scholarly journals Categorical properties of intuitionistic fuzzy groups

2021 ◽  
Vol 27 (4) ◽  
pp. 55-70
Author(s):  
P. K. Sharma ◽  
◽  
Chandni ◽  
Keyword(s):  
Category Theory ◽  
Abelian Category ◽  
Mathematical Physics ◽  
Theoretical Computer Science ◽  
Contravariant Functor ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
Intuitionistic Fuzzy ◽  
Categorical Properties ◽  
The Relationship

The category theory deals with mathematical structures and relationships between them. Categories now appear in most branches of mathematics and in some areas of theoretical computer science and mathematical physics, and acting as a unifying notion. In this paper, we study the relationship between the category of groups and the category of intuitionistic fuzzy groups. We prove that the category of groups is a subcategory of category of intuitionistic fuzzy groups and that it is not an Abelian category. We establish a function β : Hom(A, B) → [0; 1] × [0; 1] on the set of all intuitionistic fuzzy homomorphisms between intuitionistic fuzzy groups A and B of groups G and H, respectively. We prove that β is a covariant functor from the category of groups to the category of intuitionistic fuzzy groups. Further, we show that the category of intuitionistic fuzzy groups is a top category by establishing a contravariant functor from the category of intuitionistic fuzzy groups to the lattices of all intuitionistic fuzzy groups.

scholarly journals Introduction: special issue ICICTA 2012

2014 ◽  
Vol 24 (5) ◽  
Author(s):  
ZHIXIANG HOU
Keyword(s):  
Computer Science ◽  
Software Design ◽  
Category Theory ◽  
Theoretical Computer Science ◽  
Special Issue ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
And Mathematics

Mathematical Structures in Computer Science bridges the gap between theoretical computer science and software design. By publishing original perspectives from all areas of computing, the journal stresses applications from logic, algebra, geometry, category theory and other areas of logic and mathematics. Through issues such as this special issue, the journal also plans to play an occasional, but important role in the fields of intelligent computation and automation.

PROPOSAL OF A SEMIFORMAL MODEL OF ANONYMOUS COMMUNICATION

2009 ◽  
Vol 20 (03) ◽  
pp. 523-548 ◽  
Author(s):  
JOSEF ŠPROJCAR
Keyword(s):  
Computer Science ◽  
Probability Distributions ◽  
Estimation Procedure ◽  
Expressive Power ◽  
Building Blocks ◽  
Theoretical Computer Science ◽  
Anonymous Communication ◽  
Theoretical Computer ◽  
The Relationship ◽  
Channel Formalism

We present a semiformal model of anonymous communication with several participants performing several anonymous actions on several messages, e.g. in digital pseudosignatures. The goal is to design a model having enough expressive power to model simple as well as very complex anonymous communication patterns.Our model concentrates on anonymity of a sender, a receiver, and on the relationship anonymity. However, the model is easy to adopt to other types of anonymity. A special anonymous channel formalism is introduced and extensively explored in this paper. The formalism builds on the top of so-called estimation procedure which takes knowledge of the adversary and processes it to find anonymous participants. Some other, already published, models of anonymity, e.g. the model of Hughes and Shmatikov or of Halpern and O'Neill, are compatible with our model – they could be used as building blocks together with (or instead of) our estimation procedure. Therefore, the tools developed for those models can be easily adapted to be used with our model.We use protocol runs and an observational equivalence on the runs which is induced by adversary's knowledge. This is a well developed area of the theoretical computer science and many tools developed therein can be adapted to work with our model. Our model is also open to many additional features, e.g. the possibility to include probability distributions on anonymity sets.

