Soft Spaces Research Articles

Yakın esnek ayırma aksiyomları ve kuratowski kapanış operatörü üzerine

Bu çalışmada ilk bölümde kullanacağımız temel kavramlar verilmiştir. Daha sonra yakın esnek topolojik uzay ve bu yapının bazı özellikleri verildi. Üçüncü bölümde yakın esnek topolojik uzayın ayırma aksiyomları ile ilgili bağlantısı incelenmiş olup yakın esnek topolojik uzayının ayırma aksiyomları verildi. Kuratowski kapanış operatörü ile yakın esnek topoloji olma aksiyomlarının sağlandığını gösterdik.

Progress, Challenges, and Prospects of Soft Robotics for Space Applications

The development of space robots is vital to broadening human cognitive boundaries. Space robots have been deployed in space science experiments, extravehicular operations, and deep space exploration. The application of space robots undoubtedly reduces the risk and cost of space activities. Traditional space robots primarily utilize rigid structures, resulting in limited degrees of freedom, which restricts their operational capabilities. In contrast, soft robots with greater flexibility and robustness may be used for future space exploration. Soft robots applied in space environments must overcome significant challenges associated with ultrahigh vacuum, microgravity, extreme temperatures, and high‐energy radiation. Herein, a comprehensive analysis of the key advantages of soft robots is presented based on the special requirements of the space environments for soft robots. Furthermore, brief insights into how soft robots must be changed in terms of their design, modeling, fabrication, sensing, and control to adapt to space environments are discussed. Specifically, soft robot scenarios with potential space application value are introduced. Finally, opinions regarding the potential directions of soft space robots are provided.

Neutrosophic soft bi-topological structures concerning some special neutrosophic soft open sets

In this article, new generliased neutrosophic soft *b open set is introduced in neutrosophic soft bi-topological spaces (NSBTS) concerning soft points of the space. This new set is produced by the combination of soft semi-open and soft pre-open sets of neutrosophic soft topological space. Different results are ushered in NSBTS. Appropriate examples are provided for verification of different results. The non-validity of some results is verified with appropriate examples.

Regionales Flächenmanagement in den deutschen Metropolregionen

Metropolitan regions result from spatial rescaling processes and region formations and are considered as “soft spaces of governance”, referring to international debates on the “new regionalism”. This paper addresses the criticism that the focus on competitive metropolitan regions distracts from the need for action on classic spatial planning issues. For this, the paper examines and discusses the institutional integration of regional planning in the German metropolitan regions and the activities of regional growth management as well as the regulatory intensity of regional plans based on a group comparison of metropolitan regions. As a result, the thesis of an institutionally fragmented regulatory growth management by regional planning can only be confirmed for a few metropolitan regions, where no relevant institutions and instruments are implemented in the core area. Regarding the “soft” instruments of growth management, the situation is very different. Here, the action potential is not yet fully utilized, even in metropolitan regions with strong institutional cores

A non-continuous soft mapping that preserves some structural soft sets

As everyday problems contain a lot of data and ambiguity, it has become necessary to develop new mathematical approaches to address them and soft set theory is the best tool to deal with such problems. Hence, in this article, we introduce a non-continuous mapping in soft settings called soft U -continuous. We mainly focus on studying soft U -continuity and its connection to soft continuity. We further show that soft U -continuity preserves soft compact sets and soft connected sets. The later sets have various applications in computing science and decision making theory. In the end, we show that if each soft U -continuous mapping f from a soft space X into a soft T0-space Y is soft continuous, then Y is soft T1.

Soft spaces, soft planning, soft law: Examining the institutionalisation of city-regional planning in Finland

This article discusses the concepts of soft spaces and soft planning in the context of city-regional planning, complementing the discussion with an excursion to “soft law”. The point of departure is the current debate on the legitimacy deficits of the often power-laden processes where “soft” planning spaces are enacted or “performed”, and decisions made concerning planning of these spaces. Through legal theory and the concept of soft law, the article provides first, a new perspective on the performative nature of soft planning, and second, new conceptual tools for addressing legitimacy and effectiveness of soft planning. The article also uses the concepts of soft spaces, soft planning, and soft law for scrutinising the ongoing renewal of the Finnish planning system, where some, but not all aspects of currently largely informal city-regional planning are purported to be formalised or hardened.

Beyond soft planning: Towards a Soft turn in planning theory and practice?

