标题 | Sup-T合成方程的极小解的判别与构造 |
范文 | 张迪 周艳红 付航 【摘要】本文主要討论[0,1]上Sup-T合成模糊关系方程的极小解的判别与构造,这里的T是t-模.首先给出了方程的解是极小解的充要条件,同时,给出了一个构造方程极小解的算法. 【关键词】模糊关系方程;t-模;极小解;判别;算法 输出X=X(1234)=(0,0,0,0.75)T,易知X为方程的解且为极小解. 例4.4 考虑方程T(0.8,x1)∨T(0.6,x2)=0.6,易知X=(0.6,1)T是方程的一个解.由算法4.1可得方程的极小解:X(12)=(0,0.6)T,X(21)=(0.6,0)T,显然X(12)=X(21). 【参考文献】 [1]SANCHEZ E.Resolution of composite fuzzy relation equations[J].Inform and Control,1976(30):38-48. [2]CZOGALA E, DREWNIAK J and PEDRYCZ W.Fuzzy relation equations on a finite set[J].Fuzzy Sets and Systems, 1987(7): 89-101. [3]王学平.完备Brouwerian格上Fuzzy关系方程有极小解的条件[J].数学进展, 2002(3): 220-228. [4]HIGASHI M and KLIR G J.Resolution of finite fuzzy relation equations[J].Fuzzy Sets and Systems, 1988(13): 65-82. [5]汪培庄, 罗承忠.有限Fuzzy关系方程极小解的个数[J].模糊数学, 1984(3): 63-70. [6]PEDRYCZ W.Fuzzy relational equations with triangular norms and their resolution[J].BUSEFAL, 1982(11): 24-32. [7]PEDRYCZ W.Fuzzy relational equations with generalized connectives and their applications[J].Fuzzy Sets and Systems, 1983(10): 185-201. [8]MIYAKOSHI M and SHIMBO M.Solutions of composite fuzzy relational equations with triangular norms[J].Fuzzy Sets and Systems, 1985(16):53-63. [9]BIRKHOFF G.Lattice Theory[M].vol.XXV, third ed,American Mathematical Society Colloquium Publications, Providence, RI, 1979. [10]ALSINA C, FRANK M J, SCHWEIZER B.Associative Functions: Trangular Norms and copulas[M].World Scientific Press, Singapore, 2006. [11]KLEMENT E P, MESIAR R.Trangular Norms[M].Kluwer Academic Publishers, Dordrecht, 2000. |
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