Assessing most productive scale size with fuzzy stochastic data envelopment analysis

Classic data envelopment analysis (DEA) is a linear programming method for evaluating the relative efficiency of decision making units (DMUs) that uses multiple inputs to produce multiple outputs. In the classic DEA model inputs and outputs of DMUs are deterministic, while in the real world, are often fuzzy, random, or fuzzy-random. Many researchers have proposed different approaches to evaluate the relative efficiency with fuzzy and random data in DEA. In many studies, the most productive scale size (mpss) of decision making units has been estimated with fuzzy and random inputs and outputs. Also, the concept of fuzzy random variable is used in the DEA literature to describe events or occurrences in which fuzzy and random changes occur simultaneously. This paper has proposed the fuzzy stochastic DEA model to assess the most productive scale size of DMUs that produce multiple fuzzy random outputs using multiple fuzzy random inputs with respect to the possibility-probability constraints. For solving the fuzzy stochastic DEA model, we obtained a nonlinear deterministic equivalent for the probability constraints using chance constrained programming approaches (CCP). Then, using the possibility theory the possibilities of fuzzy events transformed to the deterministic equivalents with definite data. In the final section, the fuzzy stochastic DEA model, proposed model, has been used to evaluate the most productive scale size of sixteen Iranian hospitals with four fuzzy random inputs and two fuzzy random outputs with symmetrical triangular membership functions.

Bilevel Optimization of Taxing Strategies for Carbon Emissions Using Fuzzy Random Matrix Generators

Bilevel (BL) optimization of taxing strategies in consideration of carbon emissions was carried out in this work. The BL optimization problem was considered with two primary targets: (1) designing an optimal taxing strategy (imposed on power generation companies) and (2) developing optimal economic dispatch (ED) schema (by power generation companies) in response to tax rates. The resulting interaction was represented using Stackelberg game theory – where the novel fuzzy random matrix generators were used in tandem with the cuckoo search (CS) technique. Fuzzy random matrices were developed by modifying certain aspects of the original random matrix theory. The novel methodology was tailored for tackling complex optimization systems with intermediate complexity such as the application problem tackled in this work. Detailed performance and comparative analysis are also presented in this chapter.

Fuzzy Decision Tree Based Method in Decision-Making of COVID-19 Patients’ Treatment

A new method in decision-making of timing of tracheostomy in COVID-19 patients is developed and discussed in this paper. Tracheostomy is performed in critically ill coronavirus disease (COVID-19) patients. The timing of tracheostomy is important for anticipated prolonged ventilatory wean when levels of respiratory support were favorable. The analysis of this timing has been implemented based on classification method. One of principal conditions for the developed classifiers in decision-making of timing of tracheostomy in COVID-19 patients was a good interpretation of result. Therefore, the proposed classifiers have been developed as decision tree based because these classifiers have very good interpretability of result. The possible uncertainty of initial data has been considered by the application of fuzzy classifiers. Two fuzzy classifiers as Fuzzy Decision Tree (FDT) and Fuzzy Random Forest (FRF) have been developed for the decision-making in tracheostomy timing. The evaluation of proposed classifiers and their comparison with other show the efficiency of the proposed classifiers. FDT has best characteristics in comparison with other classifiers.

Hybrid Uncertainty-Goal Programming Model with Scaled Index for Production Planning Assessment

Goal programming (GP) can be thought of as an extension or generalization of linear programming to handle multiple, normally conflicting objective measures. Each of these measures is given a goal or target value to be achieved. Unwanted deviations from this set of target values are then minimized in an achievement function. Production planning is an important process that aims to leverage the resources available in industry to achieve one or more business goals. However, the production planning that typically uses mathematical models has its own challenges where parameter models are sometimes difficult to find easily and accurately. Data collected with various data collection methods and human experts’ judgments are often prone to uncertainties that can affect the information presented by quantitative results. This study focuses on resolving data uncertainties as well as multi-objective optimization using fuzzy random methods and GP in production planning problems. GP was enhanced with fuzzy random features. Scalable approaches and maximum minimum operators were then used to solve multi-object optimization problems. Scaled indices were also introduced to resolve fuzzy symbols containing unspecified relationships. The application results indicate that the proposed approach can mitigate the characteristics of uncertainty in the analysis and achieve a satisfactory optimized solution.

Fuzzy Random Bimatrix Games Based on Possibility and Necessity Measures

In this study, we formulate bimatrix games with fuzzy random payoffs, and introduce equilibrium solution concepts based on possibility and necessity measures. It is assumed that each player has linear fuzzy goals for his/her payoff. To obtain equilibrium solutions based on the possibility and necessity measures, we propose two algorithms in which quadratic programming problems are solved repeatedly until equilibrium conditions are satisfied.

Solving Capacitated Vehicle Routing Problem with Demands as Fuzzy Random Variable

Capacitated vehicle routing problem ( CVRP ) is a classical combinatorial optimization problem in which a network of customers with specified demands is given. The objective is to find a set of routes which originates as well as terminates at the depot node. These routes are to be traversed in such a way that the demands of all the customers in the network are satisfied and the cost associated with traversal of these routes come out to be a minimum. In real-world situations, the demand of any commodity depends upon various uncontrollable factors, such as, season, delivery time, market conditions and many more. Due to these factors, the demand can always not be told in advance and a precise information about the demand is nearly impossible to achieve. Hence, the demands of the customers always experience impreciseness and randomness in real-life. The decisions made by the customers about the demands may also have some scope of hesitation as well. In order to handle such demands of customers in the network, fuzzy random variables and intuitionistic fuzzy random variables are used in this work. The work bridges the gap between the classical version of CVRP and the real-life situation and hence makes it easier for the logistic management companies to determine the routes that should be followed for minimum operational cost and maximum profit. Mathematical models corresponding to CVRP with fuzzy stochastic demands ( CVRPFSD ) and CVRP with Intuitionistic fuzzy stochastic demands ( CVRPIFSD ) have been presented. A two-stage model has been proposed to find out the solution for the same. To explain the working of the methodology defined in this work, two different example of a network with fuzzy and intuitionistic fuzzy demands have been worked out. The proposed solution approach is also tested on modified fuzzy versions of some benchmark instances.