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Logic and Foundations Commons™

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Branch Mathematics and Statistics Faculty and Staff Publications

2018

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Articles 1 - 22 of 22

Full-Text Articles in Logic and Foundations

On Rugina’S System Of Thought, Florentin Smarandache Apr 2018

On Rugina’S System Of Thought, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This article investigates Rugina's orientation table and gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's orientation table in systems which are s percent stable and 100 ÿ s percent unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. Classical logic and modern logic are united in Rugina's integrated logic, and then generalized in neutrosophic logic.

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Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun Apr 2018

Some Studies On Algebraic Integers In Q(I,√3) By Using Coset Diagram, Florentin Smarandache, Saima Anis, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we studied the action of Picard modular group PSL(2,Z[i])

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Strong Degrees In Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Manjeet Singh Apr 2018

Strong Degrees In Single Valued Neutrosophic Graphs, Florentin Smarandache, Said Broumi, Assia Bakali, Seema Mehra, Mohamed Talea, Manjeet Singh

Branch Mathematics and Statistics Faculty and Staff Publications

The concept of single valued neutrosophic graphs (SVNGs) generalizes the concept of fuzzy graphs and intuitionistic fuzzy graphs. The purpose of this research paper is to define different types of strong degrees in SVNGs and introduce novel concepts, such as the vertex truth-membership, vertex indeterminacy-membership and falsity-membership sequence in SVNG with proof and numerical illustrations.

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Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi Feb 2018

Neutrosophic Soft Rough Graphs With Application, Florentin Smarandache, Muhammad Akram, Hafsa M. Malik, Sundas Shahzadi

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic sets (NSs) handle uncertain information while fuzzy sets (FSs) and intuitionistic fuzzy sets (IFs) fail to handle indeterminate information. Soft set theory, neutrosophic set theory, and rough set theory are different mathematical models for handling uncertainties and they are mutually related. The neutrosophic soft rough set (NSRS) model is a hybrid model by combining neutrosophic soft sets with rough sets. We apply neutrosophic soft rough sets to graphs. In this research paper, we introduce the idea of neutrosophic soft rough graphs (NSRGs) and describe different methods of their construction. We consider the application of NSRG in decision-making problems. In …

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Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri Feb 2018

Nn-Harmonic Mean Aggregation Operators-Based Mcgdm Strategy In A Neutrosophic Number Environment, Florentin Smarandache, Kalyan Mondal, Surapati Pramanik, Bibhas C. Giri

Branch Mathematics and Statistics Faculty and Staff Publications

A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and …

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Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez Jan 2018

Fundamentals Of Neutrosophic Logic And Sets And Their Role In Artificial Intelligence (Fundamentos De La Lógica Y Los Conjuntos Neutrosóficos Y Su Papel En La Inteligencia Artificial ), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophy is a new branch of philosophy which studies the origin, nature and scope of neutralities. This has formed the basis for a series of mathematical theories that generalize the classical and fuzzy theories such as the neutrosophic sets and the neutrosophic logic. In the paper, the fundamental concepts related to neutrosophy and its antecedents are presented. Additionally, fundamental concepts of artificial intelligence will be defined and how neutrosophy has come to strengthen this discipline.

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Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral Jan 2018

Subset Vertex Graphs For Social Networks, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the notion of subset vertex graph using the vertex set as the subset of the power set P(S), S is assumed in this book to be finite; however it can be finite or infinite. We have defined two types of subset vertex graphs, one is directed and the other one is not directed. The most important fact which must be kept in record is that for a given set of vertices there exists one and only one subset vertex graph be it of type I or type II. Several important and …

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Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy Jan 2018

Mod Rectangular Natural Neutrosophic Numbers, Florentin Smarandache, K. Ilanthenral, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the new notion of MOD rectangular planes. The functions on them behave very differently when compared to MOD planes (square). These are different from the usual MOD planes. Algebraic structures on these MOD rectangular planes are defined and developed. However we have built only MOD interval natural neutrosophic products

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Neutrosophic Multi-Criteria Decision Making, Florentin Smarandache, Jun Ye, Yanhui Guo Jan 2018

Neutrosophic Multi-Criteria Decision Making, Florentin Smarandache, Jun Ye, Yanhui Guo

