Mở rộng phạm trù các không gian mở hữu hạn chiều thành hệ đầy đủ.

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Mở rộng phạm trù các không gian mở hữu hạn chiều thành hệ đầy đủ. Chế tạo lớp phủ titan nitrua trên nền thép không gỉ mác 304 và 316L, thử nghiệm cơ lý tính và khả năng tương thích sinh học trong dung dịch mô phỏng cơ thể người.

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T?-p chi Tin hoc va f)i'eu khi€n hqc, T. 17, S.2 (2001), 35-38 COMPLETION OF THE CATEGORY OF FINITE-DIMENSIONAL FUZZY SPACES NGUYEN NHUY, PHAM QUANG TRINH and VU THI HONG THANH Abstract. In this paper we introduce a method to expand the category 1of all finite-dimensional fuzzy spaces associated with finite-dimensional Chu spaces in to a complete system. Torn tli t. Ba.i nay tiep tuc nghien CUll pham tr u cac kh orig gian- mo' h iru h an chie u d a dU'
36 NGUYEN NHUY, PHAM qUANG TRINH, VU THI HONG THANH Now for a : X = rr=l Xi ---t Y = TI~'=1Y; we define F*(a) = (TI7=1 Xi, fa, Y*), where Y* denotes the collection of all fuzzy sets of Y = TI~~1 y;, and fa : TI7=1 Xi X Y* ---t [0,1] is given by fa (Xl, X2,··· ,Xn, a) = a(a(xI' X2, ... ,xn)) for every (Xl, X2, ... , Xn, a) E TI7=1 Xi X Y*. The (n+1)-dimensional Chu space F*(a) = (TI7=1 Xi, fa, Y*) is called the (n+l)-dimensional *-fuzzy space associated with the map a : X = TI7=1 Xi ---t Y = TI~1 Y;. The category of all (n+1)-dimensional *-fuzzy spaces associated with maps in the n-set category S is called the (n+l)- dimensional *-fuzzy category and denoted by 1*. 3. RESULTS At first, we will show that the (n+ 1)-dimensional *-fuzzy category 1* defined above contains the category 1 as a subcategory. In fact, we have the following theorem. Theorem 1. Any (n+l)-dimensional fuzzy space is a (n+l)-dimensional *-fuzzy space. Proof. If F(X) = (TI7=IXi,fx',X*) then clearly that F(X) = F*(lx) is a (n+1)-dimensional *-fuzzy space. \ Theorem 2. 1* is a complete system. Proof. Assume that = (TI7=1
COMPLETION OF THE CATEGORY OF FINITE-DIMENSIONAL FUZZY SPACES 37 [[';=1 Xi X v': ('Po,ly,.) ------>1 ITni=1 x:i X Y * , (L,'P*a'*) 1 In fact, for every (Xl, ... ,Xn) E IT;';" 1 Xi and bEY'*, we have fa(x1,'" ,xn,
38 NGUYEN NHUY, PHAM QUANG TRINH, VU THI HONG THANH [7] Nguyen Nhuy, Ph am Quang Trinh, and Vu Hong Thanh, Finite-dinesional Chu space, Journal of Computer Science and Cybernetics 15 (4) (1999). [8] Nguyen Nhuy and Vu Hong Thanh, Finite-dimensional Chu space, Fuzzy space and the game Invariance Theorem, to apper in Journal of Computer Science and Cybernetics. [9] Paradopoulos B. K. and Syropoulos A., Fuzzy sets and fuzzy relational structures as Chu spaces, Proceedings of the First International Workshop on Current Trends and Developments of Fuzzy Logic, Thessaloniki, Greece, Oct. 16-20, 1998; Electronic Notes in Theoretical Computer Science (1998). [10] Pratt V. R., Type as procsses, via Chu spaces, Electronic Notes in Theoretical Computer Science 7 (1997). [11] Pratt V. R., Chu spaces as a sematic bridge between linear logic and mathematics, Electronic Notes in Theoretical Computer Science 12 (1998). Received August 11, 2000 Department of Information Technology, Vinh University, Nqhe An, Vietnam.