Set Theory Commons^™

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.

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.

Fuzzy And Neutrosophic Sets In Semigroups, Florentin Smarandache, Young Bae Jun, Madad Khan

Branch Mathematics and Statistics Faculty and Staff Publications

The first chapter, Characterizations of regular and duo semigroups based on int-soft set theory, investigates the relations among int-soft semigroup, int-soft (generalized) bi-ideal, int-soft quasi-ideal and int-soft interior ideal. Using int-soft left (right) ideal, an int-soft quasi-ideal is constructed. We show that every int-soft quasi-ideal can be represented as the soft intersection of an int-soft left ideal and an int-soft right ideal. Using int-soft quasiideal, an int-soft bi-ideal is established. Conditions for a semigroup to be regular are displayed.

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.

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.

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 …

On The Girth And Diameter Of Generalized Johnson Graphs, Louis Anthony Agong, Carmen Amarra, John Caughman, Ari J. Herman, Taiyo S. Terada

Mathematics and Statistics Faculty Publications and Presentations

Let v > k > i be non-negative integers. The generalized Johnson graph, J(v,k,i), is the graph whose vertices are the k-subsets of a v-set, where vertices A and B are adjacent whenever |A∩B|= i. In this article, we derive general formulas for the girth and diameter of J(v,k,i). Additionally, we provide a formula for the distance between any two vertices A and B in terms of the cardinality of their intersection.

Neutrosophic N -Structures Applied To Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Hashem Bordbar

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.

Neutrosophic N -Structures And Their Applications In Semigroups, Florentin Smarandache, Madad Khan, Saima Anis, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of neutrosophic N -structure is introduced, and applied it to semigroup. The notions of neutrosophic N -subsemigroup, neutrosophic N -product and ε-neutrosophic N -subsemigroup are introduced, and several properties are investigated. Conditions for neutrosophic N -structure to be neutrosophic N -subsemigroup are provided. Using neutrosophic N -product, characterization of neutrosophic N -subsemigroup is discussed. Relations between neutrosophic N -subsemigroup and εneutrosophic N -subsemigroup are discussed. We show that the homomorphic preimage of neutrosophic N -subsemigroup is a neutrosophic N - subsemigroup, and the onto homomorphic image of neutrosophic N - subsemigroup is a neutrosophic N -subsemigroup.

Transfinite Ordinal Arithmetic, James Roger Clark

All Student Theses and Dissertations

Following the literature from the origin of Set Theory in the late 19th century to more current times, an arithmetic of finite and transfinite ordinal numbers is outlined. The concept of a set is outlined and directed to the understanding that an ordinal, a special kind of number, is a particular kind of well-ordered set. From this, the idea of counting ordinals is introduced. With the fundamental notion of counting addressed: then addition, multiplication, and exponentiation are defined and developed by established fundamentals of Set Theory. Many known theorems are based upon this foundation. Ultimately, as part of the conclusion, …

Complex Neutrosophic Soft Set, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Mumtaz Ali, Ganeshsree Selvachandran

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we propose the complex neutrosophic soft set model, which is a hybrid of complex fuzzy sets, neutrosophic sets and soft sets. The basic set theoretic operations and some concepts related to the structure of this model are introduced, and illustrated. An example related to a decision making problem involving uncertain and subjective information is presented, to demonstrate the utility of this model.

Joint Laver Diamonds And Grounded Forcing Axioms, Miha Habič

Dissertations, Theses, and Capstone Projects

In chapter 1 a notion of independence for diamonds and Laver diamonds is investigated. A sequence of Laver diamonds for κ is joint if for any sequence of targets there is a single elementary embedding j with critical point κ such that each Laver diamond guesses its respective target via j. In the case of measurable cardinals (with similar results holding for (partially) supercompact cardinals) I show that a single Laver diamond for κ yields a joint sequence of length κ, and I give strict separation results for all larger lengths of joint sequences. Even though the principles get …

The Classification Problem For Models Of Zfc, Samuel Dworetzky

Boise State University Theses and Dissertations

Models of ZFC are ubiquitous in modern day set theoretic research. There are many different constructions that produce countable models of ZFC via techniques such as forcing, ultraproducts, and compactness. The models that these techniques produce have many different characteristics; thus it is natural to ask whether or not models of ZFC are classifiable. We will answer this question by showing that models of ZFC are unclassifiable and have maximal complexity. The notions of complexity used in this thesis will be phrased in the language of Borel complexity theory.

