# Journal of Uncertainty Analysis and Applications

## List of Papers (Total 74)

#### Expected Value of Exponential Fuzzy Number and Its Application to Multi-item Deterministic Inventory Model for Deteriorating Items

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...

#### Dependent-Chance Programming on Sugeno Measure Space

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...

#### Controller Parameter Optimization for the Robust Synchronization of Chaotic Systems with Known and Unknown Parameters

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...

#### Pricing Decision in a Two-Echelon Supply Chain with Competing Retailers Under Uncertain Environment

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...

#### Uncertain Dynamic Network Flow Problems

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...

#### Expectations of the reductions for type-2 trapezoidal fuzzy variables and its application to a multi-objective solid transportation problem via goal programming technique

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...

#### L-fuzzy Fixed Point Theorems for L-fuzzy Mappings via $\beta _{F_{L}}$ -admissible with Applications

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.

#### Transient Uncertainty Analysis in Solar Thermal System Modeling

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...

#### Uncertain Resource-Constrained Project Scheduling Problem with Net Present Value Criterion

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...

#### Some Preliminary Results about Uncertain Matrix

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.

#### A Three-Layer Supply Chain EPQ Model for Price- and Stock-Dependent Stochastic Demand with Imperfect Item Under Rework

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...

#### Predicting Human Interest: An Application of Artificial Intelligence and Uncertainty Quantification

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...

#### Equilibrium Analysis of Channel Structure Strategies in Uncertain Environment

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...

#### Importance Index of Components in Uncertain Reliability Systems

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...

#### Percentile Matching Estimation of Uncertainty Distribution

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...

#### Optimal Control Problem for Uncertain Linear Systems with Multiple Input Delays

Based on the concept of uncertain process, uncertain linear systems with multiple input delays are considered in this paper. An optimal problem for such systems is introduced and solved by using the equation of optimality and maximum principle. Finally, an example is given to show how to solve an uncertain optimal control model with time-delay.

#### Hidden Markov Bayesian Game with Application to Chinese Education Game

In real game situations, players are often not perfectly informed about true states but can observe signals, and decision-making may involve several periods. In order to formulate such situations, this paper uses a hidden Markov model to describe the state process, thus introducing a repeated game with hidden Markovian states, called hidden Markov Bayesian game. For the new model...

#### Delphi Method for Estimating Membership Function of Uncertain Set

Uncertain set is a set-valued function on an uncertainty space, and attempts to model unsharp concepts. Membership function is used to describe the membership degree that a value belongs to the uncertain set. In order to estimate the membership function for an uncertain set via multiple experts’ experimental data, this paper presents a new method by the combination of the method...

#### A Simple but Efficient Approach for Testing Fuzzy Hypotheses

In this paper, a new method is proposed for testing fuzzy hypotheses based on the following two generalized p-values: (1) the generalized p-value of null fuzzy hypothesis against alternative fuzzy hypothesis and (2) the generalized p-value of alternative fuzzy hypothesis against null fuzzy hypothesis. In the proposed method, each generalized p-value is formulated on the basis of...

#### Multi-asset Option Pricing in an Uncertain Financial Market with Jump Risk

Multi-asset options are created to accelerate investment among countries with the development of globalization and financial market integration. Considering the human uncertainty and the influence of sudden events such as wars and economic crisis, this paper proposes an uncertain model of multi-asset price with uncertain jumps. Option pricing formulas for the European-style dual...

#### Runge-Kutta Method for Solving Uncertain Differential Equations

Uncertain differential equations have been widely applied to many fields especially to uncertain finance. Unfortunately, we cannot always get the analytic solution of uncertain differential equations. Early researchers have put up a numerical method based on the Euler method. This paper designs a new numerical method for solving uncertain differential equations via the widely...

#### Determination of Target Values of Engineering Characteristics in QFD Using Uncertain Programming

Quality function deployment (QFD) is a new product development tool remarked with interpreting customer requirements into engineering characteristics of the design process. On account of the inherent imprecise and uncertain elements in the weights of customer requirements, the relationships between customer requirements and engineering characteristics, and the correlations among...

#### An Improvement on the Standard Linear Uncertainty Quantification Using a Least-Squares Method

Linear uncertainty analysis based on a first order Taylor series expansion, described in ASME PTC (Performance Test Code) 19.1 “Test Uncertainty” and the ISO Guide for the “Expression of Uncertainty in Measurement,” has been the most widely technique used both in industry and academia. A common approach in linear uncertainty analysis is to use local derivative information as a...

#### Inclusion Relationship of Uncertain Sets

Uncertain set is a set-valued function on an uncertainty space, and membership function is used to describe an uncertain set. This paper discusses the inclusion relationship between two uncertain sets and illustrates the relationship via some examples. A formula is derived to calculate the uncertain measure that an uncertain set is included in another one.

#### Uncertain pricing decision problem in closed-loop supply chain with risk-averse retailer

This paper considers a pricing and remanufacturing problem in closed-loop supply chain which includes one dominant manufacturer and one retailer under uncertain environment. The remanufacturing cost, market demand, and collection cost are characterized as uncertain variables. The firms’ optimal strategies are obtained by uncertainty-theory-based and game-theory-based models...