{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,11]],"date-time":"2025-11-11T22:25:06Z","timestamp":1762899906980},"reference-count":56,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:00:00Z","timestamp":1585612800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T00:00:00Z","timestamp":1585612800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,5]]},"DOI":"10.1007\/s40314-020-01142-6","type":"journal-article","created":{"date-parts":[[2020,3,31]],"date-time":"2020-03-31T09:02:48Z","timestamp":1585645368000},"update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Some studies in the approximation of $$(\\in _{\\gamma }, \\in _{\\gamma }\\vee q_{\\delta })$$-fuzzy substructures in quantales"],"prefix":"10.1007","volume":"39","author":[{"given":"Saqib Mazher","family":"Qurashi","sequence":"first","affiliation":[]},{"given":"Muhammad","family":"Shabir","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,3,31]]},"reference":[{"key":"1142_CR1","volume-title":"Fuzzy lie algebras, infosys science foundation series in mathematical sciences","author":"M Akram","year":"2018","unstructured":"Akram M (2018) Fuzzy lie algebras, infosys science foundation series in mathematical sciences. Springer, Berlin"},{"key":"1142_CR2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-16020-3","author":"M Akram","year":"2020","unstructured":"Akram M, Zafar F (2020) Hybrid soft computing models applied to graph theory. Stud Fuzziness Soft Comput. https:\/\/doi.org\/10.1007\/978-3-030-16020-3","journal-title":"Stud Fuzziness Soft Comput"},{"issue":"1","key":"1142_CR3","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1007\/s00521-011-0757-5","volume":"21","author":"MI Ali","year":"2012","unstructured":"Ali MI, Shabir M (2012) Samina, roughness in hemirings. Neural Comput Appl 21(1):171\u2013180","journal-title":"Neural Comput Appl"},{"key":"1142_CR4","doi-asserted-by":"publisher","first-page":"8","DOI":"10.1155\/2019\/8326124","volume":"2019","author":"F Bouaziz","year":"2019","unstructured":"Bouaziz F, Yaqoob N (2019) Rough hyperfilters in po-LA-semihypergroups. Discret Dyn Nat Soc 2019:8","journal-title":"Discret Dyn Nat Soc"},{"key":"1142_CR5","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1016\/j.ins.2003.10.001","volume":"164","author":"B Davvaz","year":"2004","unstructured":"Davvaz B (2004) Roughness in rings. Inf Sci 164:147\u2013163","journal-title":"Inf Sci"},{"key":"1142_CR6","doi-asserted-by":"publisher","first-page":"3247","DOI":"10.1016\/j.ins.2008.03.014","volume":"178","author":"B Davvaz","year":"2008","unstructured":"Davvaz B (2008) A short note on algebraic T-rough sets. Inf Sci 178:3247\u20133252","journal-title":"Inf Sci"},{"key":"1142_CR7","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1080\/03081079008935107","volume":"17","author":"D Dubois","year":"1990","unstructured":"Dubois D, Prade H (1990) Rough fuzzy sets and fuzzy rough sets. Int J Gen Syst 17:191\u2013209","journal-title":"Int J Gen Syst"},{"key":"1142_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0304-3975(87)90045-4","volume":"50","author":"JY Girard","year":"1987","unstructured":"Girard JY (1987) Linear logic. Theor Comput Sci 50:1\u2013101","journal-title":"Theor Comput Sci"},{"issue":"1","key":"1142_CR9","doi-asserted-by":"publisher","first-page":"43","DOI":"10.3176\/proc.2019.1.06","volume":"68","author":"M Gulistan","year":"2019","unstructured":"Gulistan M, Yaqoob N, Kadry S, Azhar M (2019) On generalized fuzzy sets in ordered LA-semihypergroups. Proc Estonian Acad Sci 68(1):43\u201354","journal-title":"Proc Estonian Acad