On Functions Preserving Convergence of Series in Fuzzy n-Normed Spaces

The purpose of this paper is to introduce finite convergence sequences and functions preserving convergence of series in fuzzy n-normed spaces

Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces

الغرض الرئيسي من هذا العمل هو تقديم بعض أنواع متتابعات التقارب الضبابية للمؤثرات المعرفة  على الفضاءات المعيارية الضبابية والبحث في  بعض الخصائص والعلاقات بين هذه المفاهيم  في البداية , يتم تقديم تعريف متتابعة التقارب  (SFN-spaces)القياسية الحد نفسه  تتقارب تقارباً ضبابيا ضعيفا مع  الضبابي الضعيف بدلالة الدوال الخطية الضبابية المقيدة. بعد ذلك تم برهان أن المتتابعة  ( fuzzy Baire's and uniform fuzzyboundedness   تم ذكروبرهان نظريتين مهمتين(  متقاربة ضبابياً. في حالة أن المتتابعة  للمؤثرات وهذه النظريات ضرورية  في الاتصال مع التقارب الضبابي الضعيف. يتم تقديم مفاهيم متتابعات التقارب الضبابي القوي والضعيف   حيث  متتابعة متقاربة ضبابياً بقوة مع   . على وجه الخصوص, إذا كان واثبات النظريات الأساسية المتعلقة بهذه المفاهيم  تنتمي    فأن  الى الفضاء المعياري  الضبابي القياسي  المؤثر الخطي من الفضاء المعياري الضبابي القياسي التام الى مجموعة كل المؤثرات الخطية الضبابية المقيدة. . اضافة الى ذلك , تم تقديم مفهوم المؤثر الخطي المتراص الضبابي في الفضاء المعياري الضبابي القياسي. أيضا ، تتم دراسة العديد من النظريات الأساسية للمؤثرات الخطية المتراصة الضبابية على نفس الفضاء. بتعبير أدق ، ثبت   فضاء معياري ضبابي قياسي. و أن كل مؤثر خطي متراص ضبابي يكون مقيد ضبابي بحيث أن كل من على الفضاء المعياري الضبابي القياسي  والمؤثر الخطي الضبابي المقيد    في نهاية البحث ، أثبتنا أن المؤثر الخطي الضبابي المتراص يجب أن يكون متراصاً ضبابياً.  The main purpose of this work is to introduce some types of fuzzy convergence sequences of operators defined on a standard fuzzy normed space (SFN-spaces) and investigate some properties and relationships between these concepts. Firstly, the definition of weak fuzzy convergence sequence in terms of fuzzy bounded linear functional is given. Then the notions of weakly and strongly fuzzy convergence sequences of operators  are introduced and essential theorems related to these concepts are proved. In particular, if ( ) is a strongly fuzzy convergent sequence with a limit  where linear operator from complete standard fuzzy normed space  into a standard fuzzy normed space  then  belongs to the set of all fuzzy bounded linear operators . Furthermore, the concept of a fuzzy compact linear operator in a standard fuzzy normed space is introduced. Also, several fundamental theorems of fuzzy compact linear operators are studied in the same space. More accurately, every fuzzy compact linear operator  is proved to be fuzzy bounded  where  and  are two standard fuzzy normed space

The Fuzzification of Classical Structures: A General View

The aim of this survey article, dedicated to the 50th anniversary of Zadeh’s pioneering paper "Fuzzy Sets" (1965), is to offer a unitary view to some important spaces in fuzzy mathematics: fuzzy real line, fuzzy topological spaces, fuzzy metric spaces, fuzzy topological vector spaces, fuzzy normed linear spaces. We believe that this paper will be a support for future research in this field

Set-Valued Analysis

This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers

Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications

Tesis por compendioMathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence and uniqueness of such mappings which can be viewed as a positive contribution towards an advancement of metric fixed point theory iii) Initiative of soft fixed point theory in framework of soft metric spaces and proving the results lying at the intersection of soft set theory and fixed point theory which would help in establishing a bridge between these two flourishing areas of research. iv) This study is also a starting point for the future research in the area of fuzzy soft fixed point theory.Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48470TESISCompendi

Conference Program

Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications