Plithogeny, Plithogenic Set, Logic, Probability, and Statistics
  In this book we introduce the plithogenic set (as generalization of crisp,
fuzzy, intuitionistic fuzzy, and neutrosophic sets), plithogenic logic (as
generalization of classical, fuzzy, intuitionistic fuzzy, and neutrosophic
logics), plithogenic probability (as generalization of classical, imprecise,
and neutrosophic probabilities), and plithogenic statistics (as generalization
of classical, and neutrosophic statistics). Plithogenic Set is a set whose
elements are characterized by one or more attributes, and each attribute may
have many values. An attribute value v has a corresponding (fuzzy,
intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the
element x, to the set P, with respect to some given criteria. In order to
obtain a better accuracy for the plithogenic aggregation operators in the
plithogenic set, logic, probability and for a more exact inclusion (partial
order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction
(dissimilarity) degree is defined between each attribute value and the dominant
(most important) attribute value. The plithogenic intersection and union are
linear combinations of the fuzzy operators tnorm and tconorm, while the
plithogenic complement, inclusion, equality are influenced by the attribute
values contradiction (dissimilarity) degrees. Formal definitions of plithogenic
set, logic, probability, statistics are presented into the book, followed by
plithogenic aggregation operators, various theorems related to them, and
afterwards examples and applications of these new concepts in our everyday
life.
