Mathematical and Computational Applications

529 KiB

Open AccessArticle

A Method of Hybrid Multiple Attributes Group Decision Making with Risk Considering Decision-Makers' Confidence

by Xingzi Wen, Junlin Ouyang and Youjin Liu

Math. Comput. Appl. 2015, 20(1), 62-75; https://doi.org/10.3390/mca20010075 - 01 Apr 2015

Viewed by 1451

With respect to different confidence on evaluation result from different decision-makers to the hybrid multi-attribute with risk, an approach to group decision- making based on prospect theory and projection theory is proposed. Firstly, a tuple is established to record the evaluation result and [...] Read more.

With respect to different confidence on evaluation result from different decision-makers to the hybrid multi-attribute with risk, an approach to group decision- making based on prospect theory and projection theory is proposed. Firstly, a tuple is established to record the evaluation result and the hybrid decision information. Then the element of the tuple is changed into a single triangular fuzzy number by the transformation rule. Considering the confidence degree from single decision-maker to evaluation information, the group decision information is aggregated and the weights of attributes are calculated based on the intuitionistic fuzzy set theory. The improved projection method and prospect theory are proposed to rank the alternatives respectively. Finally, an application case is given to demonstrate the effectiveness and feasibility of the proposed approach. Full article

481 KiB

Open AccessArticle

Homotopic Approximate Solutions for the General Perturbed Nonlinear Schrödinger Equation

by Baojian Hong, Dianchen Lu and Yangzheng Liu

Math. Comput. Appl. 2015, 20(1), 50-61; https://doi.org/10.3390/mca20010061 - 01 Apr 2015

Cited by 1 | Viewed by 1307

Abstract

In this work, a class of perturbed nonlinear Schrödinger equation is studied by using the homotopy perturbation method. Firstly, we obtain some Jacobi-like elliptic function solutions of the corresponding typical general undisturbed nonlinear Schrödinger equation through the mapping deformation method, and secondly, a [...] Read more.

In this work, a class of perturbed nonlinear Schrödinger equation is studied by using the homotopy perturbation method. Firstly, we obtain some Jacobi-like elliptic function solutions of the corresponding typical general undisturbed nonlinear Schrödinger equation through the mapping deformation method, and secondly, a homotopic mapping transform is constructed, then the approximate solution with arbitrary degree of accuracy for the perturbed equation is researched, it is pointed out that the series of approximate solution is convergent. Finally, the efficiency and accuracy of the approximate solution is also discussed by using the fixed point theorem. Full article

407 KiB

Open AccessArticle

Analysis of an M ^(λ1,λ2) / M /1 / WV Queue with Controlled Vacation Interruption and Variable Arrival Rate

by Wenqing Wu and Yinghui Tang

Math. Comput. Appl. 2015, 20(1), 39-49; https://doi.org/10.3390/mca20010049 - 01 Apr 2015

Viewed by 1533

Abstract

This paper studies a Markovian queue with multiple working vacations and controlled vacation interruption. If there are at least N customers waiting upon completion of a service at a lower rate, the vacation is interrupted and the server returns to the system to [...] Read more.

This paper studies a Markovian queue with multiple working vacations and controlled vacation interruption. If there are at least N customers waiting upon completion of a service at a lower rate, the vacation is interrupted and the server returns to the system to resume the normal working level. Otherwise, the server continues the vacation until the system is non-empty after a vacation ends or there are at least N customers after a service ends. Moreover, the variable arrival rate of the customers is taken into account. Under such assumptions, by using the quasi-birth-and-death process, the matrix- geometric method and the difference equation theory, the steady-state queue length distribution along with various performance measures are derived. Additionally, under a certain cost structure, the optimal threshold N* that minimizes the long-run expected cost function per unit time is numerically determined. Full article

826 KiB

Open AccessArticle

A Difference-Index Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Multiattribute Decision Making

by Deng-Feng Li and Jie Yang

Math. Comput. Appl. 2015, 20(1), 25-38; https://doi.org/10.3390/mca20010038 - 01 Apr 2015

Cited by 6 | Viewed by 1579

Abstract

The order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature. Ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) is more difficult due to the fact that the TrIFNs are a generalization of the [...] Read more.

The order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature. Ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) is more difficult due to the fact that the TrIFNs are a generalization of the fuzzy numbers. The aim of this paper is to develop a new methodology for ranking TrIFNs. We define the value-index and ambiguity-index based on the value and ambiguity of the membership and non-membership functions, and then propose a difference-index based ranking method, which is applied to multiattribute decision making (MADM) problems. The proposed method is compared to show its advantages and applicability. Full article

506 KiB

Open AccessArticle

Dtm-Bf Method for the Flow and Heat Transfer Over a Nonlinearly Stretching Sheet With Nanofluids

by Cao Limei, Sun Yina, Shen Yanan and Si Xinhui

Math. Comput. Appl. 2015, 20(1), 15-24; https://doi.org/10.3390/mca20010024 - 01 Apr 2015

Viewed by 1698

Abstract

This paper investigates an analytical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet. The governing partial differential equations are transformed into coupled nonlinear differential equations by introducing a siφmilarity transformation. The asymptotic analytical solutions are [...] Read more.

This paper investigates an analytical analysis for the flow and heat transfer in a viscous fluid over a nonlinear stretching sheet. The governing partial differential equations are transformed into coupled nonlinear differential equations by introducing a siφmilarity transformation. The asymptotic analytical solutions are obtained by using differential transform method-basic functions (DTM-BF). Four types of nanofluids, namely Cu-water, Ag-water, Al₂O₃ -water and TiO₂ -water were studied. The influence of the nanoparticle volume fraction φ, the nonlinear stretching parameter n , Prandtl number Pr, Eckert number Ec and different nanoparticles on the velocity and temperature are discussed and shown graphically. The comparison with the numerical results is presented and it is found to be in excellent agreement. Full article

513 KiB

Open AccessArticle

Positive Almost Periodic Solution for Impulsive Nicholson’s Blowflies Model with Linear Harvesting Term on the Bounded Domain

by Zhijian Yao

Math. Comput. Appl. 2015, 20(1), 1-14; https://doi.org/10.3390/mca20010014 - 01 Apr 2015

Viewed by 1105

Abstract

In this paper, impulsive Nicholson’s blowflies model with linear harvesting term is studied. By using the contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of a unique positive almost periodic solution. In addition, the exponential convergence of positive almost [...] Read more.

In this paper, impulsive Nicholson’s blowflies model with linear harvesting term is studied. By using the contraction mapping fixed point theorem, we obtain sufficient conditions for the existence of a unique positive almost periodic solution. In addition, the exponential convergence of positive almost periodic solution is investigated. Full article

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Math. Comput. Appl., Volume 20, Issue 1 (April 2015) – 6 articles , Pages 1-75

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