About Nonstandard Neutrosophic Logic
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About Nonstandard Neutrosophic Logic Answers To Imamura S Note On The Definition Of Neutrosophic Logic
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
About Nonstandard Neutrosophic Logic Answers To Imamura S Note On The Definition Of Neutrosophic Logic written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical unit interval [0, 1], and a brief evolution of neutrosophic operators.
Answers To Imamura S Note On The Definition Of Neutrosophic Logic
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Answers To Imamura S Note On The Definition Of Neutrosophic Logic written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In order to more accurately situate and fit the neutrosophic logic into the framework of nonstandard analysis, we present the neutrosophic inequalities, neutrosophic equality, neutrosophic infimum and supremum, neutrosophic standard intervals, including the cases when the neutrosophic logic standard and nonstandard components T, I, F get values outside of the classical unit interval [0, 1], and a brief evolution of neutrosophic operators.
Advances Of Standard And Nonstandard Neutrosophic Theories
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
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Advances Of Standard And Nonstandard Neutrosophic Theories written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
In this book, we approach different topics related to neutrosophics, such as: Neutrosophic Set, Intuitionistic Fuzzy Set, Inconsistent Intuitionistic Fuzzy Set, Picture Fuzzy Set, Ternary Fuzzy Set, Pythagorean Fuzzy Set, Atanassov’s Intuitionistic Fuzzy Set of second type, Spherical Fuzzy Set, n-HyperSpherical Neutrosophic Set, q-Rung Orthopair Fuzzy Set, truth-membership, indeterminacy-membership, falsehood-nonmembership, Regret Theory, Grey System Theory, Three-Ways Decision, n-Ways Decision, Neutrosophy, Neutrosophication, Neutrosophic Probability, Refined Neutrosophy, Refined Neutrosophication, Nonstandard Analysis; Extended Nonstandard Analysis; Open and Closed Monads to the Left/Right; Pierced and Unpierced Binads; MoBiNad Set; infinitesimals; infinities; nonstandard reals; standard reals; Nonstandard Neutrosophic Lattices of First Type (as poset) and Second Type (as algebraic structure); Nonstandard Neutrosophic Logic; Extended Nonstandard Neutrosophic Logic; Nonstandard Arithmetic Operations; Nonstandard Unit Interval; Nonstandard Neutrosophic Infimum; and so on.
Extended Nonstandard Neutrosophic Logic Set And Probability Based On Extended Nonstandard Analysis
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
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Extended Nonstandard Neutrosophic Logic Set And Probability Based On Extended Nonstandard Analysis written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad—all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations.
Improved Definition Of Nonstandard Neutrosophic Logic And Introduction To Neutrosophic Hyperreals Fifth Version
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Improved Definition Of Nonstandard Neutrosophic Logic And Introduction To Neutrosophic Hyperreals Fifth Version written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Antiques & Collectibles categories.
In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented.
Improved Definition Of Nonstandard Neutrosophic Logic And Introduction To Neutrosophic Hyperreals Third Version
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2018-01-01
Improved Definition Of Nonstandard Neutrosophic Logic And Introduction To Neutrosophic Hyperreals Third Version written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-01 with Mathematics categories.
On the third version of this response-paper to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise they would be inapplicable. We point out several errors and false statements by Imamura with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the transfer principle is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations.
A Unifying Field In Logics Neutrosophic Logic Neutrosophy Neutrosophic Set Neutrosophic Probability Fourth Edition
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2005
A Unifying Field In Logics Neutrosophic Logic Neutrosophy Neutrosophic Set Neutrosophic Probability Fourth Edition written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
N-Norm and N-conorm are extended in Neutrosophic Logic/Set.
Proceedings Of The First International Conference On Neutrosophy Neutrosophic Logic Neutrosophic Set Neutrosophic Porbability And Statistics
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Author : Florentin Smarandache editor
language : en
Publisher: Infinite Study
Release Date : 2003-01-01
Proceedings Of The First International Conference On Neutrosophy Neutrosophic Logic Neutrosophic Set Neutrosophic Porbability And Statistics written by Florentin Smarandache editor and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
Collected papers on neutrosophics [such as: ?neutrosophy? - a new branch of philosophy, ?neutrosophic logic? ? a generalization of the fuzzy logic, ?neutrosophic set? ? a generalization of the fuzzy set, and ?neutrosophic probability? ? a generalization of classical probability and imprecise probability] by Florentin Smarandache, Jean Dezert, Andrzej Buller, Mohammad Khoshnevisan, Sarjinder Singh, Sukanto Bhattacharya, Feng Liu, Gh. C. Dinulescu-Campina, Chris Lucas, and Carlos Gershenson.Neutrosophic Logic involved the foundation of the Dezert-Smarandache Theory of Plausible and Paradoxical Reasoning, which has taken into consideration the combination of uncertain and contradictory information, used now in artificial intelligence.
Neutrosophic Logic A Generalization Of The Intuitionistic Fuzzy Logic
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
Neutrosophic Logic A Generalization Of The Intuitionistic Fuzzy Logic written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.
About Nonstandard Neutrosophic Logic
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date :
About Nonstandard Neutrosophic Logic written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The paper intends to answer Imamura’s criticism that we found benefic in better understanding the nonstandard neutrosophic logic – although the nonstandard neutrosophic logic was never used in practical applications.