Sci"},{"key":"1142_CR10","doi-asserted-by":"crossref","unstructured":"Hohle U (2014) Topological representation of right-sided and idempotent quantales, Semigroup Forum","DOI":"10.1007\/s00233-014-9634-8"},{"key":"1142_CR11","first-page":"337","volume":"7","author":"SB Hosseini","year":"2012","unstructured":"Hosseini SB, Jafarzadeh N, Gholami A (2012) Some results on T-rough (prime, primary) ideal and T-rough fuzzy (prime, primary) ideal on commutative rings. Int J Contemp Math Sci 7:337\u2013350","journal-title":"Int J Contemp Math Sci"},{"key":"1142_CR12","doi-asserted-by":"publisher","first-page":"4915","DOI":"10.4028\/www.scientific.net\/AMR.433-440.4915","volume":"433","author":"SB Hosseini","year":"2012","unstructured":"Hosseini SB, Jafarzadeh N, Gholami A (2012) T-rough ideal and T-rough fuzzy ideal in a semigroup. Adv Mater Res 433:4915\u20134919","journal-title":"Adv Mater Res"},{"key":"1142_CR13","first-page":"673","volume":"35","author":"TB Iwinski","year":"1987","unstructured":"Iwinski TB (1987) Algebraic approach to rough sets. Bull Polish Acad 35:673\u2013683","journal-title":"Bull Polish Acad"},{"key":"1142_CR14","doi-asserted-by":"crossref","unstructured":"Kanwal RS, Qurashi SM, Shabir M (2020) Generalized approximation of substructures in quantales by soft relations. Comput Appl Math 39\u201324","DOI":"10.1007\/s40314-019-1001-7"},{"key":"1142_CR15","doi-asserted-by":"crossref","unstructured":"Kanwal RS, Shabir M (2019b) Rough approximation of a fuzzy set in semigroups based on soft relations. Comput Appl Math 38\u201389","DOI":"10.1007\/s40314-019-0851-3"},{"key":"1142_CR16","doi-asserted-by":"publisher","first-page":"3895","DOI":"10.3233\/JIFS-18834","volume":"35","author":"RS Kanwal","year":"2018","unstructured":"Kanwal RS, Shabir M (2018) Approximation of ideals in semigroups by soft relations. J Intell Fuzzy Syst 35:3895\u20133908","journal-title":"J Intell Fuzzy Syst"},{"key":"1142_CR17","doi-asserted-by":"publisher","first-page":"7977","DOI":"10.3233\/JIFS-190328","volume":"37","author":"RS Kanwal","year":"2019","unstructured":"Kanwal RS, Shabir M (2019) Approximation of soft ideals by soft relations in semigroups. J Intell Fuzzy Syst 37:7977\u20137989","journal-title":"J Intell Fuzzy Syst"},{"issue":"32","key":"1142_CR18","doi-asserted-by":"publisher","first-page":"278","DOI":"10.1134\/S1995080211040123","volume":"4","author":"FM Khan","year":"2011","unstructured":"Khan FM, Khan A, Sarmin NH (2011) Characterizations of ordered semigroup by $$(\\in _{\\gamma }, \\in _{\\gamma } \\vee q_{\\delta })$$-fuzzy interior ideals. Lobachevskii J Math 4(32):278\u2013288","journal-title":"Lobachevskii J Math"},{"key":"1142_CR19","doi-asserted-by":"crossref","unstructured":"Kruml D, Paseka J (2008) Algebraic and categorical aspects of quantales. In: Hazewinkel M (ed) Handbook of algebra. 5:323-362","DOI":"10.1016\/S1570-7954(07)05006-1"},{"key":"1142_CR20","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1016\/j.ins.2014.02.105","volume":"271","author":"Q Luo","year":"2014","unstructured":"Luo Q, Wang G (2014) Roughness and fuzziness in quantales. Inf Sci 271:14\u201330","journal-title":"Inf Sci"},{"key":"1142_CR21","doi-asserted-by":"publisher","first-page":"493","DOI":"10.1002\/malq.200810022","volume":"55","author":"X Ma","year":"2009","unstructured":"Ma X, Zhan J, Jun YB (2009) On $$(\\in,\\in \\vee q)$$-fuzzy filters of RO-algebras. Math Log Quart 55:493\u2013508","journal-title":"Math Log Quart"},{"issue":"4","key":"1142_CR22","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1016\/j.camwa.2010.12.049","volume":"61","author":"X Ma","year":"2011","unstructured":"Ma