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[22] viXra:2212.0196 [pdf] submitted on 2022-12-28 02:45:28
Authors: Rayd Majeed Al-Shammari
Comments: 5 Pages.
There is a hidden limits in our mathematics itself that's make us cannot keep counting to infinity not because our human species incompetent but because in reality our numbers by itself are finite, in fact we will never have infinite numbers not just because we are incapable of counting to infinity but because in our mathematics there is no such thing. Numbering is not just counting, numbering is counting that’s holds a definitive value but infinity is undefined so no number could be a represent for infinity. Infinity of numbers cannot exist, because any number you think of no matter how big it’s in the end it will have value then it will be define but infinity is undefined. If we have infinite numbers then there summation will give us a well definitive value and that's would be closer to zero than to infinity and by this infinity just cannot be exist and this what I will prove in this work and to certify this theory I will use it to disprove Riemann hypothesis among other.
Category: Set Theory and Logic
[21] viXra:2212.0139 [pdf] submitted on 2022-12-17 02:15:44
Authors: Dragisa Stanujkic, Assia Bakali, Darjan Karabasevic, Edmundas Kazimieras Zavadskas, Florentin Smarandache, Willem K.m. Brauers
Comments: 18 Pages.
The aim of this paper is to make a proposal for a new extension of the MULTIMOORA method extended to deal with bipolar fuzzy sets. Bipolar fuzzy sets are proposed as an extension of classical fuzzy sets in order to enable solving a particular class of decision-making problems. Unlike other extensions of the fuzzy set of theory, bipolar fuzzy sets introduce a positive membership function, which denotes the satisfaction degree of the element x to the property corresponding to the bipolar-valued fuzzy set, and the negative membership function, which denotes the degree of the satisfaction of the element x to some implicit counter-property corresponding to the bipolar-valued fuzzy set. By using single-valued bipolar fuzzy numbers, the MULTIMOORA method can be more efficient for solving some specific problems whose solving requires assessment and prediction. The suitability of the proposed approach is presented through an example.
Category: Set Theory and Logic
[20] viXra:2212.0137 [pdf] submitted on 2022-12-16 08:45:34
Authors: Florentin Smarandache
Comments: 16 Pages.
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. 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.
Category: Set Theory and Logic
[19] viXra:2212.0110 [pdf] submitted on 2022-12-09 12:19:51
Authors: Florentin Smarandache
Comments: 5 Pages.
In this paper, one extends the single-valued complex neutrosophic set to the subsetvalued complex neutrosophic set, and afterwards to the subset-valued complex refined neutrosophic set
Category: Set Theory and Logic
[18] viXra:2212.0109 [pdf] submitted on 2022-12-09 12:21:51
Authors: Florentin Smarandache
Comments: 19 Pages. Spanish
En el presente artículo, introducimos el conjunto plitogénico (como generalización de conjuntos nítidos, borrosos, intuicionistas, borrosos y neutrosóficos), que es un conjunto cuyos elementos se caracterizan por los valores de muchos atributos. Un valor de atributo v tiene un grado correspondiente (difuso, intuicionista difuso o neutrosófico) de pertenencia d (x, v) del elemento x, al conjunto P, con respecto a algunos criterios dados.
Category: Set Theory and Logic
[17] viXra:2212.0108 [pdf] submitted on 2022-12-09 12:22:51
Authors: Florentin Smarandache
Comments: 3 Pages.
In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.
Category: Set Theory and Logic
[16] viXra:2212.0107 [pdf] submitted on 2022-12-09 12:23:42
Authors: Florentin Smarandache
Comments: 6 Pages. Spanish
La introducción del grado de dependencia (y en consecuencia el grado de independencia) entre los componentes del conjunto difuso, y también entre los componentes del conjunto neutrosófico, se introduce por primera vez en la quinta edición del libro de Neutrosofía en el año 2006, basado en los elementos descritos en dicha edición del libro, se comienza a conocer conceptos de conjuntos neutrosóficos de los componentes borrosos así como los grados de dependencia e independencia.
Category: Set Theory and Logic
[15] viXra:2212.0098 [pdf] submitted on 2022-12-09 13:50:34
Authors: Florentin Smarandache
Comments: 6 Pages.
In this paper, we define for the first time three neutrosophic actions and their properties. We then introduce the prevalence order on {T, I, F} with respect to a given neutrosophic operator "o", which may be subjective - as defined by the neutrosophic experts; and the refinement of neutrosophic entities. Then we extend the classical logical operators to neutrosophic literal logical operators and to refined literal logical operators, and we define the refinement neutrosophic literal space.
Category: Set Theory and Logic
[14] viXra:2212.0095 [pdf] submitted on 2022-12-09 13:53:18
Authors: Florentin Smarandache
Comments: 19 Pages.
