Picture fuzzy set is an extension of fuzzy sets and intuitionistic sets. It is demonstrated have a wide application in the fact and theoretical. In this paper, we propose some novel similarity measures between picture fuzzy sets. The novel similarity measure is constructed by combining negative functions of each degree membership of picture fuzzy set. This similarity is shown that is better other similarity measures of picture fuzzy sets in some cases. Next, we apply them in several pattern recognition problems. Finally, we apply them to find the fault diagnosis of the steam turbine.

The role of materials in the proper design and operation of products has been acknowledged. An incorrectly selected material for a certain product may cause premature failure of the final product. The right choice of available materials is very important to the success and competitiveness of manufacturing organizations. In Vietnam, tropical monsoon climate conditions greatly affect mushroom cultivation. The raw materials, additives and the ratio between them will also affect the quality and yield of mushrooms. Therefore, selecting the options for growing mushrooms or choosing good materials to grow mushrooms effectively is also a matter of concern. This is a problem of many decision-making problems. In this paper we multi-objective optimization on the basis of ratio analysis (MOORA) method to evaluate mushroom cultivation options in Vietnam.

Evaluation of water reuse options is also one of the applications of multi-criteria decision-making (MCDM) problems. In this paper, we refer to a new method for selecting the best water reuse option in the available options by using picture fuzzy MCDM.

To measure the difference of two fuzzy sets / intuitionistic sets, we can use the distance measure and dissimilarity measure between fuzzy sets. Characterization of distance/dissimilarity measure between fuzzy sets/intuitionistic fuzzy set is important as it has application in different areas: pattern recognition, image segmentation, and decision making. Picture fuzzy set (PFS) is a generalization of fuzzy set and intuitionistic set, so that it have many application. In this paper, we introduce concepts: difference between PFS-sets, distance measure and dissimilarity measure between picture fuzzy sets, and also provide the formulas for determining these values. We also present an application of dissimilarity measures in multi-attribute decision making.