In particular, we will show that the class of countable models …

Classification Of Vertex-Transitive Structures, Stephanie Potter

Boise State University Theses and Dissertations

When one thinks of objects with a significant level of symmetry it is natural to expect there to be a simple classification. However, this leads to an interesting problem in that research has revealed the existence of highly symmetric objects which are very complex when considered within the framework of Borel complexity. The tension between these two seemingly contradictory notions leads to a wealth of natural questions which have yet to be answered.

Borel complexity theory is an area of logic where the relative complexities of classification problems are studied. Within this theory, we regard a classification problem as an …

Combinatorial Polynomial Hirsch Conjecture, Sam Miller

HMC Senior Theses

The Hirsch Conjecture states that for a d-dimensional polytope with n facets, the diameter of the graph of the polytope is at most n-d. This conjecture was disproven in 2010 by Francisco Santos Leal. However, a polynomial bound in n and d on the diameter of a polytope may still exist. Finding a polynomial bound would provide a worst-case scenario runtime for the Simplex Method of Linear Programming. However working only with polytopes in higher dimensions can prove challenging, so other approaches are welcome. There are many equivalent formulations of the Hirsch Conjecture, one of which is the …

Neutrosophic Perspectives: Triplets, Duplets, Multisets, Hybrid Operators, Modal Logic, Hedge Algebras. And Applications (Second Extended And Improved), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is part of the book-series dedicated to the advances of neutrosophic theories and their applications, started by the author in 1998. Its aim is to present the last developments in the field. For the first time, we now introduce:

— Neutrosophic Duplets and the Neutrosophic Duplet Structures;

— Neutrosophic Multisets (as an extension of the classical multisets);

— Neutrosophic Spherical Numbers;

— Neutrosophic Overnumbers / Undernumbers / Offnumbers;

— Neutrosophic Indeterminacy of Second Type;

— Neutrosophic Hybrid Operators (where the heterogeneous t-norms and t-conorms may be used in designing neutrosophic aggregations);

— Neutrosophic Triplet Loop;

— Neutrosophic Triplet …

Computation Of Shortest Path Problem In A Network With Sv-Triangular Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea

Branch Mathematics and Statistics Faculty and Staff Publications

In this article, we present an algorithm method for finding the shortest path length between a paired nodes on a network where the edge weights are characterized by single valued triangular neutrosophic numbers. The proposed algorithm gives the shortest shortest path length from source node to destination node based on a ranking method. Finally, a numerical example is also presented to illustrate the efficiency of the proposed approach.

Complex Valued Graphs For Soft Computing, 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 in a systematic way the notion of complex valued graphs, strong complex valued graphs and complex neutrosophic valued graphs. Several interesting properties are defined, described and developed. Most of the conjectures which are open in case of usual graphs continue to be open problems in case of both complex valued graphs and strong complex valued graphs. We also give some applications of them in soft computing and social networks. At this juncture it is pertinent to keep on record that Dr. Tohru Nitta was the pioneer to use complex valued graphs …

Computation Of Shortest Path Problem In A Network With Sv-Trapezoidal Neutrosophic Numbers, Florentin Smarandache, Said Broumi, Assia Bakali, Mohamed Talea, Luige Vladareanu

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, a neutrosophic network method is proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach

The Density Topology On The Reals With Analogues On Other Spaces, Stuart Nygard

Boise State University Theses and Dissertations

A point x is a density point of a set A if all of the points except a measure zero set near to x are contained in A. In the usual topology on ℝ, a set is open if shrinking intervals around each point are eventually contained in the set. The density topology relaxes this requirement. A set is open in the density topology if for each point, the limit of the measure of A contained in shirking intervals to the measure of the shrinking intervals themselves is one. That is, for any point x and a small enough …