Control charts are widely used in industrial processes as well as in health sciences and particularly for monitoring the performance of cardiac surgeon or a group of surgeons based on the preoperative risk of patients. Since the preoperative risk is a vague and nonprecise variable and the anesthesiologists after checking how many risk factors a patient has, determine the risk of mortality before the surgery as a linguistic term such as low, medium, high or others like that, it is better to be considered as a fuzzy number, which can be determined by using fuzzy regression models. In this condition, we need a special chart to monitor the performance of surgeons based on these fuzzy data. In this article, we propose risk-adjusted control charts based on LR-fuzzy data and then test our conclusions on real data.

In this paper, the fuzzy matrix equation AeX B = e C in which A; B are n × n crisp matrices respectively and e C is an n×n arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a suffcient condition for the existence of strong fuzzy solution is derived. Some examples are given to illustrate the proposed method.

‎This paper aims at solving a class of linear LR complex fuzzy matrix equations $A\widetilde{X}B=\widetilde{C}$ using a matrix approach‎. ‎By using the basic operation of LR fuzzy number matrix‎, ‎the original complex fuzzy matrix equation is transformed into a clear matrix equation group‎. ‎Two new and simplified models for calculating fuzzy solutions are designed in detail‎, ‎and sufficient conditions for strong fuzzy solutions are analyzed‎. ‎Finally‎, ‎two examples are given to illustrate the feasibility and effectiveness of the proposed method‎. ‎Now that the complex fuzzy numbers can describe uncertain factors more vivid and reasonable than the real fuzzy numbers sometimes and the wide application of matrix equations under uncertain conditions‎, ‎our research work enriches the fuzzy linear systems theory‎.

In many real applications, the data of production processes can't be precisely measured.We develop some fuzzy versions of the classical DEA models (in particular, the CCR model) by using some ranking methods based on the comparison of cuts. Our approaches can be seen as an extension of the DEA methodology. The provides users and practitioners with models which represent some real life processes more appropriately. DEA- based Malmquist productivity index measures the productivity change over time. In this paper we provide an extension to the DEA- based Malmquist productivity index for all DMUs with fuzzy data.

In this paper, the calculation methods of the real eigenvalues and LR fuzzy eigenvectors of clear real symmetry matrices are deeply considered. The original fuzzy feature problem is extended by using the arithmetic algorithm of LR fuzzy numbers into a simple feature problem with a high-order clear real symmetry matrix. We discuss two cases: (a) λ is a non-negative unknown eigenvalue; (b) λ is a negative unknown eigenvalue. We established two computational models and proposed an algorithm for finding the fuzzy eigenvectors of the true symmetry matrix. Some numerical examples are used to illustrate our proposed method.

Text Classification is an important research field in information retrieval and text mining. The main task in text classification is to assign text documents in predefined categories based on documents’ contents and labeled-training samples. Since word detection is a difficult and time consuming task in Persian language, Bayesian text classifier is an appropriate approach to deal with different word formats and new words.Also, fuzzy theory may be used to manage uncertainty in imprecise Persian sentences.In this paper, we utilize L-R type fuzzy numbers in Bayesian text classifier to classify textual Persian documents (Fuzzy Bayesian text classifier). The obtained results on simulated imprecise textual Persian documents show improvements in both recall and precision parameters by using Fuzzy Bayesian text classification approach over Naïve Bayesian text classifier.

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System (FFLS) of equations in which all the components of the coefficient matrix are either nonnegative or non-positive. First, in discussing an FFLS with a nonnegative coefficient matrix, we consider an equivalent FFLS by using an appropriate permutation to simplify fuzzy multiplications. To solve the m n permutated system, we convert it to three m  n real linear systems, one being concerned with the cores and the other two being related to the left and right spreads. To decide whether the core system is consistent or not, we use the modified Huang algorithm of the class of ABS methods. If the core system is inconsistent, an appropriate unconstrained least squares problem is solved for an approximate solution. The sign of each component of the solution is decided by the sign of its core. Also, to know whether the left and right spread systems are consistent or not, we apply the modified Huang algorithm again. Appropriate constrained least squares problems are solved, when the spread systems are inconsistent or do not satisfy fuzziness conditions. Then, we consider the FFLS with a mixed single-signed coefficient matrix, in which each component of the coefficient matrix is either nonnegative or non-positive. In this case, we break the m n coefficient matrix up to two mn matrices, one having only nonnegative and the other having only non-positive components, such that their sum yields the original coefficient matrix. Using the distributive law, we convert each m n FFLS into two real linear systems where the first one is related to the cores with size mn and the other is 2m 2n and is related to the spreads. Here, we also use the modified Huang algorithm to decide whether these systems are consistent or not. If the first system is inconsistent or the second system does not satisfy the fuzziness conditions, we find an approximate solution by solving a respective least squares problem. We summarize the proposed approach by presenting two computational algorithms. Finally, the algorithms are implemented and effectively tested by solving various randomly generated consistent as well as inconsistent numerical test problems.