Journal of Mathematical Analysis and Applications, 2011
In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions... more In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions in R n . In general, since it is hard to solve (LOP) directly, (LOP) is transformed into a certain problem (MP) constrained by a ball in R n+1 . Despite there is no guarantee that the objective function of (MP) is quasi-convex, by using the idea of the quasi-conjugate function defined by Thach [1], we can construct its dual problem (DP) as a quasiconvex maximization problem. We show that the optimal value of (DP) coincides with the multiplication of the optimal value of (MP) by −1, and that each optimal solution of the primal and dual problems can be easily obtained by the other. Moreover, we formulate a bidual problem (BDP) for (MP) (that is, a dual problem for (DP)). We show that the objective function of (BDP) is a quasi-convex function majorized by the objective function of (MP) and that both optimal solution sets of (MP) and (BDP) coincide. Furthermore, we propose an outer approximation method for solving (DP).
In this article, we propose two successive search methods for solving a canonical DC programming ... more In this article, we propose two successive search methods for solving a canonical DC programming problem constrained by the difference set between two compact convex sets in the case where the dimension number is greater than or equal to three. In order to find feasible solutions, the algorithms generate the directions based on a branch and bound procedure, successively. By
In this paper, we propose a new class of necessity measures which satisfy (Rl) NA(B) >... more In this paper, we propose a new class of necessity measures which satisfy (Rl) NA(B) > 0 ⇔ ∃ε> 0; [A]1-ε ⊆ (B)ε, (R2) ∃h* ∈ (0,1); N A(B) ≥ h* ⇔ A ⊆ B and (R3) N A(B) = 1 ⇔ (A)0 ⊆ [B]1. It is shown that such a necessity measure is designed easily by level cut conditioning approach. A simple example of such a necessity measure is given. The proposed necessity measure is applied to fuzzy rough set based on certainty qualifications. It is demonstrated that the proposed necessity measure gives better upper and lower approximations of a fuzzy set than necessity measures defined by S-, R- and reciprocal R-implications.
In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzz... more In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.
In this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. O... more In this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. Oblique fuzzy vectors are extensions of fuzzy numbers and vectors of non-interactive fuzzy numbers. The interactivity among fuzzy numbers can be treated by a non-singular matrix in an oblique fuzzy vector. We discuss characterization of an oblique fuzzy vector and the tractability of manipulation of oblique fuzzy vectors in fuzzy linear functions. Moreover, we discuss possibilistic linear programming problems with oblique fuzzy vectors. It is shown that the possibilistic linear programming problems are reduced to linear programming problems with a special structure.
In this paper, we introduce a class of fuzzy linear programming problems and define the concepts ... more In this paper, we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions—the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we define the concept of duality and prove the weak and strong duality theorems. Further, we define a class of interval linear programming problems as a special subclass of FLP problems and apply the previous results to this special case.
This paper deals with a portfolio selection problem with independently estimated possibilistic re... more This paper deals with a portfolio selection problem with independently estimated possibilistic return rates. Under such a circumstance, a distributive investment has been regarded as a good solution in the traditional portfolio theory. However, the conventional possibilistic approach yields a concentrated investment solution. Considering the reason why a distributive investment is advocated, a new approach to the possibilistic portfolio selection is proposed.
International Journal of Systems Science - IJSySc, 1989
A set-theoretic approach to uncertain dynamical systems by using convex polytopes is treated. In ... more A set-theoretic approach to uncertain dynamical systems by using convex polytopes is treated. In some points, this approach is superior to the one using ellipsoids, though it also has some disadvantages. First, some fundamental operations are discussed, such as addition, intersection, and the linear transformation of convex polytopes. The results are applied to the analysis of reachable sets for discrete-time linear dynamical systems and also to the state estimation.
Solid-state Electronics - SOLID STATE ELECTRON, 1995
The output voltage/current wave forms and load lines of a common emitter HBT under constant base ... more The output voltage/current wave forms and load lines of a common emitter HBT under constant base current and constant base voltage bias conditions at several input power levels were simulated with a non-linear simulator. The simulated output power characteristics of each set of bias conditions were compared with measured data. It was learnt that good gain linearity and good efficiency were obtained across a wide input power range, by using a constant base current bias mode. This is because operation of the HBT changes from class A to class C with a constant base current bias.
Journal of Optimization Theory and Applications - J OPTIMIZ THEOR APPL, 1988
Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family o... more Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps. Particularly, it is shown that the sensitivity is closely related to the Lagrange multipliers in multiobjective programming.
