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

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Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory firstly proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Smarandache introduce for the first time the neutrosophic quadruple numbers (of the form + + + ) and the refined neutrosophic quadruple numbers

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