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This paper focuses on mathematical models constructed using parameterization tools. The existence of possible interactions between the elements of the parameter set expressed for such mathematical models directly affects the decision-making process. In order to manage the decision-making processes for uncertainty problems in the most accurate way, the soft sets and fuzzy soft sets, which are among the first theories in which parameterization tools are used, are discussed. These sets were re-evaluated and the concepts of the pure (fuzzy) soft set were proposed. In addition, some properties of these concepts are explained by making examples. [ABSTRACT FROM AUTHOR]

In this paper, it is aimed to express more accurately the intuitionistic fuzzy values expressed by the decision-makers for intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets. For this purpose, virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets are proposed by defining the concepts of virtual lower and upper intuitionistic fuzzy approaches. Moreover, the basic set operations for this hybrid set type are examined together with their associated properties. In addition, a decision-making algorithm focusing on virtual intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets is constructed. Finally, an analysis of the obtained results was made. [ABSTRACT FROM AUTHOR]

In this paper, fuzzy parametrized intuitionistic fuzzy soft (briefly FPIFS-) set theory, which is a generalization of virtual fuzzy parametrized intuitionistic fuzzy soft (briefly VFPIFS-) sets proposed for uncertainty problems, is given and some important properties of it are examined. In addition, an uncertainty problem was exemplified and the best object was selected by giving a decision-making approach for VFPIFS-sets. Finally, a comparative analysis was done for both mathematical models. [ABSTRACT FROM AUTHOR]

Bipolar fuzzy soft set theory, which is a very useful hybrid set in decision making problems, is a mathematical model that has been emphasized especially recently. In this paper, the concepts of (α,β)-cuts, first type semi-strong (α,β)-cuts, second type semi-strong (α,β)-cuts, strong (α,β)-cuts, inverse (α,β)-cuts, first type semi-weak inverse (α,β)-cuts, second type semi-weak inverse (α,β)-cuts and weak inverse (α,β)-cuts of bipolar fuzzy soft sets were introduced together with some of their properties. In addition, some distinctive properties between (α,β)-cuts and inverse (α,β)-cuts were established. Moreover, some related theorems were formulated and proved. It is further demonstrated that both (α,β)-cuts and inverse (α,β)-cuts of bipolar fuzzy soft sets were useful tools in decision making. [ABSTRACT FROM AUTHOR]

In this study, we have introduced the bipolar fuzzy soft (D-)metric space which is based on bipolar fuzzy soft point of bipolar fuzzy soft sets and give some of their properties. Also, the bipolar fuzzy soft sequences and bipolar fuzzy soft cauchy sequences concepts have been studied with the help of defined metric spaces and some of their properties have been investigated. In addition to all this, many examples are given in order to better understand the concepts and features studied and contribute to a better understanding of the paper. [ABSTRACT FROM AUTHOR]