We constructed a novel system for periplasmic localization of target proteins, using yeast extern... more We constructed a novel system for periplasmic localization of target proteins, using yeast external invertase (INV) as anchor protein, in which the C-or N-terminal of the target protein was fused to the invertase and the fusion proteins expressed under the control of the constitutive glyceraldehyde-3-phosphate dehydrogenase promoter (GAPDH). Unlike in conventional cell-surface display, the system enables the target fusion protein to localize in yeast periplasm in a free state. As a model, enhanced green fluorescence protein (EGFP) was localized in yeast periplasm using the new system. Yeast-periplasm localization of INV-EGFP and EGFP-INV fusion proteins was confirmed by fluorescence microscopy and immunoblotting: green fluorescence was observed at the cell outline and, in western blot analysis, most fusion proteins were detected in the cell-surface fraction, indicating that the fusion proteins had been transported to the cell-surface layer. In addition, in both Cand N-terminal fusion, invertase showed activity, indicating dimer formation. These results demonstrate that invertase is a useful anchor for localizing target protein in the yeast periplasm.
In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the... more In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating such improvements by applying quadratic programming techniques. Furthermore, since all equations constructing the efficient frontiers of the CCR and BCC models are necessary to execute the algorithm, we present a procedure for calculating them.► We calculate equations forming the efficient frontiers of the CCR and BCC models. ► We suggest four types of improvements for making inefficient DMUs efficient. ► We propose an algorithm for calculating such improvements.
Markovian deterioration models of parallel unit systems are dealt with. Units of a system are sup... more Markovian deterioration models of parallel unit systems are dealt with. Units of a system are supposed to be of different types, and a state of the system is represented by a vector whose component corresponds to the state of each unit. Therefore all the states of the system are only partially ordered, while they are totally ordered in ordinary markovian deterioration models. It is proved under some conditions that the optimal maintenance policy is a partial control limit policy, which is a generalization of the well-known control limit policy in the ordinary case. An algorithm improving the successive approximation method is proposed for obtaining the optimal policy. A typical case of the model is also discussed.
Journal of Mathematical Analysis and Applications, 2011
In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions... more In this paper, we consider a Lipschitz optimization problem (LOP) constrained by linear functions in R n . In general, since it is hard to solve (LOP) directly, (LOP) is transformed into a certain problem (MP) constrained by a ball in R n+1 . Despite there is no guarantee that the objective function of (MP) is quasi-convex, by using the idea of the quasi-conjugate function defined by Thach [1], we can construct its dual problem (DP) as a quasiconvex maximization problem. We show that the optimal value of (DP) coincides with the multiplication of the optimal value of (MP) by −1, and that each optimal solution of the primal and dual problems can be easily obtained by the other. Moreover, we formulate a bidual problem (BDP) for (MP) (that is, a dual problem for (DP)). We show that the objective function of (BDP) is a quasi-convex function majorized by the objective function of (MP) and that both optimal solution sets of (MP) and (BDP) coincide. Furthermore, we propose an outer approximation method for solving (DP).
In this article, we propose two successive search methods for solving a canonical DC programming ... more In this article, we propose two successive search methods for solving a canonical DC programming problem constrained by the difference set between two compact convex sets in the case where the dimension number is greater than or equal to three. In order to find feasible solutions, the algorithms generate the directions based on a branch and bound procedure, successively. By
In this paper, we propose a new class of necessity measures which satisfy (Rl) NA(B) >... more In this paper, we propose a new class of necessity measures which satisfy (Rl) NA(B) > 0 ⇔ ∃ε> 0; [A]1-ε ⊆ (B)ε, (R2) ∃h* ∈ (0,1); N A(B) ≥ h* ⇔ A ⊆ B and (R3) N A(B) = 1 ⇔ (A)0 ⊆ [B]1. It is shown that such a necessity measure is designed easily by level cut conditioning approach. A simple example of such a necessity measure is given. The proposed necessity measure is applied to fuzzy rough set based on certainty qualifications. It is demonstrated that the proposed necessity measure gives better upper and lower approximations of a fuzzy set than necessity measures defined by S-, R- and reciprocal R-implications.
In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzz... more In this paper, we propose a scenario decomposition approach for the treatment of interactive fuzzy numbers. Scenario decomposed fuzzy numbers (SDFNs) reflect a fact that we may have different estimations of possible ranges of uncertain variables depending on scenarios, which are expressed by fuzzy if-then rules. The properties of SDFNs are investigated. Possibilistic linear programming problems with SDFNs are formulated by two different approaches, fractile and modality optimization approaches. It is shown that the problems are reduced to linear programming problems in fractile optimization models with the necessity measures and that the problems can be solved by a linear programming technique and a bisection method in modality optimization models with necessity measures. A simple numerical example is given.
In this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. O... more In this paper, we propose oblique fuzzy vectors to treat the interactivity among fuzzy numbers. Oblique fuzzy vectors are extensions of fuzzy numbers and vectors of non-interactive fuzzy numbers. The interactivity among fuzzy numbers can be treated by a non-singular matrix in an oblique fuzzy vector. We discuss characterization of an oblique fuzzy vector and the tractability of manipulation of oblique fuzzy vectors in fuzzy linear functions. Moreover, we discuss possibilistic linear programming problems with oblique fuzzy vectors. It is shown that the possibilistic linear programming problems are reduced to linear programming problems with a special structure.
