Interval-Valued Fuzzy Parameterized Intuitionistic Fuzzy Soft Sets and Their Applications

In recent years, the fuzzy sets, interval-valued fuzzy sets, intuitionistic fuzzy sets and soft sets, which offer different perspectives for the structures containing the uncertainties, have attracted the interest of many researchers. Also, the intuitionistic fuzzy soft sets produced by combining the intuitionistic fuzzy sets with the soft sets have been widely studied. In this work, the concept of interval-valued fuzzy parameterized intuitionistic fuzzy soft set (IVFPIFS set) is introduced. This set is the generalization of soft sets, fuzzy soft sets, fuzzy parameterized (fuzzy) soft sets, interval-valued fuzzy parameterized (fuzzy) soft sets, intuitionistic fuzzy soft sets and fuzzy parameterized intuitionistic fuzzy soft sets. For the IVFPIFS sets, basic operations such as complement, union and intersection are defined. Also, the properties of these operations are investigated in detail. Lastly, an algorithm by using the aggregation operators based on the IVFPIFS sets is constructed. The examples are given to verify the feasibility and validity of the proposed algorithm