Some properties of residual mapping and convexity in ∧-hyperlattices

The aime of this paper is the study of residual mappings and convexity in hyperlattices. To get this point, we study principal down set in hyperlattices and we give some conditions for a mapping between two hyperlattices to be equivalent with a residual maping. Also, we investigate convex subsets in ∧-hyperlattices

Quantum Matrix Models for Simple Current Orbifolds

An algebraic formulation of the stringy geometry on simple current orbifolds of the WZW models of type A_N is developed within the framework of Reflection Equation Algebras, REA_q(A_N). It is demonstrated that REA_q(A_N) has the same set of outer automorphisms as the corresponding current algebra A^{(1)}_N which is crucial for the orbifold construction. The CFT monodromy charge is naturally identified within the algebraic framework. The ensuing orbifold matrix models are shown to yield results on brane tensions and the algebra of functions in agreement with the exact BCFT data.Comment: 31 pages, LaTeX; typos corrected, new elements added, the contents restructure

Extension for neutrosophic vague subbisemirings of bisemirings

Neutosophic vague subbisemirings (NSVSBS) are discussed here, as well as their level sets. Subbisemirings are a generalization of bisemirings, and NSVSBSs are a generalization of sub-bisemirings. A number of illustrative examples are provided to illustrate the theory for (ξ, τ )-NSVSBS over bisemiring theory. Following is an outline of the preliminary definitions and results presented in Section 2. The concept of a NSVSBS is introduced in Section 3

Collected Papers (on Neutrosophic Theory and Its Applications in Algebra), Volume IX

This ninth volume of Collected Papers includes 87 papers comprising 982 pages on Neutrosophic Theory and its applications in Algebra, written between 2014-2022 by the author alone or in collaboration with the following 81 co-authors (alphabetically ordered) from 19 countries: E.O. Adeleke, A.A.A. Agboola, Ahmed B. Al-Nafee, Ahmed Mostafa Khalil, Akbar Rezaei, S.A. Akinleye, Ali Hassan, Mumtaz Ali, Rajab Ali Borzooei , Assia Bakali, Cenap Özel, Victor Christianto, Chunxin Bo, Rakhal Das, Bijan Davvaz, R. Dhavaseelan, B. Elavarasan, Fahad Alsharari, T. Gharibah, Hina Gulzar, Hashem Bordbar, Le Hoang Son, Emmanuel Ilojide, Tèmítópé Gbóláhàn Jaíyéolá, M. Karthika, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Huma Khan, Madad Khan, Mohsin Khan, Hee Sik Kim, Seon Jeong Kim, Valeri Kromov, R. M. Latif, Madeleine Al-Tahan, Mehmat Ali Ozturk, Minghao Hu, S. Mirvakili, Mohammad Abobala, Mohammad Hamidi, Mohammed Abdel-Sattar, Mohammed A. Al Shumrani, Mohamed Talea, Muhammad Akram, Muhammad Aslam, Muhammad Aslam Malik, Muhammad Gulistan, Muhammad Shabir, G. Muhiuddin, Memudu Olaposi Olatinwo, Osman Anis, Choonkil Park, M. Parimala, Ping Li, K. Porselvi, D. Preethi, S. Rajareega, N. Rajesh, Udhayakumar Ramalingam, Riad K. Al-Hamido, Yaser Saber, Arsham Borumand Saeid, Saeid Jafari, Said Broumi, A.A. Salama, Ganeshsree Selvachandran, Songtao Shao, Seok-Zun Song, Tahsin Oner, M. Mohseni Takallo, Binod Chandra Tripathy, Tugce Katican, J. Vimala, Xiaohong Zhang, Xiaoyan Mao, Xiaoying Wu, Xingliang Liang, Xin Zhou, Yingcang Ma, Young Bae Jun, Juanjuan Zhang

Fuzzy Mathematics

This book provides a timely overview of topics in fuzzy mathematics. It lays the foundation for further research and applications in a broad range of areas. It contains break-through analysis on how results from the many variations and extensions of fuzzy set theory can be obtained from known results of traditional fuzzy set theory. The book contains not only theoretical results, but a wide range of applications in areas such as decision analysis, optimal allocation in possibilistics and mixed models, pattern classification, credibility measures, algorithms for modeling uncertain data, and numerical methods for solving fuzzy linear systems. The book offers an excellent reference for advanced undergraduate and graduate students in applied and theoretical fuzzy mathematics. Researchers and referees in fuzzy set theory will find the book to be of extreme value