X, Zhan J, Jun YB (2011) Some kinds of $$(\\in _{\\gamma }, \\in _{\\gamma } \\vee q_{\\delta })$$-fuzzy ideals of BCI-algebras. Comput Math Appl 61(4):1005\u20131015","journal-title":"Comput Math Appl"},{"key":"1142_CR23","doi-asserted-by":"crossref","unstructured":"Mahmood T, Ali MI, Hussain A (2018) Generalized roughness in fuzzy filters and fuzzy ideals with thresholds in ordered semigroups. Comput Appl Math 1\u201321","DOI":"10.1007\/s40314-018-0615-5"},{"key":"1142_CR24","unstructured":"Mulvey CJ (1986) Rendiconti del Circolo Matematico di Palermo 12(2):99\u2013104"},{"issue":"5","key":"1142_CR25","first-page":"341","volume":"11","author":"Z Pawlak","year":"1982","unstructured":"Pawlak Z (1982) Rough sets. Int J Comput 11(5):341\u2013356","journal-title":"Int J Comput"},{"key":"1142_CR26","doi-asserted-by":"publisher","first-page":"422","DOI":"10.1109\/91.784201","volume":"7","author":"V Petridis","year":"1999","unstructured":"Petridis V, Kaburlasos VG (1999) Learning in the framework of fuzzy lattices. Fuzzy Syst IEEE Trans 7:422\u2013440","journal-title":"Fuzzy Syst IEEE Trans"},{"key":"1142_CR27","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1016\/0022-247X(80)90048-7","volume":"76","author":"PM Pu","year":"1980","unstructured":"Pu PM, Liu YM (1980) Fuzzy topology I, neighbourhood structure of a fuzzy point and MooreCSmith convergence. J Math Anal Appl 76:571\u2013599","journal-title":"J Math Anal Appl"},{"key":"1142_CR28","doi-asserted-by":"crossref","unstructured":"Qurashi SM, Shabir M (2018) Generalized rough fuzzy ideals in quantales, Discrete Dynamics in Nature and Society Volume 2018, Article ID 1085201, 11 pages","DOI":"10.1155\/2018\/1085201"},{"key":"1142_CR29","doi-asserted-by":"crossref","unstructured":"Qurashi SM, Shabir M (2018c)Characterizations of Quantales by $$(\\alpha ,\\beta )$$-fuzzy ideals. Ital J Pure Appl Math (In press)","DOI":"10.1155\/2018\/1085201"},{"key":"1142_CR30","doi-asserted-by":"crossref","unstructured":"Qurashi SM, Shabir M (2019) Characterizations of Quantales by the properties of their $$(\\in _{\\gamma }, \\in _{\\gamma } \\vee q_{\\delta })$$ -fuzzy (subquantales) ideals, Punjab University Journal of Mathematics. (Accepted)","DOI":"10.1007\/s40314-020-01142-6"},{"key":"1142_CR31","unstructured":"Qurashi SM, Shabir M (2020) On generalized fuzzy filters in quantales. (submitted)"},{"key":"1142_CR32","doi-asserted-by":"publisher","first-page":"2359","DOI":"10.3233\/JIFS-17886","volume":"35","author":"SM Qurashi","year":"2018","unstructured":"Qurashi SM, Shabir M (2018) Roughness in quantale module. J Intell Fuzzy Syst 35:2359\u20132372","journal-title":"J Intell Fuzzy Syst"},{"key":"1142_CR33","doi-asserted-by":"publisher","first-page":"6821","DOI":"10.1007\/s40314-018-0715-2","volume":"37","author":"SM Qurashi","year":"2018","unstructured":"Qurashi SM, Shabir M (2018) Generalized approximations of $$(\\in, \\in \\vee q)$$-fuzzy ideals in quantales. Comput Appl Math 37:6821\u20136837","journal-title":"Comput Appl Math"},{"issue":"3","key":"1142_CR34","first-page":"34","volume":"44","author":"M Rameez","year":"2017","unstructured":"Rameez M, Ali MI, Ejaz A (2017) Generalized roughness in $$(\\in, \\in \\vee q)$$-fuzzy ideals of hemirings. Kuwait J Sci 44(3):34\u201343","journal-title":"Kuwait J Sci"},{"key":"1142_CR35","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/S0304-3975(99)00123-1","volume":"254","author":"P Resende","year":"2001","unstructured":"Resende P (2001) Quantales, finite observations and strong bisimulation. Theor Comput Sci 254:95\u2013149","journal-title":"Theor Comput