Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

This book introduces the concept of fuzzy super matrices and operations on them. This book will be highly useful to social scientists who wish to work with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy Relational Maps, Bidirectional Associative Memories and Fuzzy Associative Memories are defined here. The authors introduce 13 multi-expert models using the notion of fuzzy supermatrices. These models are described with illustrative examples. This book has three chapters. In the first chaper, the basic concepts about super matrices and fuzzy super matrices are recalled. Chapter two introduces the notion of fuzzy super matrices adn their properties. The final chapter introduces many super fuzzy multi expert models.Comment: 280 page

Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative examples are given so that the reader can follow these concepts easily. This book has three chapters. The first chapter is introductory in nature and makes the book a self-contained one. Chapter two introduces the concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices, neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can find applications to Markov chains and Leontief economic models. Chapter three gives the application of fuzzy interval matrices and neutrosophic interval matrices to real-world problems by constructing the models already mentioned. Further these models are mainly useful when the data is an unsupervised one and when one needs a multi-expert model. The new concept of fuzzy interval matrices and neutrosophic interval matrices will find their applications in engineering, medical, industrial, social and psychological problems. We have given a long list of references to help the interested reader.Comment: 304 page

Rational and statistical approaches in enhancing yield of ethylene carbonate in urea transesterification with ethylene glycol

Aquest treball d’investigació aplica una aproximació racional per a la millora de les propietats del catalitzador emprat en la transesterificació de la urea amb etilenglicol (EG), per a la producció de carbonat d'etilè (EC) sobre òxids metàl•lics; i un enfocament estadístic per maximitzar la formació del producte desitjat. Per a l’aproximació racional, òxids metàl•lics singulars i mixtes amb combinacions elementals (Zn, Mg, Al, Fe), i amb una àmplia varietat de propietats àcid-base, han estat sintetitzats i avaluats per a la reacció de transesterificació. El rol de l’acidesa i la basicitat en les rutes de reacció identificades han estat clarificats en base a la selectivitat dels productes, i als paràmetres cinètics obtinguts a partir dels perfils de concentració dels reactius i dels productes per a cada ruta de reacció, mitjançant monitorització IR in situ i els subseqüents anàlisis multivariable. Les rutes de formació del EC són catalitzades favorablement mitjançant centres de reacció àcids, mentre que els centres bàsics catalitzen totes les rutes de reacció cap a productes indesitjats. No obstant això, els centres superficials estan obstruïts quan l’acidesa es massa elevada i, per tant, existeix un valor òptim per a la relació del total de centres àcids i bàsics, el qual permetrà obtenir un catalitzador eficient per a la reacció desitjada. L’òxid metàl•lic mixt basat en Zn i Fe amb una relació atòmica 3:1 ha estat identificat com el catalitzador òptim ja que posseeix propietats àcid-base equilibrades adequadament. Els estudis mecanístics han mostrat la formació d’espècies sobre la superfície del catalitzador - isocianats i cianats – indicant diferents mecanismes per a l’activació dels reactius. Els isocianats han estat observats, majoritàriament, sobre òxids basats en Mg, mentre que els òxids acídics així com els basats en Zn promouen la formació de cianat. A més a més, l’aproximació al disseny d’experiments (DoE) ha estat utilitzada per a identificar, d’una forma estadística, els paràmetres crítics de reacció i per a optimitzar dits paràmetres per als millors catalitzadors basats en Zn i Fe. Aquestes aproximacions han permès, de forma exitosa, l’obtenció de coneixements sobre els factors materials determinants en la reacció objectiu i assolir una selectivitat excel•lent per al EC i amb un rendiment elevatEn este trabajo se presenta: (i) un enfoque racional, con el objetivo de mejorar las propiedades de materiales como catalizadores para la transesterificación de urea mediante la conversión de etilenglicol (EG) a carbonato de etileno (EC) sobre óxidos metálicos y, (ii) un enfoque estadístico para maximizar el producto deseado. Para el enfoque racional se han sintetizado y evaluado diversas combinaciones elementales de óxidos metálicos individuales y mixtos (Zn, Mg, Al, Fe) con una variedad de propiedades ácido-base. Los roles de la acidez y la basicidad en el camino de la reacción se han clarificado en base a la selectividad de los productos y, a los parámetros cinéticos extraídos de los perfiles de concentración de los reactivos y de los productos en cada camino de la reacción, por medio de in situ IR monitoring y el posterior análisis multivariable. El camino hacia EC es catalizado favorablemente por sitios ácidos, mientras que los sitios básicos, catalizan todos los caminos hacia los productos no deseados. Sin embargo, los sitios superficiales son bloqueados cuando la acidez es demasiado alta. Existe un valor óptimo para la proporción de sitios ácidos y básicos, para que el catalizador sea eficiente en una reacción específica. La mezcla de óxidos metálicos consistente en Zn y Fe con una proporción atómica de 3:1 ha sido identificada como el catalizador óptimo con unas propiedades ácido-base equilibradas. Estudios mecanísticos, muestran la formación de diferentes especies sobre el catalizador - cianatos e isocianatos - indicando así, diferentes mecanismos para la activación de los reactivos. Los isocianatos se observan principalmente sobre óxidos básicos que contienen Mg. En cambio, la formación de cianatos, se observa en óxidos ácidos que contienen Zn. Además, un enfoque de diseño de experimentos (DoE) se ha utilizado para identificar estadísticamente los parámetros críticos de la reacción, así como, para optimizarlos con el propósito de encontrar el mejor catalizador compuesto por Zn y Fe. Estos enfoques, nos han permitido determinar con éxito, conocimientos acerca de los factores materiales determinantes para dicha reacción, además de obtener una excelente selectividad para EC (hasta un 99.6%) con un alto rendimiento.This work employs (i) a rational approach to improve material properties as catalyst for urea transesterification with ethylene glycol (EG) to ethylene carbonate (EC) over metal oxides and (ii) a statistical approach to maximize the desired product. For the rational approach, single and mixed metal oxides with different elemental combinations (Zn, Mg, Al, Fe) with a variety of acid-base properties were synthesized and evaluated for the reaction. The roles of acidity and basicity in the identified reaction paths were clarified based on product selectivities and kinetic parameters extracted from the concentration profiles of reactants and products in every reaction path by means of in situ IR monitoring and subsequent multivariate analysis. The paths towards EC are favorably catalyzed by acidic sites, while basic sites catalyze all paths towards undesired products. However, surface sites are blocked when acidity is too high and there exists an optimum value for the ratio of total acidic and basic sites to be an efficient catalyst in the targeted reaction. Mixed metal oxide consisting of Zn and Fe at 3:1 atomic ratio was found to be the optimum catalyst with a well-balanced acid-base property. Mechanistic study showed formation of species over catalyst surface – isocyanates and cyanates– indicating different mechanism of reagent activation. Isocyanates were mostly observed over basic Mg-containing oxides, whereas acidic and Zn-containing oxides promote cyanate formation.Furthermore, design of experiments (DoE) approach was used to statistically identify critical reaction parameters and optimize them for the best Zn- and Fe- containing catalyst. These approaches successfully gained insights into the determining material factors for the reaction and afforded excellent EC selectivity (up to 99.6%) with high yield

