## Branch Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2017

#### Abstract

In this book we introduce for the first time, as generalization of dialectics and neutrosophy, the philosophical concept called *plithogeny*. And as its derivatives: 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).

Plithogeny is the genesis or origination, creation, formation, development, and evolution of *new entities *from dynamics and organic fusions of contradictory and/or neutrals and/or non-contradictory *multiple old entities*.

Plithogenic Set is a set whose elements are characterized by one or more attributes, and each attribute may have many values.

An attribute’s 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.

#### Publisher

Pons, Brussels

#### Language (ISO)

English

#### Keywords

neutrosophy, plithogeny, neutrosophic set, plithogenic set, plithogenic logic, plithogenic probability

#### Recommended Citation

Smarandache, Florentin. "Plithogeny, Plithogenic Set, Logic, Probability, and Statistics." (2017). https://digitalrepository.unm.edu/math_fsp/20