Over the last decade, soft planning has become an increasingly visible concept in planning literature. Since the term soft spaces was firstly coined, soft planning has been used to describe a growing number of practices that occur at the margins of statutory planning systems. However, as soft planning-related literature proliferates, so does the diversity of approaches and planning practices it encompasses. Such diversity fuels long-standing questions about what can or cannot be considered as soft planning as well as about its usefulness for today’s planning theory and practice. To shed light on this still unclear conceptual outline, this article divides the soft planning debate into five contextual components (ethos; governance; politics; policies; spaces; and scale) while paying particular attention to the relationship between soft planning and strategic spatial planning. The aim is to foreground soft planning as a concept, and add clarity and awareness on the challenges, the risks and opportunities, planning currently faces.

On Soft Generalized ω-Closed Sets and Soft T1/2 Spaces in Soft Topological Spaces

In this paper, we define a soft generalized ω-closed set, which is a generalization of both the soft ω-closed set and the soft generalized closed set. We show that the classes of generalized closed sets and generalized ω-closed sets coincide in soft anti-locally countable soft topological spaces. Additionally, in soft locally countable soft topological spaces, we show that every soft set is a soft generalized ω-closed set. Furthermore, we prove that the classes of soft generalized closed sets and soft generalized ω-closed sets coincide in the soft topological space (X,τω,A). In addition to these, we determine the behavior of soft generalized ω-closed sets relative to soft unions, soft intersections, soft subspaces, and generated soft topologies. Furthermore, we investigate soft images and soft inverse images of soft generalized closed sets and soft generalized ω-closed sets under soft continuous, soft closed soft transformations. Finally, we continue the study of soft T1/2 spaces, in which we obtain two characterizations of these soft spaces, and investigate their behavior with respect to soft subspaces, soft transformations, and generated soft topologies.

Partial soft metric spaces: Convergence

Matthew introduced a non-zero self distance which is called a partial metric as a part of the study of denotational semantics of dataflow network. In this study, we aim to extend the Matthew’s notion to the soft universe and so, we give the definition of a partial soft metric. Then we investigate the convergence of sequences in a partial soft metric space and examine some basic properties.

On the Soft Stability of Soft Picard and Soft Mann Iteration Processes

In this paper, we introduce new concepts that relates to soft space based on work that was previously presented by researchers in this regard. First we give the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give some examples to illustrate them.
 Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that are used to prove some theorems about stability of soft iteration processes (with soft contraction operator) with soft Picard iteration procedure as well as soft Mann iteration procedure.

Redundancy and overactuation in cephalopod-inspired soft robot arms.

Current soft robotic arms commonly follow traditional - i.e., hard - robot design conventions. Omnidirectional soft arms most commonly consist of segments that contain three parallel longitudinal actuators, or actuator groups, of which one or two are activated to induce bending. This design uses the minimum number of actuators required for omnidirectional bending, which is consistent with traditional robot design but unnecessarily constrains the soft arm design space. The cephalopods that frequently inspire soft robot arms have tens of bundles of longitudinal muscle fibers, and these bundles are distributed around the limb circumference rather than grouped. This article analyzes fluid-driven soft arm architectures with up to 12 actuators, which mimic the redundant and distributed nature of cephalopod arms and tentacles. Over-constraints (activating more than two actuators) were considered, which are possible because soft robots - unlike traditional robots - can tolerate conflicting constraints without jamming. A previously-developed generalizable model was used to simulate design performance, and a subset of the examined architectures were constructed and tested. Many-actuator soft arms achieved high strokes under equivalent load without sacrificing no-load reach and were able to execute near constant-curvature turns with a simple actuation pattern. The framework introduced here also enables cross section variations that are not possible with minimalist designs.

Infra Pre-open Sets and Their Applications to Generate New Types of Operators and Maps

Herein, we introduce the concepts of infra soft pre-open infra soft pre-closed sets which are respectively generalizations of infra soft open and infra soft closed sets.We characterize them and investigate their behaviours under infra soft homeomorphism maps and finite product of soft spaces. Then, we apply infra soft pre-open infra soft pre-closed sets to define the operators of infra pre-interior, infra pre-closure, infra pre-limit and infra pre-boundary. We discuss their main properties and show the interrelations between them. In the end, we introduce new types of soft maps using infra soft pre-open and infra soft pre-closed sets and explore their essential properties.

Two families of separation axioms on infra soft topological spaces

Many generalizations of soft topology were studied in the literature, an infra soft topology is the recent one of these generalizations. In this paper, we put on view two classes of soft separation axioms in the frame of infra soft topologies, namely infra pp-soft Tj and infra pt-soft Tj-spaces (j = 0, 1, 2, 3, 4). Both of them are formulated with respect to distinct ordinary points such that the first class defined using partial belong and partial non-belong relations, and the second one defined using partial belong and total non-belong relations. Following systematic lines of this type of study, we first show the relationships between them with the aid of examples. We also establish main properties and explore their behaviour under some special types of infra soft topologies. Transmission of these classes between infra soft topology and its parametric infra topologies are amply studied. Moreover, we scrutinize their features in terms of hereditary and topological properties, and finite product of soft spaces.

