Nidus idearum. Scilogs, III: Viva la Neutrosophia!

Welcome into my scientific lab! My lab[oratory] is a virtual facility with noncontrolled conditions in which I mostly perform scientific meditation and chats: a nest of ideas (nidus idearum, in Latin). I called the jottings herein scilogs (truncations of the words scientific, and gr. Λόγος – appealing rather to its original meanings ground , opinion , expectation ), combining the welly of both science and informal (via internet) talks (in English, French, and Romanian). * In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas! * Neutrosophy is a new branch of philosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. I coined the words “neutrosophy” and “neutrosophic” in my 1998 book: Florentin Smarandache, Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA, 105 p., 1998; http://fs.gallup.unm.edu/eBook-neutrosophics6.pdf (last edition online)

Cubic Graphs with Application

We introduce certain concepts, including cubic graphs, internal cubic graphs, external cubic graphs, and illustrate these concepts by examples. We deal with fundamental operations, Cartesian product, composition, union and join of cubic graphs. We discuss some results of internal cubic graphs and external cubic graphs. We also describe an application of cubic graphs

History and new possible research directions of hyperstructures

We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research

Nidus Idearum. Scilogs, III: Viva la Neutrosophia!

In this third book of scilogs collected from my nest of ideas, one may find new and old questions and solutions, referring to topics on NEUTROSOPHY – email messages to research colleagues, or replies, notes about authors, articles, or books, so on. Feel free to budge in or just use the scilogs as open source for your own ideas

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc

New Development of Neutrosophic Probability, Neutrosophic Statistics, Neutrosophic Algebraic Structures, and Neutrosophic & Plithogenic Optimizations

This Special Issue puts forward for discussion state-of-the-art papers on new topics related to neutrosophic theories, such as neutrosophic algebraic structures, neutrosophic triplet algebraic structures, neutrosophic extended triplet algebraic structures, neutrosophic algebraic hyperstructures, neutrosophic triplet algebraic hyperstructures, neutrosophic n-ary algebraic structures, neutrosophic n-ary algebraic hyperstructures, refined neutrosophic algebraic structures, refined neutrosophic algebraic hyperstructures, quadruple neutrosophic algebraic structures, refined quadruple neutrosophic algebraic structures, neutrosophic image processing, neutrosophic image classification, neutrosophic computer vision, neutrosophic machine learning, neutrosophic artificial intelligence, neutrosophic data analytics, neutrosophic deep learning, neutrosophic symmetry, and their applications in the real world. This book leads to the further advancement of the neutrosophic and plithogenic theories of NeutroAlgebra and AntiAlgebra, NeutroGeometry and AntiGeometry, Neutrosophic n-SuperHyperGraph (the most general form of graph of today), Neutrosophic Statistics, Plithogenic Logic as a generalization of MultiVariate Logic, Plithogenic Probability and Plithogenic Statistics as a generalization of MultiVariate Probability and Statistics, respectively, and presents their countless applications in our every-day world

Modal paraconsistent logic

Dissertação de mestrado integrado em Engenharia FísicaSuperconducting quantum circuits are a promising model for quantum computation, al though their physical implementation faces some adversities due to the hardly unavoidable decoherence of superconducting quantum bits. This problem may be approached from a formal perspective, using logical reasoning to perform software correctness of programs executed in the non-ideal available hardware. This is the motivation for the work devel oped in this dissertation, which is ultimately an attempt to use the formalism of transition systems to design logical tools for the engineering of quantum software. A transition system to capture the possibly unexpected behaviors of quantum circuits needs to consider the phenomena of decoherence as a possible error factor. In this way, we propose a new family of transition systems, the Paraconsistent Labelled Transition Systems (PLTS), to describe processes that may behave differently from what is expected when facing specific contexts. System states are connected through transitions which simultaneously characterize the possibility and impossibility of that being the system’s evolution. This kind of formalism may be used to represent processes whose evolution is impossible to be sharply described and, thus, should be able to cope with inconsistencies, as well as with vagueness or missing information. Besides giving the formal definition of PLTS, we establish how they are related under the notions of morphism, simulation, bisimulation and trace equivalence. It is a common practice to combine transition systems through universal constructions, in a suitable category, which forms a basis for a process description language. In this dis sertation, we define a category of PLTS and propose a number of constructions to combine them, providing a basis for such a language. Transition systems are usually associated with modal logics which provide a formal set ting to express and prove their properties. We also propose a modal logic, more specifically, a modal intuitionistic paraconsistent logic (MIPL), to talk about PLTS and express their properties, studying how the equivalence relations defined for PLTS extend to relations on MIPL models and how the satisfaction of formulas is preserved along related models. Finally, we illustrate how superconducting quantum circuits may be represented by a PLTS and propose the use of PLTS equivalence relations, namely that of trace equivalence, to compare circuit effectiveness.Os circuitos quânticos que operam qubits supercondutores são um modelo promissor para a arquitetura de computadores quânticos. No entanto, a sua implementação física pode tornar-se ineficaz, devido a fenómenos de decoerência a que os qubits em questão estão altamente sujeitos. Uma possível abordagem a este problema consiste em empregar a lógica e as suas ferramentas para a correção de programas a executar nestes dispositivos. A proposta desta dissertação é que se utilize o formalismo dos sistemas de transição para modelar e descrever o comportamento dos circuitos quânticos, que, por vezes, pode ser imprevisível. Para tal, considera-se a decoerência de qubits como um possível fator de erro nas computações. Assim surge uma nova família de sistemas de transição, os Paraconsistent Labelled Transition systems (PLTS), como um modelo para descrever processos que, em determinados contextos, se comportam de forma diferente do que é esperado. Os estados de um PLTS estão conectados por transições que caracterizam, simultaneamente, a possibilidade e a impossibilidade de o sistema evoluir transitando de um estado para o outro. Este é um modelo em que a informação acerca das transições pode ser incompleta ou mesmo contraditória. Além da definição formal dos PLTS, são também sugeridas, como relações entre PLTS, as noções de morfismo, simulação, bissimulação e equivalência por traços. Muitas vezes, os sistemas de transição são combinados através de construções universais numa categoria adequada, de forma a definir uma álgebra de processos. Também neste trabalho é definida uma categoria de PLTS e são propostas algumas construções, típicas nas álgebras de processos, para os combinar. Os sistemas de transição são geralmente associados a lógicas modais, que permitem expressar e provar as suas propriedades. A definição dos PLTS conduziu à definição de uma lógica modal, MIPL, que permitiu determinar de que forma as relações de equivalência definidas para PLTS, e estendidas para modelos da logica MIPL, se refletem na preservação da satisfação de fórmulas sobre os modelos relacionados. Por fim, propõe-se utilizar PLTS para a representação de circuitos quânticos e comparar a eficácia dos circuitos através da relação de equivalência por traços

