One advantage of process incapability index over the classical process capability index is that it provides uncontaminated separation between process accuracy and process precision. However, the value of the index is difficult to determine accurately when process parameters cannot be determined precisely. In such a case, fuzzy set theory can be applied to obtain more flexible and sensitive information. In this paper, a fuzzy process incapability index is proposed when the specification limits are assumed to be type-2 fuzzy. When the process mean and variance are unknown and when the observations are measured imprecisely, three fuzzy estimators are considered. A simulation study is conducted based on the Thin-Film-Transistor Liquid-Crystal Display (TFT-LCD) fuzzy process. By applying the total integral value method to the membership function of a fuzzy index, it becomes easier to make a comparison of the quality of different processes.

In this paper, a new approach is proposed in order to select an optimal membership function for inputs of wind speed prediction system. Then using a fuzzy method and the stochastic characteristics of wind speed in the previous year, the wind speed modeling is performed and the wind speed for the future year will be predicted. In this proposed method, the average and the standard deviation of inputs data are calculated. The membership function shape and the domain intervals are evaluated using the variance of system. This technique prevents from trial and error method for defining the shape and domain intervals of optimal membership function and helps to achieve the desired prediction in a quick way. The wind speed is estimated in the fuzzy inference system and simulated with the fuzzy logic. The sensitivity analyses are performed by changing the input parameters and membership functions shape and the results are compared. The results demonstrate that this new prediction method is a fast and applicable method compared to the other methods since the calculated error will be more than the error of this method if the shape and domain interval of membership function are changed.

Groundwater is one of the most important sources of drinking, industrial, and agricultural water in arid and semi-arid regions, where the occurrence of droughts, rapid population growth, and the corresponding increase in water demand threaten groundwater resources. Over-exploitation and mismanagement of groundwater resources result in environmental problems such as subsidence and saltwater intrusion in coastal aquifers. The risk of saltwater intrusion threatens the Urmia aquifer due to the proximity of the aquifer to Lake Urmia and severe groundwater decline. This study evaluates the vulnerability of saltwater intrusion by the GALDIT framework. The results show the conservative vulnerability index with low efficiency, where vulnerable areas are limited to a narrow strip near the coastline. Fuzzy membership functions were employed within the GALDIT framework to increase efficiency. The results of the modified GALDIT resolve the weakness of presenting conservative results in the basic GALDIT framework.

Data envelopment analysis (DEA) is a method to evaluate the relative efficiency of decision making units (DMUs). In this method, the issue has always been to determine a set of weights for each DMU which often caused many problems. Since the DEA models also have the multi-objective linear programming (MOLP) problems nature, a rational relationship can be established between MOLP and DEA problems to overcome the problem of determining weights. In this study, a membership function was defined base on the results of CCR model and cross efficiency, and by using this membership function in a proposed model, we obtained a common set of weights for all DMUs. Finally, by solving a sample problem, the proposed algorithm was explained.

Fuzziness is ever presented in real life decision making problems. In this paper, we adapt the pessimistic approach to study a pair of linear primal-dual problem under intuitionistic fuzzy (I-fuzzy) environment and prove certain duality results. We generate the duality results using exponential membership and non-membership functions to represent the decision maker's satisfaction and dissatisfaction level. Further, two numerical examples have been given. In each of these illustrations, varying the values of the shape variables in the exponential membership functions, various nonlinear optimization problems have been constructed, analyzed and solved. The duality gaps for all these optimization problems have been computed and compared with the duality gap under the linear membership function. We found that these gaps for the I-fuzzy linear primal-dual pair under the exponential membership functions are smaller as compared with the linear membership functions. The main advantage of using the exponential membership function is that it has the exibility of altering the values of the shape parameters (as per the decision-maker's satisfaction). Finally, with the help of a suitable ranking defuzzification function, we have extended our approach to the I-fuzzy linear problem with fuzzy parameters and fuzzy constraints.