Negative-Weight Single-Source Shortest Paths in Near-Linear Time: Now Faster!

In this work we revisit the fundamental Single-Source Shortest Paths (SSSP) problem with possibly negative edge weights. A recent breakthrough result by Bernstein, Nanongkai and Wulff-Nilsen established a near-linear $O(m \log^8(n) \log(W))$-time algorithm for negative-weight SSSP, where $W$ is an upper bound on the magnitude of the smallest negative-weight edge. In this work we improve the running time to $O(m \log^2(n) \log(nW) \log\log n)$, which is an improvement by nearly six log-factors. Some of these log-factors are easy to shave (e.g. replacing the priority queue used in Dijkstra's algorithm), while others are significantly more involved (e.g. to find negative cycles we design an algorithm reminiscent of noisy binary search and analyze it with drift analysis). As side results, we obtain an algorithm to compute the minimum cycle mean in the same running time as well as a new construction for computing Low-Diameter Decompositions in directed graphs

Reducible M-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons

We associate real and regular algebraic--geometric data to each multi--line soliton solution of Kadomtsev-Petviashvili II (KP) equation. These solutions are known to be parametrized by points of the totally non--negative part of real Grassmannians $Gr^{TNN}(k,n)$. In Ref.[3] we were able to construct real algebraic-geometric data for soliton data in the main cell $Gr^{TP} (k,n)$ only. Here we do not just extend that construction to all points in $Gr^{TNN}(k,n)$, but we also considerably simplify it, since both the reducible rational $M$-curve $\Gamma$ and the real regular KP divisor on $\Gamma$ are directly related to the parametrization of positroid cells in $Gr^{TNN}(k,n)$ via the Le-networks introduced by A. Postnikov in Ref [62]. In particular, the direct relation of our construction to the Le--networks guarantees that the genus of the underlying smooth $M$-curve is minimal and it coincides with the dimension of the positroid cell in $Gr^{TNN}(k,n)$ to which the soliton data belong to. Finally, we apply our construction to soliton data in $Gr^{TP}(2,4)$ and we compare it with that in Ref [3].Comment: 72 pages; several figures. We have decided to split our paper in Arxiv:1801.00208v1 into two parts. This preprint is the fully revised version of the first part of it. In the next version Arxiv:1801.00208 this part will be removed V2: Minor modifications, proof of Theorem 3.1 improve

Fuzzy Sets, Fuzzy Logic and Their Applications 2020

The present book contains the 24 total articles accepted and published in the Special Issue “Fuzzy Sets, Fuzzy Logic and Their Applications, 2020” of the MDPI Mathematics journal, which covers a wide range of topics connected to the theory and applications of fuzzy sets and systems of fuzzy logic and their extensions/generalizations. These topics include, among others, elements from fuzzy graphs; fuzzy numbers; fuzzy equations; fuzzy linear spaces; intuitionistic fuzzy sets; soft sets; type-2 fuzzy sets, bipolar fuzzy sets, plithogenic sets, fuzzy decision making, fuzzy governance, fuzzy models in mathematics of finance, a philosophical treatise on the connection of the scientific reasoning with fuzzy logic, etc. It is hoped that the book will be interesting and useful for those working in the area of fuzzy sets, fuzzy systems and fuzzy logic, as well as for those with the proper mathematical background and willing to become familiar with recent advances in fuzzy mathematics, which has become prevalent in almost all sectors of the human life and activity