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

Collected Papers (on Neutrosophic Theory and Applications), Volume VIII

This eighth volume of Collected Papers includes 75 papers comprising 973 pages on (theoretic and applied) neutrosophics, written between 2010-2022 by the author alone or in collaboration with the following 102 co-authors (alphabetically ordered) from 24 countries: Mohamed Abdel-Basset, Abduallah Gamal, Firoz Ahmad, Ahmad Yusuf Adhami, Ahmed B. Al-Nafee, Ali Hassan, Mumtaz Ali, Akbar Rezaei, Assia Bakali, Ayoub Bahnasse, Azeddine Elhassouny, Durga Banerjee, Romualdas Bausys, Mircea Boșcoianu, Traian Alexandru Buda, Bui Cong Cuong, Emilia Calefariu, Ahmet Çevik, Chang Su Kim, Victor Christianto, Dae Wan Kim, Daud Ahmad, Arindam Dey, Partha Pratim Dey, Mamouni Dhar, H. A. Elagamy, Ahmed K. Essa, Sudipta Gayen, Bibhas C. Giri, Daniela Gîfu, Noel Batista Hernández, Hojjatollah Farahani, Huda E. Khalid, Irfan Deli, Saeid Jafari, Tèmítópé Gbóláhàn Jaíyéolá, Sripati Jha, Sudan Jha, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, M. Karthika, Kawther F. Alhasan, Giruta Kazakeviciute-Januskeviciene, Qaisar Khan, Kishore Kumar P K, Prem Kumar Singh, Ranjan Kumar, Maikel Leyva-Vázquez, Mahmoud Ismail, Tahir Mahmood, Hafsa Masood Malik, Mohammad Abobala, Mai Mohamed, Gunasekaran Manogaran, Seema Mehra, Kalyan Mondal, Mohamed Talea, Mullai Murugappan, Muhammad Akram, Muhammad Aslam Malik, Muhammad Khalid Mahmood, Nivetha Martin, Durga Nagarajan, Nguyen Van Dinh, Nguyen Xuan Thao, Lewis Nkenyereya, Jagan M. Obbineni, M. Parimala, S. K. Patro, Peide Liu, Pham Hong Phong, Surapati Pramanik, Gyanendra Prasad Joshi, Quek Shio Gai, R. Radha, A.A. Salama, S. Satham Hussain, Mehmet Șahin, Said Broumi, Ganeshsree Selvachandran, Selvaraj Ganesan, Shahbaz Ali, Shouzhen Zeng, Manjeet Singh, A. Stanis Arul Mary, Dragiša Stanujkić, Yusuf Șubaș, Rui-Pu Tan, Mirela Teodorescu, Selçuk Topal, Zenonas Turskis, Vakkas Uluçay, Norberto Valcárcel Izquierdo, V. Venkateswara Rao, Volkan Duran, Ying Li, Young Bae Jun, Wadei F. Al-Omeri, Jian-qiang Wang, Lihshing Leigh Wang, Edmundas Kazimieras Zavadskas