• Communications of the Korean Mathematical Society
• /
• v.16 no.4
• /
• pp.679-690
• /
• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.12 no.7
• /
• pp.3128-3149
• /
• 2018

A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts' preferences, aggregation of experts' opinions, and comparison of the alternatives. Experts' preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts' preferences with IVIFN is presented. In this approach, experts' preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.

• Communications for Statistical Applications and Methods
• /
• v.12 no.2
• /
• pp.463-472
• /
• 2005

In this paper, the problem of estimating a p-variate (p $\ge$4) normal mean vector is considered in decision-theoretic set up. Using a simple property of the noncentral chi-square distribution, a sequence of estimators dominating the Lindley type estimator with the cases of unknown covariance matrices has been produced and each improved estimator is better than previous one.

• Journal of the Korea Safety Management & Science
• /
• v.16 no.1
• /
• pp.213-220
• /
• 2014

This study suggests new approach to identify core technologies through patent analysis. Specially, the approach applied data mining technique and multi-criteria decision making method to the co-classification information of registered patents. First, technological interrelationship matrices of intensity, relatedness, and cross-impact perspectives are constructed with support, lift and confidence values calculated by conducting an association rule mining on the co-classification information of patent data. Second, the analytic network process is applied to the constructed technological interrelationship matrices in order to produce the importance values of technologies from each perspective. Finally, data envelopment analysis is employed to the derived importance values in order to identify priorities of technologies, putting three perspectives together. It is expected that suggested approach could help technology planners to formulate strategy and policy for technological innovation.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.56 no.7
• /
• pp.1199-1204
• /
• 2007

In a cost based pool market, the generation capacity can be used as strategic bids by generation companies (Gencos) with the cost functions open to the market. Competition using strategic capacities is modeled by Cournot and Perfect Competiton (PC) model, and transformed into two by two payoff matrix game with Gencos' decision variables of Cournot and PC model. The payoff matrices vary when capacity payments are given to Gencos in accordance with their capacity bids. Nash Equilibrium (NE) in the matrices also moves with capacity price changes. In order to maximize social welfare of the market, NE should locate in a certain position of the payoff matrices, which corresponds to a PC NE. A concept of a critical capacity price is proposed and calculated in this paper that is defined as a minimum capacity price leading to PC NE. The critical capacity price is verified to work as a tool for suppressing a strategic capacity withholding in simulations of a test system.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.10 no.4
• /
• pp.287-295
• /
• 2010

Based on the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued in tuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy numbers, and the information about attribute weights is partially known. Anumerical example is used to illustrate the applicability of the proposed approach.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2008.04a
• /
• pp.29-32
• /
• 2008

Based on the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy numbers, and the information about attribute weights is partially known. A numerical example is used to illustrate the applicability of the proposed approach.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.2
• /
• pp.265-272
• /
• 2009

Fuzzy number intuitionistic fuzzy sets (FNIFSs), each of which is characterized by a membership function and a non-membership function whose values are trigonometric fuzzy number rather than exact numbers, are a very useful means to describe the decision information in the process of decision making. Wang [10] developed some arithmetic aggregation operators, such as the fuzzy number intuitionistic fuzzy weighted averaging (FIFWA) operator, the fuzzy number intuitionistic fuzzy ordered weighted averaging (FIFOWA) operator and the fuzzy number intuitionistic fuzzy hybrid aggregation (FIFHA) operator. In this paper, based on the FIFHA operator and the FIFWA operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as fuzzy number intuitionistic fuzzy decision matrices where each of the elements is characterized by fuzzy number intuitionistic fuzzy numbers, and the information about attribute weights is partially known. An example is used to illustrate the applicability of the proposed approach.

• Journal of Korean Institute of Industrial Engineers
• /
• v.36 no.1
• /
• pp.1-6
• /
• 2010

The Analytic Hierarchy Process (AHP) has been applied widely in various decision making fields. One of advantages of the AHP is the consistency test. However, it has several problems such as the limit of its concept, the limit of 9 scales and stern criteria, contradictory pairwise comparison. In this paper, we propose new criteria for the consistency with more realistic and ideal conditions. To derive the criteria, we conduct the simulation and use the bootstrap method, which is one of resampling techniques in the simulation area.

• Journal of the Korean Institute of Landscape Architecture
• /
• v.23 no.1
• /
• pp.23-38
• /
• 1995

ELEECTRE is a less demanding and potentially Bffective multiattribute evaluation method for pre-editing proeedure. The method, however, was developed based on probabilistic mathematicsand its reliability has never'been emprieally tested. This article examined the reliability of ELECTRo under various conditions of linear and non-linear utility func- tions using a Monte-Carlo shnulation, and found the method eausea a considerably high rate of error. To enhance the reliability of ELECTRE, two ways of modi(ication - adjust- ment of threshold values of concordance and discordance matrices, and adjustment of the required nunlber of probably-dominant alternatives to eliminate a probably-dominated alternative - were suggested, and their effctiveness was also tesed by a Monte-Carlo simulation. The simulation result chows that these modifications cponsiderably improve the reliability of ELECTRE, and yet maintain a reasonably high level of efficiency. Through these modifications, ELECTRE can be used as an efficient and feliable pre-editing method. Ways to implement ELECTRE in the construction of plainning decision support systens were discussed. The impli(els combination of this method and other multiattribute evaluation methods will help to create more effective decision suport systems.