Many valued logics: interpretations, representations and applications

2015 - 2016This thesis, as the research activity of the author, is devoted to establish new connections and to strengthen well-established relations between different branches of mathematics, via logic tools. Two main many valued logics, logic of balance and L ukasiewicz logic, are considered; their associated algebraic structures will be studied with different tools and these techniques will be applied in social choice theory and artificial neural networks. The thesis is structured in three parts. Part I The logic of balance, for short Bal(H), is introduced. It is showed: the relation with `-Groups, i.e. lattice ordered abelian groups (Chapter 2); a functional representation (Chapter 3); the algebraic geometry of the variety of `-Groups with constants (Chapter 4). Part II A brief historical introduction of L ukasiewicz logic and its extensions is provided. It is showed: a functional representation via generalized states (Chapter 5); a non-linear model for MV-algebras and a detailed study of it, culminating in a categorical theorem (Chapter 6). Part III Applications to social choice theory and artificial neural network are presented. In particular: preferences will be related to vector lattices and their cones, recalling the relation between polynomials and cones studied in Chapter 4; multilayer perceptrons will be elements of non-linear models introduced in Chapter 6 and networks will take advantages from polynomial completeness, which is studied in Chapter 2. We are going to present: in Sections 1.2 and 1.3 all the considered structures, our approach to them and their (possible) applications; in Section 1.4 a focus on the representation theory for `-Groups and MV-algebras. Note that: algebraic geometry for `-Groups provides a modus operandi which turns out to be useful not only in theoretical field, but also in applications, opening (we hope) new perspectives and intuitions, as we made in this first approach to social theory; non-linear models here presented and their relation to neural networks seem to be very promising, giving both intuitive and formal approach to many concrete problems, for instance degenerative diseases or distorted signals. All these interesting topics will be studied in future works of the author. [edited by author]Questa tesi, come l’attivit`a di ricerca dell’autore, `e dedicata a stabilire nuove connessioni e a rafforzare le relazioni ben consolidate tra diversi settori della matematica, attraverso strumenti logici. Sono considerate due principali logiche a piu` valori, logic of balance e L ukasiewicz logic; le loro strutture algebriche associate verranno studiate con strumenti diversi e queste tecniche saranno applicate nella teoria della scelta sociale e nelle reti neurali artificiali. La tesi `e strutturata in tre parti. Part I Viene introdotta la Logic of balance. Viene mostrato: la relazione con `-Groups, gruppi abeliani ordinati reticolarmente (Chapter 2); una rappresentazione funzionale (Chapter 3); geometria algebrica della variet`a degli `-Groups con costanti (Chapter 4). Part II Viene fornita una breve introduzione storica della logica di L ukasiewicz e delle sue estensioni. Viene mostrato: una rappresentazione funzionale tramite stati generalizzati (Chapter 5); Un modello non lineare per le MV-algebre e uno studio dettagliato di esso, culminando in un teorema categoriale (Chapter 6). Part III Sono presentate applicazioni alla teoria delle scelte sociali e delle rete neurali artificiali. In particolare: le preferenze saranno correlate ai reticoli vettoriali e ai loro coni, richiamando la relazione tra polinomi e coni studiati nel Capitolo 4; I multilayer perceptrons saranno elementi di modelli non lineari introdotti nel Capitolo 6 e le reti prenderanno vantaggi dalla completezza polinomiale, studiata nel Capitolo 2. La geometria algebrica per gli `-Groups fornisce un modus operandi che risulta utile non solo nel campo teorico, ma anche nelle applicazioni, aprendo (speriamo) nuove prospettive e intuizioni, come abbiamo fatto in questo primo approccio alla teoria sociale; I modelli non lineari qui presentati e la loro relazione con le reti neurali sembrano molto promettenti, offrendo un approccio intuitivo e formale a molti problemi concreti, ad esempio malattie degenerative o segnali distorti. Tutti questi argomenti saranno oggetto di studio in opere future dell’autore. [a cura dell'autore]XV n.s. (XXIX

Towards an M5-Brane Model I: A 6d Superconformal Field Theory

We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the string Lie 2-algebra as a gauge structure, which we motivated in previous work. The kinematical data contains a connection on a categorified principal bundle, which is the appropriate mathematical description of the parallel transport of self-dual strings. Our action can be written down for each of the simply laced Dynkin diagrams, and each case reduces to a four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie algebra. Our action also reduces nicely to an M2-brane model which is a deformation of the ABJM model. While this action is certainly not the desired M5-brane model, we regard it as a key stepping stone towards a potential construction of the (2,0)-theory.Comment: 1+39 pages, v3: minor improvements, published versio