id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-2920	Ghlaim, Fatima M. ; Kareem, Fatema F.	Cubic Ideals of TM-algebras	2023	13	.pdf	application/pdf	5265	298	91	Similarly, if 𝜔 = 〈�̃�𝜔 , 𝛼𝜔〉 is a cubic subset of 𝑌, then the cubic subset defined by �̃�𝛿(𝜌) = �̃�𝜔(𝑓(𝜌)) and 𝛼𝛿(𝜌) The operations≥ , ≤ , = , 𝑟𝑚𝑖𝑛, 𝑎𝑛𝑑 𝑟𝑚𝑎𝑥 of two elements in 𝐷[0,1] is defined as follows: let �̃� = [𝑎𝐿 , 𝑎𝑈], �̃� = [𝑏𝐿 , 𝑏𝑈] in 𝐷[0,1], then (1) �̃� ≥ �̃� 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑎𝐿 ≥ 𝑏𝐿 𝑎𝑛𝑑 𝑎𝑈 ≥ 𝑏𝑈, (2) �̃� ≤ �̃� 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑎𝐿 ≤ 𝑏𝐿 𝑎𝑛𝑑 𝑎𝑈 ≤ 𝑏𝑈, (3) �̃� = �̃� 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓 𝑎𝐿 = 𝑏𝐿 𝑎𝑛𝑑 𝑎𝑈 = 𝑎𝑈, (4) 𝑟𝑚𝑖𝑛{�̃�, �̃�} = [𝑚𝑖𝑛{𝑎𝐿 , 𝑏𝐿}, 𝑚𝑖𝑛{𝑎𝑈, 𝑏𝑈}], (5) 𝑟𝑚𝑎𝑥{�̃�, �̃�} = [𝑚𝑎𝑥{𝑎𝐿 , 𝑏𝐿}, 𝑚𝑎𝑥{𝑎𝑈, 𝑏𝑈}], And if �̃�𝑖 ∈ 𝐷[0,1] where 𝑖 ∈ ⋀. We define 𝑟 inf 𝑖∈⋀ �̃�𝑖 = [inf 𝑖∈⋀ 𝑎𝑖 𝐿 , inf 𝑖∈⋀ 𝑎𝑖 𝑈] , 𝑟 sup 𝑖∈⋀ �̃�𝑖 =	cache/iajs-2920.pdf	txt/iajs-2920.txt