In this paper, we introduce for the first time the neutrosophic system and neutrosophic dynamic system that represent new per-spectives in science. A neutrosophic system is a quasi- or (��, ��, ��)—classical system, in the sense that the neutrosophic system deals with quasi-terms/concepts/attributes, etc. [or (��, ��, ��) − terms/ concepts/attributes], which are approximations of the classical terms/concepts/attributes, i.e. they are partially true/membership/probable (t%), partially indeterminate (i%), and partially false/nonmember-ship/improbable (f%), where ��, ��, �� are subsets of the unitary interval [0,1]. {We recall that ‘quasi’ means relative(ly), approximate(ly), almost, near, partial(ly), etc. or mathematically ‘quasi’ means (��, ��, ��) in a neutrophic way.}
Category: Set Theory and Logic
[13] viXra:2212.0093 [pdf] submitted on 2022-12-09 13:54:50
Authors: Florentin Smarandache
Comments: 4 Pages. Spanish
Neutrosophic Over-/Under-/Off-Set and Logic were defined for the first time in 1995 and published in 2007. During 1995-2016 was presented them to various national and international conferences and seminars. These new notions are totally different from other sets/logics/probabilities. We extended the neutrosophic set respectively to Neutrosophic Overset {when some neutrosophic component is > 1}, to Neutrosophic Underset {when some neutrosophic component is < 0}, and to Neutrosophic Offset {when some neutrosophic components are off the interval [0, 1], i.e. some neutrosophic component > 1 and other neutrosophic component < 0}.
Category: Set Theory and Logic
[12] viXra:2212.0091 [pdf] submitted on 2022-12-09 13:56:28
Authors: Florentin Smarandache
Comments: 14 Pages.
In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes (parameters)’ 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, and for a more exact inclusion (partial order), a (fuzzy, intuitionistic fuzzy, or neutrosophic) contradiction (dissimilarity) degree is defined be-tween 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 (inequality), equality are influenced by the attribute values contradiction (dissimilarity) degrees.
Category: Set Theory and Logic
[11] viXra:2212.0090 [pdf] submitted on 2022-12-09 13:57:24
Authors: Florentin Smarandache
Comments: 15 Pages.
The newly introduced theories, proposed as extensions of the fuzzy theory, such as the Neutrosophic, Pythagorean, Spherical, Picture, Cubic theories, and their numerous hybrid forms, are criticized by the authors of [1]. In this paper we respond to their critics with respect to the neutrosophic theories and show that the DST, that they want to replace the A-IFS with, has many flaws.
Category: Set Theory and Logic
[10] viXra:2212.0089 [pdf] submitted on 2022-12-09 13:58:17
Authors: Florentin Smarandache
Comments: 4 Pages.
In this paper we define the Soft Set Product as a product of many soft sets and afterwards we extend it to the HyperSoft Set. Similarly, the IndetermSoft Product is extended to the IndetermHyperSoft Set. We also present several applications of the Soft Set Product to Fuzzy (and fuzzy-extensions) Soft Set Product and to IndetermSoft Set and IndetermHyperSoft Set.
Category: Set Theory and Logic
[9] viXra:2212.0088 [pdf] submitted on 2022-12-09 13:59:08
Authors: Florentin Smarandache
Comments: 14 Pages.
In this paper we prove that the Single-Valued (and respectively Interval-Valued, as well as Subset-Valued) Score, Accuracy, and Certainty Functions determine a total order on the set of neutrosophic triplets (T, I, F). This total order is needed in the neutrosophic decision-making applications.
Category: Set Theory and Logic
[8] viXra:2212.0087 [pdf] submitted on 2022-12-09 14:00:27
Authors: Florentin Smarandache
Comments: 7 Pages.
En el presente estudio se realiza una revisión de las tripletas de estructura neutrosófica y tripleta de estructura neutrosófica extendida, con el fin de introducir nuevos conceptos a emplear en trabajos futuros.
Category: Set Theory and Logic
[7] viXra:2212.0079 [pdf] submitted on 2022-12-09 17:25:53
Authors: Nivetha Martin; Florentin Smarandache; I.Pradeepa; N.Ramila Gandhi; P.Pandiamma
Comments: 7 Pages.
Neutrosophic sets are comprehensively used in decision making environment. The manifestation of neutrosophic sets in concentric hypergraphs is proposed in this research work. The intention of developing a decision making model using the combination of Fuzzy Cognitive Maps and concentric neutrosophic hypergraph is to rank the core factors of decision making problem and find the inter relational impacts. This proposed model is validated with the exploration of the causative factors of autoimmune diseases. The proposed model is highly compatible as it assists in determining the core factors and their inter association. This model will certainly benefit the decision maker at all managerial levels to design optimal decisions.
Category: Set Theory and Logic
[6] viXra:2212.0069 [pdf] submitted on 2022-12-07 07:00:24
Authors: Florentin Smarandache
Comments: 22 Pages.
