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.

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.

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.

In this study fuzzy arithmetic is presented as a tool to tackle the prediction of the amount of barium, strontium and calcium sulfates scales in oilfield operations. Since the shape of fuzzy numbers’ membership functions is a spread representative of the whole possible values for a special model parameter, fuzzy numbers are able to consider the uncertainties in parameter determinations and thus give more real results than crisp values. Solubility product models and other required Equations for scale prediction contain uncertain parameters and therefore application of fuzzy numbers can be useful. LR fuzzy numbers and related primary arithmetical operations based on Zadeh's extension principle have been introduced and their use in predicting scale depositions has been investigated. Parameters such as solubility products, free sulfate concentration and scale mass have been determined as fuzzy numbers. As a case study, scale depositions of barium and strontium sulfate resulted from mixing two incompatible waters have been obtained and compared with none fuzzy approach. fuzzy computations are able to predict the maximum scale mass with respect to existing information.

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.