A formal deductive system L * for fuzzy propositional calculus, and the revised Kleene logic system W-,W, W k were studied. Both of them were first proposed by professor WANG Guo jun. A kind of weak completely dual formal deductive system WC L- * was given.
However, no constraint qualifications are needed and yet perfect duality maintains between the primal and dual programs.
A note on perfect duality and limiting lagrangeans
In this note we derive and extend the substance of recent results on Perfect Duality and Limiting Lagrangeans by using standard convex analysis and convex duality theory.
Perfect duality in semi-infinite and semidefinite programming
This paper develops new relationships between the recently constructed semidefinite programming perfect duality and the earlier perfect duality achieved for linear semi-infinite programming.
In this note, at first, We point out an error in reference [2]. Next,we give a class of new dual ideals which is exactly dual to the idealintroduced by Iseki [1] .We also construct the quotient algdbras withrespect to these dual ideals and study some of their importantproperties. Moreover, we show that in setting of bounded implicativeBCK-algebras, our results will imply those of [2] §4. and so theerror of [2] is corrected.
he upper bound of system reliability predicted by the upper bound method pres-ented in ref.[1]will monotonically converge to a wrong value which is less than the precise one,and the predicted single value of the system reliability will be too conservative.A new method for calcula-ting upper bounds of system reliability arid fully coupled practical calculation formulas for upper and lower bounds are presented in this paper.Examples show that for any complex system with non-sin-gle series,the application of the...
he upper bound of system reliability predicted by the upper bound method pres-ented in ref.[1]will monotonically converge to a wrong value which is less than the precise one,and the predicted single value of the system reliability will be too conservative.A new method for calcula-ting upper bounds of system reliability arid fully coupled practical calculation formulas for upper and lower bounds are presented in this paper.Examples show that for any complex system with non-sin-gle series,the application of the formulas given in this paper can make the calculated results monotonically converged to the true value,and the predicted single value of the system reliability of higher aecuracy.
A formal deductive system L * for fuzzy propositional calculus, and the revised Kleene logic system W-,W, W k were studied. Both of them were first proposed by professor WANG Guo jun. A kind of weak completely dual formal deductive system WC L- * was given. And the equivalence between them was proved. This work offers a useful tool for further studying and developing L * system.
完全对偶
completely dual
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