In this paper one introduces for the first time the IndetermSoft Set, as extension of the classical (determinate) Soft Set, that deals with indeterminate data, and similarly the HyperSoft Set extended to IndetermHyperSoft Set, where ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, not unique outcome). They are built on an IndetermSoft Algebra that is an algebra dealing with IndetermSoft Operators resulted from our real world. Afterwards, the corresponding Fuzzy / Intuitionistic Fuzzy / Neutrosophic / and other fuzzy-extension IndetermSoft Set & IndetermHyperSoft Set are presented together with their applications.
Category: Set Theory and Logic
[5] viXra:2212.0068 [pdf] submitted on 2022-12-08 02:22:02
Authors: Florentin Smarandache
Comments: 22 Pages. In Spanish
This paper presents for the first time the IndetermSoft Set, as an extension of the classical (determinate) Soft Set, which operates on indeterminate data, and similarly the HyperSoft Set extended to the IndetermHyperSoft Set, where 'Indeterm' means 'Indeterminate' (uncertain, conflicting, non-unique result). They are built on an IndetermSoft Algebra which is an algebra dealing with IndetermSoft Operators resulting from our real world. Subsequently, the IndetermSoft and IndetermHyperSoft Sets and their Fuzzy/Fuzzy Intuitionistic/Neutrosophic and other fuzzy extensions and their applications are presented.
Category: Set Theory and Logic
[4] viXra:2212.0066 [pdf] submitted on 2022-12-07 07:02:46
Authors: Florentin Smarandache
Comments: 7 Pages.
A Plithogenic Logical proposition P is a proposition that is characterized by many degrees of truth-values with respect to many corresponding attribute-values (or random variables) that characterize P. Each degree of truth-value may be classical, fuzzy, intuitionistic fuzzy, neutrosophic, or other fuzzy extension type logic. At the end, a cumulative truth of P is computed.
Category: Set Theory and Logic
[3] viXra:2212.0061 [pdf] submitted on 2022-12-07 16:49:26
Authors: Peng Wang, Xiang-Yun Wang, Kai-Yuan Cai
Comments: 9 Pages.
This paper considers a new class of discrete event systems under partial observations. The problem is presented within the background of a manufacturing process where workpieces are loaded and transported, and this process is controlled with the partial information collected by sensors. The model extracted is novel because the observation of an event does not only depend on an event itself, but also the state where the system stays. Two standard problems are discussed in this paper: supervisor existence problem and supervisor synthesis problem. With a natural revision of observable languages, a necessary and sufficient condition is given for the existence of a supervisor. For supervisor synthesis problem, two algorithms are developed: one algorithm is to check the properties of a control specification given by a regular language,and the other one is to synthesize a supervisor if the properties hold. Within the background of manufacturing systems, an example is illustrated to show how the algorithms are applied to practical computing.
Category: Set Theory and Logic
[2] viXra:2212.0054 [pdf] submitted on 2022-12-07 02:21:38
Authors: Florentin Smarandache
Comments: 20 Pages. In Spanish
In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise they would be inapplicable. We pointed out several errors and false statements by Imamura [21] regarding the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is incorrect, as is his definition of nonstandard unit interval, and we showed that there is no total order in Neutrosophic Computing and Machine Learning , Vol. 23, 2022 Florentin Smarandache, Definición mejorada de la lógica neutrosófica no estándar e introducción a los hiperreales neutrosóficos (Quinta versión) 2 the set of hyperreals (due to the recently introduced Neutrosophic Hyperreals which are indeterminate), so the Transfer Principle from R to R* is questionable. After his critique, several reply posts on non-standard theoretical neutrosophy followed in 2018-2022. As such, I extended the Nonstandard Analysis by adding the right-closed left monad, the left-closed right monad, the punctured binad (which we introduced in 1998), and the nonpunctured binad - all 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 the Nonstandard Unitary Interval and Nonstandard Neutrosophic Logic are presented, along with Nonstandard Neutrosophic Operators.
Category: Set Theory and Logic
[1] viXra:2212.0053 [pdf] submitted on 2022-12-06 21:09:31
Authors: Florentin Smarandache
Comments: 9 Pages.
The IndetermSoft Set is as an extension of the Soft Set, because the data, or the function, or the sets involved in the definition of the soft set have indeterminacy - as in our everyday life, and we still need to deal with such situations. And similarly, IndetermHyperSoft Set as extension of the HyperSoft Set, when there is indeterminate data, or indeterminate functions, or indeterminate sets. Herein, ‘Indeterm’ stands for ‘Indeterminate’ (uncertain, conflicting, incomplete, not unique outcome). We now introduce for the first time the TreeSoft Set as extension of the MultiSoft Set. Several applications are presented for each type of soft set.
Category: Set Theory and Logic
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