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In this paper, we consider the set-valued homomorphism<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi mathvariant=\"normal\">T<\/mml:mi><\/mml:mrow><\/mml:math>on<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-semihypergroup<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>H<\/mml:mi><\/mml:mrow><\/mml:math>to interpret the lower and upper approximations. We study the roughness of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"normal\">m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi mathvariant=\"normal\">n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>bi-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-hyperideals and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"normal\">m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi mathvariant=\"normal\">n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>quasi-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-hyperideals in terms of set-valued homomorphisms, which are extended notions of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"normal\">m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi mathvariant=\"normal\">n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>bi-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-hyperideals and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi mathvariant=\"normal\">m<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi mathvariant=\"normal\">n<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>quasi-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-hyperideals of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><mml:mrow><mml:mi mathvariant=\"normal\">\u0393<\/mml:mi><\/mml:mrow><\/mml:math>-semihypergroups.<\/jats:p>","DOI":"10.1155\/2014\/658252","type":"journal-article","created":{"date-parts":[[2014,7,8]],"date-time":"2014-07-08T18:17:28Z","timestamp":1404843448000},"page":"1-6","source":"Crossref","is-referenced-by-count":1,"title":["Generalized Rough \u0393-Hyperideals in \u0393-Semihypergroups"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5362-9916","authenticated-orcid":true,"given":"Naveed","family":"Yaqoob","sequence":"first","affiliation":[{"name":"Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan"},{"name":"Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1433-7662","authenticated-orcid":true,"given":"Shamsul","family":"Haq","sequence":"additional","affiliation":[{"name":"Natural Resource and Engineering Department, University of Kurdistan Hewlr, Kurdistan Region, Iraq"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","reference":[{"key":"1","first-page":"45","volume-title":"Sur une generalization de la notion de group","year":"1934"},{"issue":"1","key":"2","first-page":"11","volume":"26","year":"2010","journal-title":"Carpathian Journal of Mathematics"},{"issue":"1","key":"3","first-page":"195","volume":"72","year":"2010","journal-title":"University of Bucharest. 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