Download or read book VERY TRUE PSEUDO BCK ALGEBRAS written by LAVINIA CORINA CIUNGU and published by Infinite Study. This book was released on with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper we introduce the very true operators on pseudo-BCK algebras and we study their properties. We prove that the composition of two very true operators is a very true operator if and only if they commute.

Download or read book Non commutative Algebras Pseudo BCK Algebras Versus M pseudo BCK Algebras written by Afrodita Iorgulescu and published by . This book was released on 2024-07-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted mainly to the author's results in her research on non-commutative algebras related to logic started on October 17, 2022, results never published. It would not be written in so little time and with so many important results and examples without the help of the computer program Prover9-Mace4, developed by William W. McCune (1953 - 2011). There exist a frame-work of non-commutative algebras of logic, having in its `center' the pseudo-BCK algebra. In this monograph, the author mainly has generalized to the non-commutative case the m-BCK algebra and its related algebras, as particular cases of unital magmas, thus creating a new frame-work of non-commutative algebras, having in its `center' the new m-pseudo-BCK algebra. The pseudo-MV algebras are particular cases of m-pseudo-BCK algebras, the groups belong to this new frame-work. But, the goal of her research was to define and study the quantum-pseudo-MV algebra, the non-commutative generalization of quantum-MV algebra. She was able to reach her goal only because she has discovered the`principle' that governs the non-commutative algebras, called `transposition' principle (`m-transposition' principle, for magmas). She has also introduced and studied other non-commutative generalizations of quantum algebras: the bounded involutive pseudo-lattices, the pseudo-De Morgan algebras and the ortho-pseudo-lattices. The book has 18 chapters, divided into three parts: Part I (centered on pseudo-BCK algebras: Chapters 1 - 7), Part II (the core of the monograph, centered on m-pseudo-BCK algebras: Chapters 8 - 16) and Part III (`bridge' theorems: Chapters 17, 18).

Download or read book Advances in Natural Computation Fuzzy Systems and Knowledge Discovery written by Yong Liu and published by Springer Nature. This book was released on 2019-11-06 with total page 1004 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the recent advances in natural computation, fuzzy systems and knowledge discovery. Presenting selected, peer-reviewed papers from the 15th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2019), held in Kunming, China, from 20 to 22 July 2019, it is a useful resource for researchers, including professors and graduate students, as well as R&D staff in industry.

Download or read book BCK Algebras Versus M BCK Algebras Foundations written by Afrodita Iorgulescu and published by . This book was released on 2022-10-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gathers the author's results obtained since April 2019, which have been published in seven papers. Starting from the frame-work centered on BCK algebras, m-BCK algebras are defi ned ('m' coming from 'magma') (algebras including the MV and the Boolean algebras) and other more general algebras, thus obtaining an analogous new frame-work, centered on m-BCK algebras. 'Bridge theorems' connecting the two frameworks are obtained, in the involutive case. Incorporated within this new frame-work are the quantum structures: the bounded involutive lattices, the De Morgan algebras, the ortholattices, the quantum MV algebras, the orthomodular lattices, with important new results and many examples obtained by using the computer program Prover9/Mace4. Also included in the book are some new results, never published before, on L algebras, on quantum B algebras, pseudo-BCI/pseudo-BCK algebras and prealgebras (in the non-commutative case) and important final results on quantum structures, with many examples. This monograph has 17 chapters, divided into three parts: Part I focuses on the 'world' of BCK algebras and of pseudo-BCK algebras, Part II concentrates on the 'world' of m-BCK algebras and Part III is about 'bridge theorems' between the two 'worlds'.

Download or read book Non commutative Multiple Valued Logic Algebras written by Lavinia Corina Ciungu and published by Springer Science & Business Media. This book was released on 2013-08-23 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Download or read book BCK algebras written by Jie Meng and published by . This book was released on 1994-06-01 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Course in BE algebras written by Sambasiva Rao Mukkamala and published by Springer. This book was released on 2018-02-14 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”. Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow introduction to this field.

Download or read book Commutative Generalized Neutrosophic Ideals in BCK Algebras written by Rajab Ali Borzooei and published by Infinite Study. This book was released on with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of a commutative generalized neutrosophic ideal in a BCK-algebra is proposed, and related properties are proved. Characterizations of a commutative generalized neutrosophic ideal are considered. Also, some equivalence relations on the family of all commutative generalized neutrosophic ideals in BCK-algebras are introduced, and some properties are investigated.