Sci"},{"key":"1142_CR36","unstructured":"Rosenthal KI (1990) Quantales and their applications, Pitman Research Notes in Mathematics. Longman Scientific & Technical, New York"},{"issue":"A2","key":"1142_CR37","first-page":"117","volume":"37","author":"M Shabir","year":"2013","unstructured":"Shabir M, Ali M (2013) Characterizations of semigroups by the properties of their $$(\\in _{\\gamma }, \\in _{\\gamma } \\vee q_{\\delta })$$-fuzzy ideals. Iran J Sci Technol 37(A2):117\u2013131","journal-title":"Iran J Sci Technol"},{"key":"1142_CR38","doi-asserted-by":"publisher","DOI":"10.1007\/s00500-019-04582-3","author":"M Shabir","year":"2019","unstructured":"Shabir M, Kanwal RS, Ali MI (2019) Reduction of an information system. Soft Comput. https:\/\/doi.org\/10.1007\/s00500-019-04582-3","journal-title":"Soft Comput"},{"issue":"4","key":"1142_CR39","first-page":"7","volume":"31","author":"SQ Wang","year":"2003","unstructured":"Wang SQ, Zhao B (2003) Ideals of quantales. J Shaanxi Normal Univ (Nat Sci Edn) 31(4):7\u201310 (in Chinese)","journal-title":"J Shaanxi Normal Univ (Nat Sci Edn)"},{"key":"1142_CR40","doi-asserted-by":"crossref","unstructured":"Xiao QM, Li QG (2012) Generalized lower and upper approximations in quantales. J Appl Math","DOI":"10.1155\/2012\/648983"},{"key":"1142_CR41","doi-asserted-by":"publisher","first-page":"1759","DOI":"10.1016\/j.ins.2009.12.026","volume":"180","author":"S Yamak","year":"2010","unstructured":"Yamak S, Kazanc\u0131 O, Davvaz B (2010) Generalized lower and upper approximations in a ring. Inf Sci 180:1759\u20131768","journal-title":"Inf Sci"},{"key":"1142_CR42","doi-asserted-by":"publisher","first-page":"568","DOI":"10.1016\/j.ins.2012.07.042","volume":"220","author":"LY Yang","year":"2013","unstructured":"Yang LY, Xu LS (2013) Roughness in quantales. Inf Sci 220:568\u2013579","journal-title":"Inf Sci"},{"issue":"1","key":"1142_CR43","doi-asserted-by":"publisher","first-page":"517","DOI":"10.3233\/JIFS-18776","volume":"36","author":"N Yaqoob","year":"2019","unstructured":"Yaqoob N (2019) Approximations in left almost polygroups. J Intell Fuzzy Syst 36(1):517\u2013526","journal-title":"J Intell Fuzzy Syst"},{"issue":"13","key":"1142_CR44","doi-asserted-by":"publisher","first-page":"4167","DOI":"10.2298\/FIL1713167Y","volume":"31","author":"N Yaqoob","year":"2017","unstructured":"Yaqoob N, Aslam M, Hila K, Davvaz B (2017) Rough prime bi-$$\\Gamma $$-hyperideals and fuzzy prime bi-$$\\Gamma $$-hyperideals of $$\\Gamma $$-semihypergroups. Filomat 31(13):4167\u20134183","journal-title":"Filomat"},{"key":"1142_CR45","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/s40314-019-0876-7","volume":"38","author":"N Yaqoob","year":"2019","unstructured":"Yaqoob N, Gulistan M, Tang J, Azhar M (2019) On generalized fuzzy hyperideals in ordered LA-semihypergroups. Comput Appl Math 38:124","journal-title":"Comput Appl Math"},{"key":"1142_CR46","doi-asserted-by":"publisher","first-page":"41","DOI":"10.2307\/2274953","volume":"55","author":"D Yetter","year":"1990","unstructured":"Yetter D (1990) Quantales and non-commutative linear logic. J Symb Log 55:41\u201364","journal-title":"J Symb Log"},{"key":"1142_CR47","doi-asserted-by":"publisher","first-page":"2115","DOI":"10.1016\/j.camwa.2010.07.054","volume":"60","author":"Y Yin","year":"2010","unstructured":"Yin Y, Zhan J (2010) New types of fuzzy filters of BL-algebra. Comput Math Appl 60:2115\u20132125","journal-title":"Comput Math Appl"},{"key":"1142_CR48","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1007\/s13042-014-0305-6","volume":"7","author":"F Yousafzai","year":"2016","unstructured":"Yousafzai