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In a batch scheduling problem, jobs are grouped (group is called batch) and scheduled in batches, and a setup time is incurred when starting a new batch. Processing times are assumed to be identical for all jobs. Setup times are assumed to be identical for all batches. Though all batch sizes cannot exceed a common upper bound, the upper bound is flexible and satisfaction degree with respect to the...
Many researchers have proposed portfolio models based on the stochastic and fuzzy approaches until now, and there are some models considering both random and ambiguous conditions, particularly using fuzzy random or random fuzzy variables. However, few studies with multiobjective random fuzzy models for the portfolio selection problems have been performed. Therefore, a multiobjective random fuzzy portfolio...
This paper discusses a portfolio selection problem with type-2 fuzzy future returns involving interval numbers considering the investor's subjectivity. Since this proposed problem is not well-defined due to primary and secondary fuzziness, introducing the possibility measure that the total return is more than the target value, the main problem is transformed into the type-1 fuzzy programming problem...
This paper considers a facility construction problem in a rectangular urban area with some barriers and rectilinear distance. There exist some demand points and possible construction sites with preference of construction. For each site, its construction cost is a fuzzy number due to the difficulty of the exact estimation and we should decide suitable facility construction places under the condition...
This paper considers linear programming problems where each coefficient of the objective function is expressed by a random fuzzy variable. New decision making models are proposed based on stochastic and possibilistic programming in order to maximize both of possibility and probability with respect to the objective function value. It is shown that each of the proposed models is transformed into a deterministic...
Single input rule modules connected fuzzy inference method (SIRMs method, for short) by Yubazaki can decrease the number of fuzzy rules drastically in comparison with the conventional fuzzy inference methods. Seki et al. have proposed functional type single input rule modules connected fuzzy inference method (functional type SIRMs method, for short) which generalizes the consequent part of SIRMs method...
We have developed a well-balanced menu planning system to supply dishes to someonepsilas taste. The system implements fuzzy mathematical programming logic and rough set theory. The fuzzy mathematical programming is mainly used to select menu among database, and the rough set theory provides userpsilas selection rule for menu. This paper particularly focuses the method of rough set theory with fuzzy...
Fuzzy inference has played significant role in many applications. Although simplified fuzzy inference method is currently mostly used, the problem is that the number of fuzzy rules becomes very huge and so the setup and adjustment of fuzzy rules become difficult. On the other hand, Yubazaki et al. have proposed ldquosingle input rule modules connected fuzzy inference methodrdquo (SIRMs method, for...
We have developed a well-balanced menu planning system to supply dishes to someone's taste. The system implements fuzzy mathematical programming logic and rough set theory. The fuzzy mathematical programming is mainly used to select menu among database, and the rough set theory provides user's selection rule for menu. This paper particularly focuses the method of rough set theory with fuzzy weight...
Yubazaki et al. have proposed ldquosingle input rule modules connected type fuzzy reasoning methodrdquo (SIRMs method, for short) whose final output is obtained by summarizing the product of the importance degrees and the inference results from single input fuzzy rule module. Moreover, Seki et al. have proposed ldquofunctional type single input rule modules connected fuzzy reasoning methodrdquo (functional...
This paper considers a new model of 0-1 knapsack problem including probabilistic coefficients with ambiguous expected returns assumed as random fuzzy variables. Since the random fuzzy 0-1 knapsack problem is not well-defined integer programming problem due to involve random fuzzy variables, it is hard to construct the efficient solution method to solve this problem directly. In this paper, using chance...
This paper considers a product mix problem both maximizing the total future profit and reducing excessive inventories including uncertainty with respect to future profits and customers' demands. Furthermore, since a decision maker has a goal with respect to the total future profit and each inventory of the product, in this paper, aspiration levels for them are also introduced. The proposal product...
In this paper we introduce definitions of norms and gauges in linear spaces in order to find shortest paths in free spaces with obstacles. Secondly, Euler-Lagrange equations in the calculus of variation give the optimal solutions for the problems of shortest paths. Thirdly we consider a linear structure in a sets of fuzzy numbers and also introduce norms in fuzzy linear spaces. Finally we discuss...
Yubazaki have proposed a ldquosingle input rule modules connected type fuzzy reasoning method (SIRMs method)rdquo in which its final output is obtained by summarizing the product of importance degree and inference result from single input fuzzy rule modules. This paper proposes a ldquofunctional-type SIRMs method,rdquo which is an extended version of the SIRMs method, and clarifies the relationship...
In this paper, we propose multi-objective mathematical decision models with respect to portfolio selection problems, particularly using the scenario model to include the ambiguous factors. In real investment case, since many random and ambiguous situations exist, portfolio selection problems under such situations are considered. Mathematical programming problems including them are generally called...
In this paper, two portfolio selection problems including probabilistic future returns with ambiguous expected returns are proposed. Until now, many researchers have proposed models of portfolio selection problems, and there are some models considering both random conditions and ambiguous conditions, particularly using fuzzy random variables. However, the model including the random fuzzy variables...
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