Journal of Graphics Tools

Garai T., Chakraborty D., Roy T.K.

Possibility, necessity, and credibility measures play a significant role to measure the chances of occurrence of fuzzy events. In this paper, possibility, necessity, and credibility measures of exponential fuzzy number, and its expected value has been derived. A multi-item two-warehouse deterministic inventory model for deteriorating items with stock-dependent demand has been developed. For the proposed inventory model, the different costs and other parameters are considered in exponential fuzzy nature. Solution methodology of this model using expected value has been discussed. A numerical example is considered to illustrate the multi-item two-warehouse deterministic inventory model. Finally, few sensitivity analyses are presented under different rates of deterioration to check the validity of the proposed model.

Zhang H., Song J.

In order to solve the optimization problem of selecting the decision with maximal chance to meet the Sugeno event in Sugeno environment, dependent-chance programming on Sugeno measure space is proposed, which can be considered as a generalized extension of the stochastic dependent-chance programming. Firstly, the theoretical framework of dependent-chance programming on Sugeno measure space is established. Secondly, a Sugeno simulation-based hybrid approach, which consists of back propagation neural network and genetic algorithm, is presented to construct an approximate solution of the complex dependent-chance programming models on Sugeno measure space. Finally, some numerical examples are given to illustrate the effectiveness of the approach.

Ahmad I., Saaban A.B., Ibrahim A.B.

In this paper, a synchronization problem of a three-dimensional (3-D) Coullete chaotic system using the active- and adaptive-based synchronization control techniques is addressed. Based on the Routh-Hurwitz criterion and using the active control algorithm, a single control function is considered and a computational study is performed to identify the correct balance between the converging rates of the synchronization error signals to the origin and magnitude of the linear controlling parameters (LCPs) for the globally exponential synchronization (GES) between two identical 3-D Coullete chaotic systems. In order to achieve the complete synchronization (CS) objective with unknown model uncertainties, external disturbances, and unknown time-varying parameters, a novel nonlinear adaptive synchronous controller is proposed and suitable adaptive laws of time-varying parameters are designed that accomplish the asymptotic synchronization between two identical uncertain 3-D Coullete chaotic systems. The two synchronizing controlling approaches are applied to investigate the CS phenomenon, and the results are compared. Open research problems are also discussed. All simulations results are carried out to validate the effectiveness of the proposed synchronization control approaches by using Mathematica 10.0.

Ke H., Wu Y., Huang H., Chen Z.

This paper explores a supply chain pricing competition problem in a two-echelon supply chain with one manufacturer and two competing retailers. The manufacturing costs, sales costs, and market bases are all characterized as uncertain variables whose distributions are estimated by experts’ experienced data. In consideration of channel members’ different market powers, three decentralized game models are employed to explore the equilibrium behaviors in corresponding decision circumstances. How the channel members should choose their most profitable pricing strategies in face of uncertainties is derived from these models. Numerical experiments are conducted to examine the effects of power structures and parameters’ uncertain degrees on the pricing decisions of the members. The results show that the existence of dominant powers in the supply chain will increase the sales prices and reduce the profit of the whole supply chain. It is also found that the supply chain members may benefit from higher uncertain degrees of their own costs while the other supply chain members will gain less profits. Additionally, the results demonstrate that the uncertainty of the supply chain will make end consumers pay more. Some other interesting managerial highlights are also obtained in this paper.

Alipour H., Mirnia K.

In this paper, uncertain dynamic network flow problems (UDNFPs) are formulated, and an algorithm is proposed to solve them by noting that arc capacities are uncertain (may vary with time or not), and flow varies over time in each arc. Here, uncertainty refers to nondeterministic states, in which some factors are uncertain and cannot be determined by the probability theory. Since the uncertainty theory seems to be well applicable in these cases, thus, it is applied for the UDNFPs in this paper. Although some papers have studied uncertain network flow problems in the static case, but in the best of our knowledge, this paper is the first one about the UDNFPs.

Dutta A., Jana D.K.

In this paper, based on the concepts of credibility measure and expectation theory, we derive the expectation formulae for the three reductions of a type-2 trapezoidal fuzzy variable (T2TrFV), which are attained by adopting the critical value (CV) reduction methods. We minimize the total transportation cost and the total transportation time over a single layered distribution system consisting of vendors and customers represented as a multi-objective solid transportationproblem. To portray the uncertainty in a real life choice environment, we consider the unit cost of transportation, demands, availabilities, conveyance capacities, unit transportation time and unit loading and unloading time as T2TrFVs. The corresponding deterministic model, which is obtained by the application of expectation formulas deduced earlier, is converted to a single objective optimization problem using goal programming technique and weighted sum method via the soft computing technique—generalized reduced gradient (LINGO-14.0). A numerical experiment is finally illustrated and corresponding graphical representations are provided.

Sirajo Abdullahi M., Azam A.

In this paper, the authors use the idea of $\beta _{F_{L}}$ -admissible mappings to prove some L-fuzzy fixed point theorems for a generalized contractive L-fuzzy mappings. Some examples and applications to L-fuzzy fixed points for L-fuzzy mappings in partially ordered metric spaces are also given, to support main findings.

Cho H., Smith A., Luck R., Mago P.J.

