This website, in many languages, is dedicated to Smarandache type functions, sequences, numbers, transcendental numbers, primes, generalized palindromes, constants, continued fractions, numeration bases, algorithms, criteria of primality and simultaneously primality, criteria of coprimality, functional iterations, infinite products, k-factorials, relationships, algebraic structures, mixed non-Euclidean geometries, NeutroGeometry & AntiGeometry and Real Examples of NeutroGeometry and AntiGeometry, manifolds, NeutroAlgebra and AntiAlgebra, NeutroTopology and AntiTopology, recreational sciences, semantic paradoxes, tautologies, psychological tests and law on sensations and stimuli,  unmatter and unparticle, physics hypothesis that there is no speed barrier in the universe, Superluminal and Instantaneous Physics, quantum and Sorites paradoxes, multispace & multistructure, SC-potential, neutrosophy as a new branch of philosophy, neutrosophic logic, neutrosophic set, neutrosophic probability and statistics, and Neutrosophic Duplets, Neutrosophic Triplets, their extensions to plithogenic set, logic and probability, Advances of Standard and NonStandard Neutrosophic Theories, Neutrosophic Theory of Evolution, Law of Included Multiple-Middle & Principle of Dynamic and Law of Included Infinitely-Many-Middles, Poly-Emporium Theory, Dezert-Smarandache Theory of plausible and paradoxist reasoning in information fusion, pArAdOXisM, oUTER-aRT, foundation of new types of topologies (Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology), foundation of new types of soft sets (HyperSoft Set, IndetermSoft Set, IndetermHyperSoft Set, SuperHyperSoft Set, TreeSoft Set), Neutrosophic Genetics,  alpha-Discounting MCDM Method, SuperHyperAlgebra, SuperHyperFunction & SuperHyperTopology, SuperHyperGraph, Thesis-AntiThesis-NeutroThesis, Symbolic Plithogenic Algebraic Structures built on the set of Symbolic Plithogenic Numbers of the form a0 + a1P1 + a2P2 + ... + anPn, etc.


MATHEMATICS Algebra Geometries Multispace
  Neutrosophic Environment Number Theory Statistics
  Plithogenic Set / Logic /      Probability / Statistics

Extension of the Analytical Hierarchy Process (AHP) to α-Discounting Method

for Multi-Criteria Decision

Making (alpha-D MCDM)


Neutrosophic Sets and Systems (Scopus journal)


Neutrosophic (and fuzzy-extensions) TwoFold Algebra

Neutrosophic Operational Research

Algebra, NeutroAlgebra, & AntiAlgebra


Generalization of the


 Algebraic Structures to


Structures (or

 NeutroAlgebras) {whose

 operations and axioms are

 partially true, partially

 indeterminate, and

 partially  false} as

extensions of

Partial Algebra,


and to AntiAlgebraic

 Structures (or


 {whose operations and


 are totally false}.


 In general, extention of

 any classical Structure,

 in no matter

 what field of knowledge,

to a

 NeutroStructure and an


Geometry, NeutroGeometry, & AntiGeometry

As alternatives and

 generalizations of the

Non-Euclidean Geometries

we introduced the

NeutroGeometry &






The NeutroGeometry

 results from the partial

negation of

 one or more axioms [and

 no total negation of other


 from any geometric

 axiomatics systemd.




While the Non-Euclidean

Geometries resulted from

the total negation of only

one specific axiom

(Euclid’s Fifth Postulate),

the  AntiGeometry

results from the total

negation of any axiom

and even of more axioms

from any geometric

axiomatic system

 (Euclid’s, Hilbert’s,


SuperHyperStructure and Neutrosophic SuperHyperStructure


SuperHyperAlgebra & Neutrosophic SuperHyperAlgebra

SuperHyperFunction, SuperHyperTopology


SuperHyperGraph and




HyperSoft Set

IndetermSoft Set, IndetermHyperSoft Set, TreeSoft Set SuperHyperSoft Set
REVOLUTIONARY TOPOLOGIES NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, NonStandard Neutrosophic Topology NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology

Development of Neutrosophic Statistics (indeterminacy is introduced into classical statistics with respect to any data regarding the sample / population, probability distributions / laws / graphs / charts etc., with respect to the individuals that only partially belong to a sample / population, and so on):


Appurtenance Equation, Inclusion Equation,
& Neutrosophic Numbers used in Neutrosophic Statistic
PHILOSOPHY Neutrosophy, a new branch of philosophy Law of Included Multiple-Middle & Principle of Dynamic Neutrosophic Opposition Zarathustra & Neutrosophy
  MultiAlist System of Though

Law of Included Infinitely-Many-Middles

Upside-Down Logics: Falsification of the Truth & Truthification of the False
PHYSICS Absolute Theory of Relativity Quantum Paradoxes Unmatter
  Neutrosophic Physics Superluminal and Instantaneous Physics  
BIOLOGY Neutrosophic Theory of Evolution Syndrome  
ECONOMICS Poly-Emporium Theory    
LINGUISTICS Linguistic Paradoxes Linguistic Tautologies  
PSYCHOLOGY Neutropsychic Personality Illusion Law on Sensations and Stimuli
  Synonymity Test Complex  
SOCIOLOGY Neutrosociology Sociological Theory Social Paradox
  Literatura Romana Bancuri Travel Memories
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