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of a neutrosophic quadruple BCK/BCI-number is considered in the first article (“Neutrosophic Quadruple BCK/BCI-Algebras”, by Young Bae Jun, Seok-Zun Song, Florentin Smarandache, and Hashem Bordbar), and a neutrosophic quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers, is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied. Given subsets A and B of a BCK/BCI-algebra, the set NQ(A,B), which consists of neutrosophic quadruple BCK/BCInumbers with a condition, is established. Conditions for the set NQ(A,B) to be a (positive implicative) ideal of a …

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Conjunto Plitogénico, Una Extensión De Los Conjuntos Crisp, Difusos, Conjuntos Difusos Intuicionistas Y Neutrosóficos Revisitado, Florentin Smarandache Jan 2018

Conjunto Plitogénico, Una Extensión De Los Conjuntos Crisp, Difusos, Conjuntos Difusos Intuicionistas Y Neutrosóficos Revisitado, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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 atrib utos. 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. Para obtener una mejor precisión para los operadores d e agregación plitogénica en el conjunto plitogénico, y para una inclusión más exacta (orden parcial), se define un grado de contradicción (disimilitud difusa, intuicionista difusa o neutrosófica) …

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Special Subset Vertex Subgraphs For Social Networks, Florentin Smarandache, W. B. Vasantha Kandasamy, Ilanthenral K Jan 2018

Special Subset Vertex Subgraphs For Social Networks, Florentin Smarandache, W. B. Vasantha Kandasamy, Ilanthenral K

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors for the first time introduce the new notion of special subset vertex subgraph of subset vertex graphs introduced recently in [46]. These subset vertex graphs takes the vertex set values from the power set P(X) of any set X. The main speciality of these subset vertex graphs is that once a set of subsets from P(X) is given, the edges of the graph are fixed in a unique way, so for a given collection of subset vertices the graph is always unique [46]. The special subset vertex subgraphs of G are the ones, which have the …

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Modelo De Recomendación Basado En Conocimiento Y Números Svn, Maykel Leyva-Vazquez, Florentin Smarandache Jan 2018

Modelo De Recomendación Basado En Conocimiento Y Números Svn, Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Recommendation models are useful in the decision-making process that allow the user a set of options that are expected to meet their expectations. Recommendation models are useful in the decision-making process that offer the user a set of options that are expected to meet their SVN expectations to express linguistic terms.

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Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang Jan 2018

Neutrosophic Operational Research - Vol. 3., Florentin Smarandache, Mohamed Abdel Basset, Victor Chang

Branch Mathematics and Statistics Faculty and Staff Publications

Foreword John R. Edwards This book is an excellent exposition of the use of Data Envelopment Analysis (DEA) to generate data analytic insights to make evidence-based decisions, to improve productivity, and to manage cost-risk and benefitopportunity in public and private sectors. The design and the content of the book make it an up-to-date and timely reference for professionals, academics, students, and employees, in particular those involved in strategic and operational decisionmaking processes to evaluate and prioritize alternatives to boost productivity growth, to optimize the efficiency of resource utilization, and to maximize the effectiveness of outputs and impacts to stakeholders. It …

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New Trends In Neutrosophic Theory And Applications Volume Ii, Florentin Smarandache, Surapati Pramanik Jan 2018

New Trends In Neutrosophic Theory And Applications Volume Ii, Florentin Smarandache, Surapati Pramanik

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, …

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Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa Jan 2018

Neutrosophic Logic: The Revolutionary Logic In Science And Philosophy -- Proceedings Of The National Symposium, Florentin Smarandache, Huda E. Khalid, Ahmed K. Essa

Branch Mathematics and Statistics Faculty and Staff Publications

The first part of this book is an introduction to the activities of the National Symposium, as well as a presentation of Neutrosophic Scientific International Association (NSIA), based in New Mexico, USA, also explaining the role and scope of NSIA - Iraqi branch. The NSIA Iraqi branch presents a suggestion for the international instructions in attempting to organize NSIA's work. In the second chapter, the pivots of the Symposium are presented, including a history of neutrosophic theory and its applications, the most important books and papers in the advancement of neutrosophics, a biographical note of Prof. Florentin Smarandache in Arabic …

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Special Issue: Algebraic Structures Of Neutrosophic Triplets, Neutrosophic Duplets, Or Neutrosophic Multisets, Vol. I, Florentin Smarandache, Xiaohong Zhang, Mumtaz Ali Jan 2018

