Propositional computability logic I

In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a machine against the environment, their computability as existence of a machine that always wins the game, logical operators as operations on computational problems, and validity of a logical formula as being a scheme of "always computable" problems. The present contribution gives a detailed exposition of a soundness and completeness proof for an axiomatization of one of the most basic fragments of computability logic. The logical vocabulary of this fragment contains operators for the so called parallel and choice operations, and its atoms represent elementary problems, i.e. predicates in the standard sense. This article is self-contained as it explains all relevant concepts. While not technically necessary, however, familiarity with the foundational paper "Introduction to computability logic" [Annals of Pure and Applied Logic 123 (2003), pp.1-99] would greatly help the reader in understanding the philosophy, underlying motivations, potential and utility of computability logic, -- the context that determines the value of the present results. Online introduction to the subject is available at http://www.cis.upenn.edu/~giorgi/cl.html and http://www.csc.villanova.edu/~japaridz/CL/gsoll.html .Comment: To appear in ACM Transactions on Computational Logi

The posterity of Zadeh's 50-year-old paper: A retrospective in 101 Easy Pieces – and a Few More

International audienceThis article was commissioned by the 22nd IEEE International Conference of Fuzzy Systems (FUZZ-IEEE) to celebrate the 50th Anniversary of Lotfi Zadeh's seminal 1965 paper on fuzzy sets. In addition to Lotfi's original paper, this note itemizes 100 citations of books and papers deemed “important (significant, seminal, etc.)” by 20 of the 21 living IEEE CIS Fuzzy Systems pioneers. Each of the 20 contributors supplied 5 citations, and Lotfi's paper makes the overall list a tidy 101, as in “Fuzzy Sets 101”. This note is not a survey in any real sense of the word, but the contributors did offer short remarks to indicate the reason for inclusion (e.g., historical, topical, seminal, etc.) of each citation. Citation statistics are easy to find and notoriously erroneous, so we refrain from reporting them - almost. The exception is that according to Google scholar on April 9, 2015, Lotfi's 1965 paper has been cited 55,479 times

Design of Fuzzy Controllers for Embedded Systems With JFML

Fuzzy rule-based systems (FRBSs) have been successfully applied to a wide range of real-world problems. However, they suffer from some design issues related to the difficulty to implement them on different hardware platforms without additional efforts. To bridge this gap, recently, the IEEE Computational Intelligence Society has sponsored the publication of the standard IEEE Std 1855-2016 which is aimed at providing the fuzzy community with a well-defined approach to model FRBSs in a hardwareindependent way. In order to provide a runnable version of an FRBS that is designed in accordance with the IEEE Std 1855-2016, the open source library Java Fuzzy Markup Language (JFML) has been developed. However, due to hardware and/or software limitations of embedded systems, it is not always possible to run an IEEE Std 1855-2016 FRBS on this kind of systems. The aim of this paper is to overcome this drawback by developing a new JFML module that assists developers in the design and implementation of FRBSs for open hardware–embedded systems. In detail, the module supports several connection types (WiFi, Bluetooth, and USB) in order to make feasible running FRBSs in a remote computer when, due to hardware limitations, it is not possible that they run locally in the embedded systems. The new JFML module is ready for ArduinoTM and Raspberry Pi, but it can be easily extended to other hardware architectures. Moreover, the new JFML module allows to automatically generate runnable files on ArduinoTM or Raspberry Pi in order to support nonexpert users, that is, users without specific knowledge about embedded systems or without strong programming skills. The use of the new JFML module is illustrated in two case studies.This paper has been supported in part by the Spanish Ministry of Economy and Competitiveness (Projects TIN2017-89517-P, TIN2015-68454-R, TIN2017-84796-C2-1-R, and TIN2017-90773-REDT) and the Andalusian Government. In addition, Jose M. Alonso is Ramon y Cajal Researcher (RYC-2016-19802). Financial support from the Galician Ministry of Education (grants ED431F 2018/02, GRC2014/030 and accreditation 2016-2019, ED431G/08), co-funded by the European Regional Development Fund (ERDF/FEDER program), is also gratefully acknowledged

Fuzzy Systems

This book presents some recent specialized works of theoretical study in the domain of fuzzy systems. Over eight sections and fifteen chapters, the volume addresses fuzzy systems concepts and promotes them in practical applications in the following thematic areas: fuzzy mathematics, decision making, clustering, adaptive neural fuzzy inference systems, control systems, process monitoring, green infrastructure, and medicine. The studies published in the book develop new theoretical concepts that improve the properties and performances of fuzzy systems. This book is a useful resource for specialists, engineers, professors, and students

Neutrosophic Crisp Set Theory

Since the world is full of indeterminacy, the Neutrosophics found their place into contemporary research. We now introduce for the first time the notions of Neutrosophic Crisp Sets and Neutrosophic Topology on Crisp Sets. We develop the 2012 notion of Neutrosophic Topological Spaces and give many practical examples. Neutrosophic Science means development and applications of Neutrosophic Logic, Set, Measure, Integral, Probability etc., and their applications in any field. It is possible to define the neutrosophic measure and consequently the neutrosophic integral and neutrosophic probability in many ways, because there are various types of indeterminacies, depending on the problem we need to solve. Indeterminacy is different from randomness. Indeterminacy can be caused by physical space, materials and type of construction, by items involved in the space, or by other factors. In 1965 [51], Zadeh generalized the concept of crisp set by introducing the concept of fuzzy set, corresponding to the situation in which there is no precisely defined set;there are increasing applications in various fields, including probability, artificial intelligence, control systems, biology and economics. Thus, developments in abstract mathematics using the idea of fuzzy sets possess sound footing. In accordance, fuzzy topological spaces were introduced by Chang [12] and Lowen [33]. After the development of fuzzy sets, much attention has been paid to the generalization of basic concepts of classical topology to fuzzy sets and accordingly developing a theory of fuzzy topology [1-58]. In 1983, the intuitionistic fuzzy set was introduced by K. Atanassov [55, 56, 57] as a generalization of the fuzzy set, beyond the degree of membership and the degree of non-membership of each element. In 1999 and 2002, Smarandache [71, 72, 73, 74] defined the notion of Neutrosophic Sets, which is a generalization of Zadeh’s fuzzy set and Atanassov\u27s intuitionistic fuzzy set

APPLICATION OF THE DIBR II – ROUGH MABAC DECISION-MAKING MODEL FOR RANKING METHODS AND TECHNIQUES OF LEAN ORGANIZATION SYSTEMS MANAGEMENT IN THE PROCESS OF TECHNICAL MAINTENANCE

This paper presents a multi-criteria decision-making model based on the application of two methods, DIBR II and MABAC. The DIBR II method was used to define weight coefficients. The MABAC method was used to rank alternatives, and it was applied in a rough environment. Four experts were engaged in defining the criteria and alternatives as well as in the relation of criteria. The model was applied for ranking the methods and techniques of Lean organization systems management in the maintenance of technical systems of special purposes. At the end of the application was conducted a sensitivity analysis which proved the stability of the obtained results

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