Plithogeny, Plithogenic Set, Logic, Probability, and Statistics

TL;DR

This work introduces plithogenic sets, logic, probability, and statistics as comprehensive generalizations of existing fuzzy and neutrosophic theories, aiming to improve accuracy and inclusion in uncertain information processing.

Contribution

It presents formal definitions and operators for plithogenic concepts, extending classical, fuzzy, intuitionistic fuzzy, and neutrosophic frameworks with new aggregation and contradiction measures.

Findings

Defined plithogenic set, logic, probability, and statistics.

Developed plithogenic aggregation operators and theorems.

Provided examples and applications in real-life scenarios.

Abstract

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.