Programming Languages as Mathematical Theories

2012 ◽  
pp. 1706-1722
Author(s):  
Raymond Turner
Keyword(s):  
Computer Science ◽  
Programming Languages ◽  
Semantic Theory ◽  
Theoretical Computer Science ◽  
Mathematical Activity ◽  
Theoretical Computer ◽  
The Subject ◽  
Will Force ◽  
The Relationship

That computer science is somehow a mathematical activity was a view held by many of the pioneers of the subject, especially those who were concerned with its foundations. At face value it might mean that the actual activity of programming is a mathematical one. Indeed, at least in some form, this has been held. But here we explore a different gloss on it. We explore the claim that programming languages are (semantically) mathematical theories. This will force us to discuss the normative nature of semantics, the nature of mathematical theories, the role of theoretical computer science and the relationship between semantic theory and language design.

scholarly journals Preface

2015 ◽  
Vol 27 (2) ◽  
pp. 92-93
Author(s):  
MARIANGIOLA DEZANI ◽  
SABRINA MANTACI ◽  
MARINELLA SCIORTINO
Keyword(s):  
Data Structure ◽  
Computer Science ◽  
Programming Languages ◽  
European Association ◽  
Wide Spectrum ◽  
Theoretical Computer Science ◽  
Combinatorics On Words ◽  
Special Issue ◽  
Theoretical Computer ◽  
Mathematical Structures

This special issue of Mathematical Structures in Computer Science is devoted to the fourteenth Italian Conference on Theoretical Computer Science (ICTCS) held at University of Palermo, Italy, from 9th to 11th September 2013. ICTCS is the conference of the Italian Chapter of the European Association for Theoretical Computer Science and covers a wide spectrum of topics in Theoretical Computer Science, ranging from computational complexity to logic, from algorithms and data structure to programming languages, from combinatorics on words to distributed computing. For this reason, the contributions here included come from very different areas of Theoretical Computer Science. In fact this special issue is motivated by the desire to give people who have presented their ideas at the 14th ICTCS the opportunity to publish papers on their work. Submitted papers have been subject to a careful and severe reviewing process and 11 of them were selected for this special issue.

Programming Languages as Mathematical Theories

2010 ◽  
pp. 66-82 ◽  
Author(s):  
Ray Turner
Keyword(s):  
Computer Science ◽  
Programming Languages ◽  
Semantic Theory ◽  
Theoretical Computer Science ◽  
Mathematical Activity ◽  
Theoretical Computer ◽  
The Subject ◽  
Will Force ◽  
The Relationship

That computer science is somehow a mathematical activity was a view held by many of the pioneers of the subject, especially those who were concerned with its foundations. At face value it might mean that the actual activity of programming is a mathematical one. Indeed, at least in some form, this has been held. But here we explore a different gloss on it. We explore the claim that programming languages are (semantically) mathematical theories. This will force us to discuss the normative nature of semantics, the nature of mathematical theories, the role of theoretical computer science and the relationship between semantic theory and language design.

scholarly journals Intuitionistic Fuzzy Modeling to Travelling Salesman Problem

2013 ◽  
Vol 11 (9) ◽  
pp. 3015-3024
Author(s):  
Arindam Garai ◽  
Tapan Kumar Roy
Keyword(s):  
Travelling Salesman Problem ◽  
Optimization Technique ◽  
Theoretical Computer Science ◽  
Solution Technique ◽  
Travelling Salesman ◽  
Programming Technique ◽  
Theoretical Computer ◽  
Multi Objective ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Environment

This paper presents solution technique for travelling salesman problem (TSP) under intuitionistic fuzzy environment. Travelling salesman problem is a non-deterministic polynomial-time (NP) hard problem in combinatorial optimization, studied in graph theory, operations research and theoretical computer science. It must be noted that a traveling sales man even face a situation in which he is not able to achieve his objectives completely. There must be a set of alternatives from which he can select one that best meets his aspiration level. For Multi-Objective Symmetric TSP, in fuzzy environment, it is converted into a Linear Program using Fuzzy Multi-Objective Linear Programming technique. A route cannot be simply chosen just as it will most minimize time or it will cover the least possible distance. Examples with requirements to consider the degree of rejection or hesitation (or both) are overflowing in our materialistic world. Here comes the need to consider TSP under intuitionistic fuzzy environment. The degree of rejection as well as the degree of hesitancy must be studied to find the solution in a truly optimum sense! Proposed technique is an extension as well as collaboration of ideas of fuzzy traveling salesperson problem and intuitionistic fuzzy (IF) optimization technique.

On naturally continuous non-dcpo domains

2016 ◽  
Vol 27 (8) ◽  
pp. 1521-1552
Author(s):  
VLADIMIR SAZONOV
Keyword(s):  
Computer Science ◽  
Current Approach ◽  
Theoretical Computer Science ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
Cambridge University ◽  
Applied Logic ◽  
Cartesian Closed ◽  
Algebraic Domains ◽  
Natural Domains

After works of Normann and the author on sequentiality (Normann 2006Mathematical Structures in Computer Science16 (2) 279–289; Normann and Sazonov 2012Annals of Pure and Applied Logic163 (5) 575–603; Sazonov 2007Logical Methods in Computer Science3 (3:7) 1–50), the necessity and possibility of a non-dcpo domain theory became evident. In this paper, the category of continuous dcpo domains is generalized to a category of ‘naturally’ continuous non-dcpo domains with ‘naturally’ continuous maps as arrows. A full subcategory of the latter, assuming a kind of bounded-completeness requirement of domains and presence of ⊥ in each, proves to be Cartesian closed and equivalent to a subclass of Ershov's general A-spaces (Ershov 1974Algebra and Logics12 (4) 369–416). This extends a non-dcpo generalization of Scott (algebraic) domains introduced and proved to be equivalent to Ershov's general f-spaces (Ershov 1972Algebra and Logic11 (4) 367–437) in Sazonov (2007 op. cit.; 2009 Annals of Pure and Applied Logic159 (3) 341–355).The current approach to natural domains (v-domains) is different from f-spaces and A-spaces in that it has arisen in Sazonov (2007 op. cit.) in a different way from defining fully abstract models for some versions of the language PCF over Integers, whereas the Ershov's approach was not initially related with full abstraction, and non-dcpo version of f-spaces and A-spaces were originally considered in an abstract (mainly topological) style. In this paper devoted to naturally continuous natural domains (v-continuous v-domains), we also work in an abstract (mainly order-theoretic) style but with the hope to relate it in the future with the ideas of PCF over Reals by exploring and adapting the ideas in Escardó (1996Theoretical Computer Science162 (1) 79–115), Escardó et al. (2004Mathematical Structures in Computer Science, 14 (6), Cambridge University Press 803–814), Marcial-Romero and Escardó (2007Theoretical Computer Science379 (1-2) 120–141), Sazonov (2007 op. cit.).

scholarly journals Classical realizability and arithmetical formulæ

2016 ◽  
Vol 27 (6) ◽  
pp. 1068-1107 ◽  
Author(s):  
MAURICIO GUILLERMO ◽  
ÉTIENNE MIQUEY
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Point Of View ◽  
Theoretical Computer ◽  
Mathematical Structures ◽  
Theoretic Point ◽  
Winning Strategies ◽  
Game Theoretic ◽  
Definition Of

In this paper, we treat the specification problem in Krivine classical realizability (Krivine 2009Panoramas et synthèses27), in the case of arithmetical formulæ. In the continuity of previous works from Miquel and the first author (Guillermo 2008Jeux de réalisabilité en arithmétique classique, Ph.D. thesis, Université Paris 7; Guillermo and Miquel 2014Mathematical Structures in Computer Science, Epub ahead of print), we characterize the universal realizers of a formula as being the winning strategies for a game (defined according to the formula). In the first sections, we recall the definition of classical realizability, as well as a few technical results. In Section 5, we introduce in more details the specification problem and the intuition of the game-theoretic point of view we adopt later. We first present a game1, that we prove to be adequate and complete if the language contains no instructions ‘quote’ (Krivine 2003Theoretical Computer Science308259–276), using interaction constants to do substitution over execution threads. We then show that as soon as the language contain ‘Quote,’ the game is no more complete, and present a second game2that is both adequate and complete in the general case. In the last Section, we draw attention to a model-theoretic point of view and use our specification result to show that arithmetical formulæ are absolute for realizability models.

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