On pythagorean fuzzy soft topological spaces

Imprecision in the decision-making process is an essential consideration. In order to navigate the imprecise decision-making framework, measuring tools and methods have been developed. Pythagorean fuzzy soft sets are one of the new methods for dealing with imprecision. Pythagorean fuzzy soft topological spaces is an extension of intuitionistic fuzzy soft topological spaces. These sets generalizes intuitionistic fuzzy sets for a broader variety of implementations. This work is a gateway to study such a problem. The concept of Pythagorean fuzzy soft topological spaces(PyFSTS), interior, closure, boundary, neighborhood of Pythagorean fuzzy soft spaces PyFSS, base and subspace of PyFSTSs are presented and its properties are figured out. We established an algorithm under uncertainty based on PyFSTS for multi-attribute decision-making (MADM) and to validate this algorithm, a numerical example is solved for suitable brand selection. Finally, the benefits, validity, versatility and comparison of our proposed algorithms with current techniques are discussed.The advantage of the proposed work is to detect vagueness with more sizably voluminous valuation space than intuitionistic fuzzy sets.

Characteristics of Soft Tychonoff Spaces with New Soft Separation Axioms

The aim of this work is to investigate and study soft Tychonoff space and some new soft spaces such as soft , soft , soft , soft , soft , soft , soft and soft in this work the relationships between these new soft spaces such as soft public regular, soft public normal, soft strongly completely regular, soft semi completely normal and with well known axioms soft , soft and soft are obtained, Further, the relationships between these new soft spaces with each other are studied. We prove that each soft space is soft Tychonoff space, also in this paper we show that each soft space is soft , each soft space is soft and each soft space is soft . Finally, depending on the above soft spaces and properties of the soft fuzzy spaces, the new types of soft fuzzy spaces can be introduced like Soft fuzzy public regular, Soft fuzzy strongly completely regular, and others.

Infra Soft Semiopen Sets and Infra Soft Semicontinuity

To contribute to the area of infra soft topology, we introduce one of the generalizations of infra soft open sets called infra soft semiopen sets. We establish some characterizations of them and study their main properties. We determine under what condition this class is closed under finite intersection and show that this class is preserved under infra soft continuous mappings and finite product of soft spaces. Then, we present the concepts of infra semi-interior, infra semiclosure, infra semilimit, and infra semiboundary soft points of a soft set and elucidate the relationships between them. Finally, we exploit infra soft semiopen and infra soft semiclosed sets to define new types of soft mappings. We characterize each one of these soft mappings and explore main features.

Two Classes of Infrasoft Separation Axioms

One of the considerable topics in the soft setting is the study of soft topology which has enticed the attention of many researchers. To contribute to this scope, we devote this work to investigate two classes of separation axioms with respect to the distinct ordinary elements through one of the generalizations of soft topology called infrasoft topology. We first formulate the concepts of infra- t p -soft T j using total belong and partial nonbelong relations and then introduce the concepts of infra- t t -soft T j -spaces using total belong and partial nonbelong relations. To illustrate the relationships between them, we provide some examples. We discuss their fundamental properties and study their behaviors under some special types of infrasoft topologies. An extensive discussion is given for the transmission of these two classes between infrasoft topology and its parametric infratopologies. In the end, we demonstrate which ones have topological and hereditary properties, and we show their behaviors under the finite product of soft spaces.

Fibrewise soft bitopological spaces

We introduce and discussarecent type of fibrewise topological spaces, namely fibrewise soft bitopological spaces. Also, we introduce the concepts of fibrewise closed soft bitopological spaces, fibrewise open soft bitopological spaces, fibrewise locally sliceable soft bitopological spaces and fibrewise locally sectionable soft bitopological spaces. Furthermore, we state and prove several propositions concerning these concepts.

On soft Lindelof spaces in bitopological spaces via soft ℵ-open sets

In this paper, we define the soft ℵ -open sets in soft bitopological spaces and we discuss new types of soft Lindelof in soft bitopological spaces, namely soft ℵ - Lindelof space. Also, we study some properties about this space.

Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function

The theories of metric spaces and fuzzy metric spaces are crucial topics in mathematics. 
 Compactness is one of the most important and fundamental properties that have been widely used in Functional Analysis. In this paper, the definition of compact fuzzy soft metric space is introduced and some of its important theorems are investigated. Also, sequentially compact fuzzy soft metric space and locally compact fuzzy soft metric space are defined and the relationships between them are studied. Moreover, the relationships between each of the previous two concepts and several other known concepts are investigated separately. Besides, the compact fuzzy soft continuous functions are studied and some essential theorems are proved.