The dissimilarity measures between fuzzy sets/intuitionistic fuzzy sets/picture fuzzy sets are studied and applied in various matters. In this paper, we propose some new dissimilarity measures on picture fuzzy sets. This new dissimilarity measures overcome the restrictions of all existing dissimilarity measures on picture fuzzy sets. After that, we apply these new measures to the pattern recognition problems. Finally, we introduce a multi-criteria decision making (MCDM) method that used the new dissimilarity measures and apply them in the supplier selection problems.

There are currently many places in the world where water is scarce. Therefore, water reuse has been mentioned by many researchers. Evaluation of water reuse applications is the selection of the best water reuse application of the existing options; it is also one of the applications of multi-criteria decision making (MCDM). In this paper, we introduce a new dissimilarity measure of picture fuzzy sets. This new measure overcomes the restriction of other existing dissimilarity measures of picture fuzzy sets. Then, we apply it to the multi-criteria decision making. Finally, we refer to a new method for selecting the best water reuse application of the available options by using the picture fuzzy MCDM.

In this paper, the authors present some research results of wearing process and rock destruction by diamond grit of core bit depending on drilling regime, rock hardness, diamond grit strength, etc. through the simulation of the interaction effect between diamond grit attached to the core bit and the rock. The relationship of the wear rate and rate of penetration of diamond core bit to the rotation per minute has been tested. On the basis of the research results, the authors have proposed solutions to select the appropriate technology for diamond drilling to improve the efficiency of solid mineral exploration in Vietnam.