F, Yaqoob N, Zeb A (2016) On generalized fuzzy ideals of ordered AG-groupoids. Int J Mach Learn Cyber 7:995\u20131004","journal-title":"Int J Mach Learn Cyber"},{"key":"1142_CR49","doi-asserted-by":"publisher","first-page":"338","DOI":"10.1016\/S0019-9958(65)90241-X","volume":"8","author":"LA Zadeh","year":"1965","unstructured":"Zadeh LA (1965) Fuzzy sets. Inf Control 8:338\u2013353","journal-title":"Inf Control"},{"key":"1142_CR50","doi-asserted-by":"publisher","first-page":"671","DOI":"10.1007\/s10462-018-9674-7","volume":"53","author":"J Zhan","year":"2020","unstructured":"Zhan J, Sun B (2020) Covering-based intuitionistic fuzzy rough sets and applications in multi-attribute decision-making. Artif Intell Rev 53:671\u2013701","journal-title":"Artif Intell Rev"},{"key":"1142_CR51","doi-asserted-by":"publisher","first-page":"167","DOI":"10.1007\/s10462-018-9649-8","volume":"53","author":"J Zhan","year":"2020","unstructured":"Zhan J, Xu W (2020) Two types of coverings based multigranulation rough fuzzy sets and applications to decision making. Artif Intell Rev 53:167\u2013198","journal-title":"Artif Intell Rev"},{"key":"1142_CR52","doi-asserted-by":"publisher","first-page":"106192","DOI":"10.1016\/j.cie.2019.106192","volume":"139","author":"J Zhan","year":"2020","unstructured":"Zhan J, Sun B, Zhang X (2020) PF-TOPSIS method based on CPFRS models: an application to unconventional emergency events. Comput Ind Eng 139:106192","journal-title":"Comput Ind Eng"},{"key":"1142_CR53","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1016\/j.knosys.2015.09.036","volume":"91","author":"XH Zhang","year":"2016","unstructured":"Zhang XH, Miao D, Liu C, Le M (2016) Constructive methods of rough approximation operators and multigranulation rough sets. Knowl-Based Syst 91:114\u2013125","journal-title":"Knowl-Based Syst"},{"key":"1142_CR54","doi-asserted-by":"publisher","DOI":"10.1016\/j.ins.2020.01.003","author":"L Zhang","year":"2020","unstructured":"Zhang L, Zhan J, Yao YY (2020) Intuitionistic fuzzy TOPSIS method based on CVPIFRS models: an application to biomedical problems. Inf Sci. https:\/\/doi.org\/10.1016\/j.ins.2020.01.003","journal-title":"Inf Sci"},{"key":"1142_CR55","doi-asserted-by":"publisher","unstructured":"Zhan J, Zhang X, Yao YY (2019) Covering based multigranulation fuzzy rough sets and corresponding applications. Artif Intell Rev https:\/\/doi.org\/10.1007\/s10462-019-09690-y","DOI":"10.1007\/s10462-019-09690-y"},{"key":"1142_CR56","doi-asserted-by":"publisher","first-page":"2478","DOI":"10.1016\/j.ins.2009.02.013","volume":"179","author":"W Zhu","year":"2009","unstructured":"Zhu W (2009) Relationship among basic concepts in covering-based rough sets. Inf Sci 179:2478\u20132486","journal-title":"Inf Sci"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01142-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-020-01142-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01142-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,20]],"date-time":"2022-10-20T01:28:47Z","timestamp":1666229327000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-020-01142-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,31]]},"references-count":56,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2020,5]]}},"alternative-id":["1142"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01142-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,31]]},"assertion":[{"value":"16 November 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 February 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 March 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"117"}}