In this paper, we introduce a class of fuzzy linear programming problems and define the concepts ... more In this paper, we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions—the necessary tools for dealing with such problems. In this way, we show that the class of crisp (classical) LP problems can be embedded into the class of FLP ones. Moreover, for FLP problems we define the concept of duality and prove the weak and strong duality theorems. Further, we define a class of interval linear programming problems as a special subclass of FLP problems and apply the previous results to this special case.
This paper deals with a portfolio selection problem with independently estimated possibilistic re... more This paper deals with a portfolio selection problem with independently estimated possibilistic return rates. Under such a circumstance, a distributive investment has been regarded as a good solution in the traditional portfolio theory. However, the conventional possibilistic approach yields a concentrated investment solution. Considering the reason why a distributive investment is advocated, a new approach to the possibilistic portfolio selection is proposed.
International Journal of Systems Science - IJSySc, 1989
A set-theoretic approach to uncertain dynamical systems by using convex polytopes is treated. In ... more A set-theoretic approach to uncertain dynamical systems by using convex polytopes is treated. In some points, this approach is superior to the one using ellipsoids, though it also has some disadvantages. First, some fundamental operations are discussed, such as addition, intersection, and the linear transformation of convex polytopes. The results are applied to the analysis of reachable sets for discrete-time linear dynamical systems and also to the state estimation.
Solid-state Electronics - SOLID STATE ELECTRON, 1995
The output voltage/current wave forms and load lines of a common emitter HBT under constant base ... more The output voltage/current wave forms and load lines of a common emitter HBT under constant base current and constant base voltage bias conditions at several input power levels were simulated with a non-linear simulator. The simulated output power characteristics of each set of bias conditions were compared with measured data. It was learnt that good gain linearity and good efficiency were obtained across a wide input power range, by using a constant base current bias mode. This is because operation of the HBT changes from class A to class C with a constant base current bias.
Journal of Optimization Theory and Applications - J OPTIMIZ THEOR APPL, 1988
Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family o... more Sensitivity analysis in multiobjective optimization is dealt with in this paper. Given a family of parametrized multiobjective optimization problems, the perturbation map is defined as the set-valued map which associates to each parameter value the set of minimal points of the perturbed feasible set in the objective space with respect to a fixed ordering convex cone. The behavior of the perturbation map is analyzed quantitatively by using the concept of contingent derivatives for set-valued maps. Particularly, it is shown that the sensitivity is closely related to the Lagrange multipliers in multiobjective programming.
We constructed a novel system for periplasmic localization of target proteins, using yeast extern... more We constructed a novel system for periplasmic localization of target proteins, using yeast external invertase (INV) as anchor protein, in which the C-or N-terminal of the target protein was fused to the invertase and the fusion proteins expressed under the control of the constitutive glyceraldehyde-3-phosphate dehydrogenase promoter (GAPDH). Unlike in conventional cell-surface display, the system enables the target fusion protein to localize in yeast periplasm in a free state. As a model, enhanced green fluorescence protein (EGFP) was localized in yeast periplasm using the new system. Yeast-periplasm localization of INV-EGFP and EGFP-INV fusion proteins was confirmed by fluorescence microscopy and immunoblotting: green fluorescence was observed at the cell outline and, in western blot analysis, most fusion proteins were detected in the cell-surface fraction, indicating that the fusion proteins had been transported to the cell-surface layer. In addition, in both Cand N-terminal fusion, invertase showed activity, indicating dimer formation. These results demonstrate that invertase is a useful anchor for localizing target protein in the yeast periplasm.
In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the... more In this paper, we suggest four types of improvements for making inefficient DMUs efficient in the CCR model with the minimal change of input and output values. Moreover, we propose an algorithm for calculating such improvements by applying quadratic programming techniques. Furthermore, since all equations constructing the efficient frontiers of the CCR and BCC models are necessary to execute the algorithm, we present a procedure for calculating them.► We calculate equations forming the efficient frontiers of the CCR and BCC models. ► We suggest four types of improvements for making inefficient DMUs efficient. ► We propose an algorithm for calculating such improvements.
Markovian deterioration models of parallel unit systems are dealt with. Units of a system are sup... more Markovian deterioration models of parallel unit systems are dealt with. Units of a system are supposed to be of different types, and a state of the system is represented by a vector whose component corresponds to the state of each unit. Therefore all the states of the system are only partially ordered, while they are totally ordered in ordinary markovian deterioration models. It is proved under some conditions that the optimal maintenance policy is a partial control limit policy, which is a generalization of the well-known control limit policy in the ordinary case. An algorithm improving the successive approximation method is proposed for obtaining the optimal policy. A typical case of the model is also discussed.
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