Importance analysis on failure credibility of the fuzzy structure

To measure the effects of the fuzzy inputs on structural safety degree, this paper establishes the failure credibility-based global sensitivity by the fuzzy expected value of the absolute difference between the unconditional failure credibility and conditional one. To establish the failure credibility-based global sensitivity, the conditional failure credibility is firstly defined according to the original definition of conditional event and the relationship among the possibility, necessity and credibility, in which no extra assumption is introduced. After that, the equivalent expression of the failure credibility is deduced, on which the Bayesian transformation of the conditional failure credibility is obtained in this paper. Then, a single-loop method based on the sequential quadratic programming is applied to efficiently estimate the defined failure credibility-based global sensitivity. According to the result of the constructed failure credibility-based global sensitivity, designers can pay more attentions to the more important fuzzy inputs to have a better control of the structural safety degree. The presented examples demonstrate the feasibility of the constructed failure credibility-based global sensitivity and the efficiency of the proposed solution.

Fuzzy Bi-Objective Closed-Loop Supply Chain Network Design Problem with Multiple Recovery Options

A network design of a closed-loop supply chain (CLSC) with multiple recovery modes under fuzzy environments is studied in this article, in which all the cost coefficients (e.g., for facility establishment, transportation, manufacturing and recovery), customer demands, delivery time, recovery rates and some other factors that cannot be precisely estimated while designing are modeled as triangular fuzzy numbers. To handle these uncertain factors and achieve a compromise between the two conflicting objectives of maximizing company profit and improving customer satisfaction, a fuzzy bi-objective programming model and a corresponding two-stage fuzzy interactive solution method are presented. Applying the fuzzy expected value operator and fuzzy ranking method, the fuzzy model is transformed into a deterministic counterpart. Subsequently, Pareto optimal solutions are determined by employing the fuzzy interactive solution method to deal with the conflicting objectives. Numerical experiments address the efficiency of the proposed model and its solution approach. Furthermore, by comparing these results with the CLSC network design in deterministic environments, the benefits of modeling the CLSC network design problem with fuzzy information are highlighted.

AN AGGREGATION OF SURVEY QUESTIONNAIRES IN A FUZZY ENVIRONMENT AND ITS APPLICATION

In the response process of survey questionnaires, respondents generally express their opinions (assessment) in a fuzzy environment, i.e., assessment with a degree of membership, and in many cases, an aggregation of survey questionnaires is generally computed mathematically. In this paper, we propose a new aggregation method using the FEV (Fuzzy Expected Value) in summarizing survey questionnaires. As an application of proposed aggregation method, to quantify accurately the current state of opinions and the reasons for national IT investment increasing the rate of economic growth, we decided to circulate a survey questionnaire on national IT investment to interested parties throughout the research institute, government, IT industry. Generally, as we have already known and experienced in most of survey questionnaires, there was a little response. Moreover, according to interested parties, the result was biased views on the government IT investment. So, we consider big data analysis on the selection of the proper IT items for national investment. Proposed aggregation method is consisted of 2-phases. In phase 1, keyword selection for the proper IT items based on big data such as Facebook, Twitter, blog, Google, etc. is achieved. This phase is not mandatory (optional and dependent on the characteristic of survey). In phase 2, aggregation by using the FEV is obtained. Proposed aggregation method on survey questionnaires is particularly useful to find current focal issues such as trend, what’s new, etc., on big data such as Facebook, Twitter, blog, Google, etc. Moreover, in many cases, aggregation using the FEV is a better representative value than the arithmetic mean. Generally, the FEV is more suitable than the value of averaging computation in searching for the representative value of fuzzy set.

A Fuzzy Programming Method for Modeling Demand Uncertainty in the Capacitated Road–Rail Multimodal Routing Problem with Time Windows

Demand uncertainty is an important issue that influences the strategic, tactical, and operational-level decision making in the transportation/logistics/supply chain planning. In this study, we explore the effect of demand uncertainty on the operational-level freight routing problem in the capacitated multimodal transportation network that consists of schedule-based rail transportation and time-flexible road transportation. Considering the imprecise characteristic of the demand, we adopt fuzzy set theory to model its uncertainty and use trapezoidal fuzzy numbers to represent the fuzzy demands. We set multiple transportation orders as the optimization object and employ soft time windows to reflect the customer requirement on on-time transportation. Under the above situation, we establish a fuzzy mixed integer nonlinear programming (FMINLP) model to formulate the capacitated road–rail multimodal routing problem with demand uncertainty and time windows. We first use the fuzzy expected value model and credibility measure based fuzzy chance-constrained programming to realize the defuzziness of the model and then adopt linearization technique to reformulate the crisp model to finally generate an equivalent mixed integer linear programming (MILP) model that can be solved by standard mathematical programming software. Finally, a numerical case is presented to demonstrate the feasibility of the proposed method. Sensitivity analysis and fuzzy simulation are combined to quantify the effect of demand uncertainty on the routing problem and also reveal some helpful insights and managerial implications.

Analysis of a fuzzy epidemic model with saturated treatment and disease transmission

In this paper, we describe an SIS epidemic model where both the disease transmission rate and treatment function are considered in saturated forms. The dynamical behavior of the system is analyzed. The system is customized by considering the disease transmission rate and treatment control as fuzzy numbers and then fuzzy expected value of the infected individuals is determined. The fuzzy basic reproduction number is investigated and a threshold condition of pathogen is derived at which the system undergoes a backward bifurcation.

Modeling Portfolio Optimization Problem by Probability-Credibility Equilibrium Risk Criterion

This paper studies the portfolio selection problem in hybrid uncertain decision systems. Firstly the return rates are characterized by random fuzzy variables. The objective is to maximize the total expected return rate. For a random fuzzy variable, this paper defines a new equilibrium risk value (ERV) with credibility level beta and probability level alpha. As a result, our portfolio problem is built as a new random fuzzy expected value (EV) model subject to ERV constraint, which is referred to as EV-ERV model. Under mild assumptions, the proposed EV-ERV model is a convex programming problem. Furthermore, when the possibility distributions are triangular, trapezoidal, and normal, the EV-ERV model can be transformed into its equivalent deterministic convex programming models, which can be solved by general purpose optimization software. To demonstrate the effectiveness of the proposed equilibrium optimization method, some numerical experiments are conducted. The computational results and comparison study demonstrate that the developed equilibrium optimization method is effective to model portfolio selection optimization problem with twofold uncertain return rates.

Dynamical Behavior of an Epidemic Model in a Fuzzy Transmission

In this paper, we have formulated a simple SIS type epidemic model in the presence of treatment control, and we have discussed the dynamical behavior of the system. The system is modified by considering both the disease transmission rate and the treatment function as fuzzy numbers, and also the fuzzy expected value of the infected individuals is calculated. Furthermore, the fuzzy basic reproduction number is investigated and a threshold condition of pathogen is obtained at which the system undergoes a transcritical bifurcation.