207
  databaseCode: DOA
  dateStart: 20200101
  isFulltext: true
  titleUrlDefault: https://www.doaj.org/
  providerName: Directory of Open Access Journals
– providerCode: PRVHPJ
  databaseName: ROAD: Directory of Open Access Scholarly Resources
  customDbUrl:
  eissn: 2666-7207
  dateEnd: 99991231
  omitProxy: false
  ssIdentifier: ssj0002811281
  issn: 2666-7207
  databaseCode: M~E
  dateStart: 20200101
  isFulltext: true
  titleUrlDefault: https://road.issn.org
  providerName: ISSN International Centre
link http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELZQxQAD4inKSx7YUEQSJ449FtSKpYUBpG6Wn6KVSCvaItGB3845TlC6wIIUeYgiO_o-J3eX3H2H0DU3ueLG8ShTGoaY2oiz2EbeO6VMWyqNrJpNFKMRG4_5U6vVl88JC_LAAbhb6X0SwwunIFKgsAOZTol0xHKeOVNVj6dxwVvB1LT6ZJT4X0R1lUxI6IL3iq_2S4nPDCBJumGJKsH-lkFqGZnBPtqrvUPcC3d1gLZseYh2W5qBR2jYwxDQW4cbOREsS4M3cwcxHD2I-l_ffIkifpzbwPMCzxwerNbrTzyqOoEsjtHLoP98_xDVPREiTWiyjBgxxKYqy1ySOWZUwnOrlbPceeWuWKWx9ygAKQ4c0NwwDXA5bgnVsdZgm09Qp5yV9hRhAw-vy6V2KrHglhmV5bKQVAHGKpc87qKbBh8xD9IXoskJmwqPpvBoioBmF915CH-u9LLV1QkgU9Rkir_I7KK8IUDUHkCw7DDV5JfFz_5j8XO046cMuSoXqLN8X9lLtK0_lpPF-1W1v2AcfvW_AWad1Qk
linkProvider Directory of Open Access Journals
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=A+Brief+Analysis+and+Interpretation+on+Arithmetic+Operations+of+Fuzzy+Numbers&rft.jtitle=Results+in+control+and+optimization&rft.au=Mukherjee%2C+Asesh+Kumar&rft.au=Gazi%2C+Kamal+Hossain&rft.au=Salahshour%2C+Soheil&rft.au=Ghosh%2C+Arijit&rft.date=2023-12-01&rft.pub=Elsevier+B.V&rft.issn=2666-7207&rft.eissn=2666-7207&rft.volume=13&rft_id=info:doi/10.1016%2Fj.rico.2023.100312&rft.externalDocID=S2666720723001145
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2666-7207&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2666-7207&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2666-7207&client=summon