Neutrosophic Linear Programming Problems, Florentin Smarandache, Abdel-Nasser Hussian, Mai Mohamed, Mohamed Abdel-Baset Jan 2018

Neutrosophic Linear Programming Problems, Florentin Smarandache, Abdel-Nasser Hussian, Mai Mohamed, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Smarandache presented neutrosophic theory as a tool for handling undetermined information. Wang et al. introduced a single valued neutrosophic set that is a special neutrosophic sets and can be used expediently to deal with real-world problems, especially in decision support. In this paper, we propose linear programming problems based on neutrosophic environment. Neutrosophic sets are characterized by three independent parameters, namely truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F), which are more capable to handle imprecise parameters. We also transform the neutrosophic linear programming problem into a crisp programming model by using neutrosophic set parameters. To measure the …

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Spanning Tree Problem With Neutrosophic Edge Weights, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Arindam Dey, Le Hoang Son Jan 2018

Spanning Tree Problem With Neutrosophic Edge Weights, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Arindam Dey, Le Hoang Son

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided.

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Operadores Con Conjunto Neutrosóficos De Valor Único Oversets, Undersets Y Offset, Florentin Smarandache Jan 2018

Operadores Con Conjunto Neutrosóficos De Valor Único Oversets, Undersets Y Offset, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

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}. This is no surprise since our realworld has numerous examples and applications of over-/under-/off-neutrosophic components. Palabras clave. desbordado neutrosophic, underset neutrosophic, neutrosophic offset, neutrosophic sobre la lógica, neutrosophic bajo la lógica, neutrosophic off lógica, neutrosophic sobre la probabilidad, neutrosophic bajo probabilidad, neutrosophic de probabilidad, más de miembros (grado de pertenencia> 1), bajo de miembros (grado de pertenencia <0) , (grado de pertenencia fuera del intervalo [0, 1]) offmembership.

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Neutrosophic Computing With Sympy (Computación Neutrosófica Mediante Sympy ), Maykel Leyva-Vazquez, Florentin Smarandache Jan 2018

Neutrosophic Computing With Sympy (Computación Neutrosófica Mediante Sympy ), Maykel Leyva-Vazquez, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this article the concept of neutrosophic number is presented. Jupyter through Google Colaboratory is introduced for calculations. The Sympy library is used to perform the process of neutrosophic computation. Systems of linear neutrosóficas equations are solved by means of the symbolic computation in python. A case study was developed for the determination of vehicular traffic with indeterminacy. As future works are the development of new applications in different areas of engineering and science.

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N-Valued Refined Neutrosophic Logic And Its Applications To Physics (Lógica Neutrosófica Refinada N-Valuada Y Sus Aplicaciones A La Física), Florentin Smarandache Jan 2018

N-Valued Refined Neutrosophic Logic And Its Applications To Physics (Lógica Neutrosófica Refinada N-Valuada Y Sus Aplicaciones A La Física), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we present a short history of logics: from particular cases of 2-symbol or numerical valued logic to the general case of n-symbol or numerical valued logic. We show generalizations of 2-valued Boolean logic to fuzzy logic, also from the Kleene’s and Lukasiewicz’ 3-symbol valued logics or Belnap’s 4-symbol valued logic to the most general nsymbol or numerical valued refined neutrosophic logic. Examples of applications of neutrosophic logic to physics are listed in the last section. Similar generalizations can be done for n-Valued Refined Neutrosophic Set, and respectively.

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Mental Models And Neutrosophic Cognitive Maps (Modelos Mentales Y Mapas Cognitivos Neutrosóficos), Maykel Leyva-Vazquez, Rebeca Escobar-Jara, Florentin Smarandache Jan 2018

Mental Models And Neutrosophic Cognitive Maps (Modelos Mentales Y Mapas Cognitivos Neutrosóficos), Maykel Leyva-Vazquez, Rebeca Escobar-Jara, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, elements related to mental models elicitation and analysis are addressed through causal models. Issues related to the need to include indeterminacy in causal relationships through neutrophic cognitive maps are discussed. A proposal for static analysis in neutrosophic cognitive maps is presented. The following activities are included in the proposal: Calculate, measures of centrality, Classify nodes, De-neutrosification, and Ranking nodes. As future works, the incorporation of new metrics of centrality in neutrosophic cognitive maps is proposed. The inclusion of scenario analysis to the proposal is another area of future work.

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