Complex, dynamic, computational models are routinely used to evaluate and optimize the design and performance of solar thermal systems. As models become more complex, performing uncertainty analysis on such models can be quite challenging and computationally expensive. This paper presents an effective approach to quantify uncertainties associated with transient simulation results from a dynamic solar thermal energy system model with uncertain parameters. The proposed method utilizes the concept of impulse response and convolution process to estimate the sensitivities to time-varying external inputs. Using this method, the number of simulations required to propagate uncertainties through dynamic models can be significantly reduced. An example is presented throughout the paper to demonstrate the procedure of the proposed uncertainty analysis approach.

Zhao C., Ke H., Chen Z.

On the basis of uncertainty theory, plenty of researches have been done on uncertain resource-constrained project scheduling problems. Instead of minimizing the makespan, in this paper, we address the maximization of net present value of a project’s cash flows when activity durations are assumed to be uncertain. In addition to precedence constraint and resource constraint involved in resource-constrained project scheduling problem, a deadline constraint is taken into account. Thus, our aim is to maximize net present value and to satisfy the deadline constraint as well. Accordingly, we introduce three models and utilize a revised estimation of distribution algorithm to solve this problem. This work may provide net present value criterion for financial officers on project scheduling.

Liu B.

This paper presents a new concept of uncertain matrix that is a measurable function from an uncertainty space to the set of real matrices. It is proved that an uncertain matrix is a matrix all of whose elements are uncertain variables. The independence of uncertain matrices is also investigated.

Pal S., Mahapatra G.S., Samanta G.P.

In this paper, we have developed an integrated supplier-manufacturer-retailer, joint economic lot-sizing model for the items with stochastic demand and imperfect quality. The supplier produces the item (raw material) up to certain time, which is a decision variable, and sends it to the manufacturer. Now, the manufacturer produces the item in small cycles and the production process of manufacturer is imperfect which produces certain number of defective items. A 100 % screening process for detecting the imperfect quality items is conducted, and at the end of each cycle, the imperfect items are accumulated and are reworked by the manufacturer. Thus, ultimately the retailer receives the perfect quality item. We consider that the delivery quantity to the retailer depends on the price and stock-dependent stochastic demand of the retailer. The model considers the impact of business strategies such as optimal time, optimal ordering size of raw material, production rate, etc. in different sectors on collaborating marketing system. An analytical method is applied to optimize the production time and production rate to obtain minimum total cost. Finally, numerical results, which have several interesting managerial insights and implications, and the sensitivity analysis are presented and discussed for illustrative purposes.

Ahmed T., Srivastava A.

The idea that a machine can numerically estimate the interest of an individual towards any entity (e.g., WhatsApp, Facebook) is fascinating. Interest, however, is a complex human property that cannot be quantified by another person; to have a machine-driven method quantify this unobservable and intangible internal property is challenging. In this paper, we make an attempt to address this issue. We propose a novel approach to estimate this internal state of a human. We formulate the interest prediction problem as a hidden state estimation problem and deduce a solution through Bayesian inference. In doing so, we apply indirect inference rules to estimate interest from activity. Activity as a consequence of interest is computed via a subjective-objective weighted approach. We further propose a model for interest by taking inspiration from physics. We use mean reverting stochastic procedures to capture the long-term dynamics of interest. With this perspective, a solution is provided via Monte Carlo simulations. To demonstrate the feasibility of the framework, we develop a web-based prototype and experiment with real-world datasets.

Huang H., Ke H., Che Y.

In this paper, we consider a pricing decision problem with two competing supply chains which distribute differentiated but competing products in the same market. Each chain can be vertically integrated or decentralized based on the choice of the manufacturer. The manufacturing costs, sales costs and consumer demands are characterized as uncertain variables, whose distributions are estimated by experienced experts. Meanwhile, uncertainty theory and game theory are employed to formulate the pricing decision problems. The equilibrium behaviors (how the supply chain members make their own pricing decisions on wholesale prices and retailer markups) at operational level under three possible scenarios are derived. Numerical experiments are also given to explore the impacts of the parameters’ uncertain degrees on supply chain members’ pricing decisions. The results demonstrate that the supply chain uncertain factors have great influences on equilibrium prices. In addition, we also evaluate the effects of competing intensity (substitutability) of the two products on the strategy behaviors, vertically integrated channel strategy versus decentralized strategy, of the manufacturers. It is found that the manufacturers are better off to distribute their products through a decentralized channel rather than an integrated one when the substitutability is greater than some value. Besides, the uncertain factors in the supply chain might reduce the value contrast to the one in deterministic case. Some other interesting managerial highlights are also provided in this paper.

Gao R., Yao K.

Importance measure is an index for estimating the importance of an individual component or a group of components in a reliability system. So far, the importance measures for components in stochastic reliability systems have been investigated. In order to calculate the importance of a component or a group of components in an uncertain reliability system, this paper proposes a new concept of importance index. Some formulas are given to calculate the importance index of a component and a group of components in an uncertain reliability system. Then, some special types of uncertain reliability systems such as uncertain series, parallel, parallel-series, series-parallel, bridge, and k-out-of-n systems are studied.

Sampath S., Anjana K.

This paper considers the application of method of percentile matching available in statistical theory of estimation for estimating the parameters involved in uncertainty distributions. An empirical study has been carried out to compare the performance of the proposed method with the method of moments and the method of least squares considered by Wang and Peng (J. Uncertainty Analys. Appl. 2, (2014)) and Liu (Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty, (2010)), respectively. The numerical study clearly establishes the superiority of the proposed method over the other two methods in estimating the parameters involved in linear uncertainty distribution when appropriate orders of percentiles are used in the estimation process.