Theories Of Generalized Time-Series Fuzzy Soft Set And Their Applications On Multi-Attribute Group Decision Making

Soft set theory, as a new mathematical tool to deal with uncertain problems, fully uses parameterized tool and overcomes the shortage of other uncertain theories. Besides, both fuzzy set and rough set can be seen as specific soft fuzzy, which makes soft set theory become general theory for handling uncertain data. In recent years, many scholars have widely paid attention to decision-making methods based on soft set theory, and many theoretical results have been applied in system engineering, economic forecasting, management decision-making and so on. For further enriching soft theory to reply different types of decision-making problems, the article discusses the new concepts of generalized time-series fuzzy soft set and generalized time-series interval-valued fuzzy soft set, defines their operations, researches relevant properties for these operations, and based these theories, shows the decision-making methods for different decision-making environment. Main results are as follows:1. A new concept of generalized time-series fuzzy soft set is introduced. Based on three kinds of fuzzy operations, i.e. fuzzy complement operation, t-norms and t-conorms, intersection, union and complement of generalized time-series fuzzy soft sets are defined, and relevant properties for these operations are showed. General-ized time-series fuzzy soft set is expressed as generalized fuzzy soft matrix sequence, arithmetic weighted averaging operator and geometric weighted averaging operator of generalized fuzzy soft matrix sequence are proposed. Based on average age model, a method to calculate time weight for generalized fuzzy soft matrix sequence is given. As for group decision making under the environment of generalized time-series fuzzy soft set, two kinds of decision making methods are introduced, and an application case proves the uniformity of these two kinds of decision making methods.2. A new concept of generalized time-series interval-valued fuzzy soft set is in-troduced. Based on three kinds of fuzzy operations, i.e. fuzzy complement operation, t-norms and t-conorms, intersection, union and complement of interval-valued fuzzy sets are defined, and relevant properties for these operations are showed. Based on intersection, union and complement of interval-valued fuzzy sets, intersection, union and complement of generalized time-series interval-valued fuzzy soft sets are given, and relevant properties for these operations are showed. Generalized time-series interval-valued fuzzy soft set is expressed as generalized interval-valued fuzzy soft matrix sequence, two kinds of operations of generalized interval-valued fuzzy soft matrix sequence are proposed. After giving the score function of interval-valued fuzzy numbers, the score matrix, standardized score matrix, weighted comparison matrix of generalized interval-valued fuzzy soft matrix are showed. Using these kinds of matrixes, group decision making method under the environment of generalized time-series interval-valued fuzzy soft set is introduced, and an application case is showed.