Download or read book Combinatorics Computability and Logic written by C.S. Calude and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the Third Discrete Mathematics and Theoretical Computer Science Conference (DMTCS1), which was held at 'Ovidius'University Constantza, Romania in July 2001. The conference was open to all areas of discrete mathematics and theoretical computer science, and the papers contained within this volume cover topics such as: abstract data types and specifications; algorithms and data structures; automata and formal languages; computability, complexity and constructive mathematics; discrete mathematics, combinatorial computing and category theory; logic, nonmonotonic logic and hybrid systems; molecular computing.

Download or read book Theoretical Advances and Applications of Fuzzy Logic and Soft Computing written by Oscar Castillo and published by Springer Science & Business Media. This book was released on 2007-06-08 with total page 893 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprises a selection of papers on theoretical advances and applications of fuzzy logic and soft computing from the IFSA 2007 World Congress, held in Cancun, Mexico, June 2007. These papers constitute an important contribution to the theory and applications of fuzzy logic and soft computing methodologies.

Download or read book Petr H jek on Mathematical Fuzzy Logic written by Franco Montagna and published by Springer. This book was released on 2014-09-23 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume celebrates the work of Petr Hájek on mathematical fuzzy logic and presents how his efforts have influenced prominent logicians who are continuing his work. The book opens with a discussion on Hájek's contribution to mathematical fuzzy logic and with a scientific biography of him, progresses to include two articles with a foundation flavour, that demonstrate some important aspects of Hájek's production, namely, a paper on the development of fuzzy sets and another paper on some fuzzy versions of set theory and arithmetic. Articles in the volume also focus on the treatment of vagueness, building connections between Hájek's favorite fuzzy logic and linguistic models of vagueness. Other articles introduce alternative notions of consequence relation, namely, the preservation of truth degrees, which is discussed in a general context, and the differential semantics. For the latter, a surprisingly strong standard completeness theorem is proved. Another contribution also looks at two principles valid in classical logic and characterize the three main t-norm logics in terms of these principles. Other articles, with an algebraic flavour, offer a summary of the applications of lattice ordered-groups to many-valued logic and to quantum logic, as well as an investigation of prelinearity in varieties of pointed lattice ordered algebras that satisfy a weak form of distributivity and have a very weak implication. The last part of the volume contains an article on possibilistic modal logics defined over MTL chains, a topic that Hájek discussed in his celebrated work, Metamathematics of Fuzzy Logic, and another one where the authors, besides offering unexpected premises such as proposing to call Hájek's basic fuzzy logic HL, instead of BL, propose a very weak system, called SL as a candidate for the role of the really basic fuzzy logic. The paper also provides a generalization of the prelinearity axiom, which was investigated by Hájek in the context of fuzzy logic.

Download or read book Collected Papers Volume IX written by Florentin Smarandache and published by Infinite Study. This book was released on 2022-05-10 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Reviews written by and published by . This book was released on 2007 with total page 1208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets Volume II written by Florentin Smarandache and published by Infinite Study. This book was released on with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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; they have a similar form: (x, neut(x), anti(x), that satisfy some axioms, for each element x in a given set. This book contains the successful invited submissions to a special issue of Symmetry, reporting on 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, and several papers have been published in first rank international journals.

Download or read book Algebraic Structures of Neutrosophic Triplets Neutrosophic Duplets or Neutrosophic Multisets written by Florentin Smarandache and published by MDPI. This book was released on 2019-04-04 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Connectives written by Lloyd Humberstone and published by MIT Press. This book was released on 2011 with total page 1511 pages. Available in PDF, EPUB and Kindle. Book excerpt: In The Connectives, Lloyd Humberstone examines the semantics and pragmatics of natural language sentence connectives (and, or, if, not), giving special attention to their formal behavior according to proposed logical systems and the degree to which such treatments capture their intuitive meanings. It will be an essential resource for philosophers, mathematicians, computer scientists, linguists, or any scholar who finds connectives, and the conceptual issues surrounding them, to be a source of interest.

Download or read book Mathematica Japonicae written by and published by . This book was released on 1999 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: