Bornological structures on many-valued sets

We introduce an approach to the concept of bornology in the framework of many-valued mathematical structures and develop the basics of the theory of many-valued bornological spaces and initiate the study of the category of many-valued bornological spaces and appropriately defined bounded "mappings" of such spaces. A scheme for constructing many-valued bornologies with prescribed properties is worked out. In particular, this scheme allows to extend an ordinary bornology of a metric space to a many-valued bornology on it

On two categories of many valued relations

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An Approach to the Concept of Soft Fuzzy Proximity

The purpose of this paper is to introduce the concept of soft fuzzy proximity. Firstly, we give the definitions of soft fuzzy proximity and Katsaras soft fuzzy proximity, and also we investigate the relations between the soft fuzzy proximity and slightly modified version of Katsaras soft fuzzy proximity. Secondly, we induce a soft fuzzy topology from a given soft fuzzy proximity by using soft fuzzy closure operator. Then, we obtain the initial soft fuzzy proximity from a given family of soft fuzzy proximities. So, we describe products in the category of soft fuzzy proximities. Finally, we show that a family of all soft fuzzy proximities on a given set constitutes a complete lattice

Towards the theory of M-approximate systems: Fundamentals and examples

Mitt mål var att skapa västra söders identitet och samlingsplats, vilken helt saknas idag. Utmaningen var också att transformera Hornsbruksgatan från en baksida till en tillgänglig plats. Högalidsparken förlängs ner till gatunivå - Hornsbruksgatan blir en blandning av park/ torg genom ett specifikt grönt plattsystem. Nya stråk och ramper binder ihop nuvarande gatu- och parknivån. Bebyggelsen är småskalig och nätt, ändå är programmet större än förslagit proram. Siktlinjer från omkingliggande bebyggelse och ankomstpunkter till platsen mot Högalidskyrkan och parken bevaras. Kommersiell verksamhet, såsom flertalet gallerier och restauranger får klättra uppåt från gatunivå till parknivå och tvärtom. Det idag påbörjade projektet, stadsodling tas till vara på. Ett växthus bebyggs samt två odlingsplättar i parken förläggs. Den nya platsen är en grön kulturplats med många exponerade utställningar, utsällningar utomhus samt många uteserveringar

George-Veeramani Fuzzy Metrics Revised

In this note, we present an alternative approach to the concept of a fuzzy metric, calling it a revised fuzzy metric. In contrast to the traditional approach to the theory of fuzzy metric spaces which is based on the use of a t-norm, we proceed from a t-conorm in the definition of a revised fuzzy metric. Here, we restrict our study to the case of fuzzy metrics as they are defined by George-Veeramani, however, similar revision can be done also for some other approaches to the concept of a fuzzy metric

Fuzzy Metrics in Terms of Fuzzy Relations

In this paper, we study the concept of fuzzy metrics from the perspective of fuzzy relations. Specifically, we analyze the commonly used definitions of fuzzy metrics. We begin by noting that crisp metrics can be uniquely characterized by linear order relations. Further, we explore the criteria that crisp relations must satisfy in order to determine a crisp metric. Subsequently, we extend these conditions to obtain a fuzzy metric and investigate the additional axioms involved. Additionally, we introduce the definition of an extensional fuzzy metric or E-d-metric, which is a fuzzification of the expression d(x,y)=t. Thus, we examine fuzzy metrics from both the linear order and from the equivalence relation perspectives, where one argument is a value d(x,y) and the other is a number within the range [0,+∞)

Fuzzy Extension of Crisp Metric by Means of Fuzzy Equivalence Relation

We develop an alternative approach to the fuzzy metric concept, which we obtain by fuzzy extension of a crisp metric d on a set X by means of a fuzzy equivalence relation E on the set IR+. We call it an E-d metric and study its properties and relations with “classical” fuzzy metrics. Our special interest is in the topologies and fuzzy topologies induced by E-d metrics