The first step of this study is to recall the definition and basic theorems for convex fuzzy metr... more The first step of this study is to recall the definition and basic theorems for convex fuzzy metric space (Z, M). Then, the definition of the convex fuzzy distance between two sets F and Y as well as the convex fuzzy distance from a point z to a set Y are introduced. Furthermore, the set of all nonempty convex fuzzy compact sets CFC(Z) are proved as a convex fuzzy complete when the convex fuzzy metric space (Z, M) is convex fuzzy complete.
In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduce... more In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduced. Then we found the relation between the maximal ideals of fuzzy complete a-fuzzy normed algebra and the associated multiplicative linear function space. In this direction we proved that if ℓ is character on Z then kerℓ is a maximal ideal in Z. After this we introduce the notion structure of the a-fuzzy normed algebra then we prove that the structure, st(Z) is ω *-fuzzy closed subset of fb(Z, ℂ) when (Z, , ⊛, ⊙) is a commutative fuzzy complete a-fuzzy normed algebra with identity e.
International Journal of Mathematics and Computer Science,, 2024
The main goal here is to introduce another type of fuzzy normed space which we call a convex fuzz... more The main goal here is to introduce another type of fuzzy normed space which we call a convex fuzzy normed space. Moreover, we give important properties of such a space.
Journal of Al-Qadisiyah for Computer Science and Mathematics
Our goal in the present paper is to introduce new type of fuzzy metric space called algebra fuzzy... more Our goal in the present paper is to introduce new type of fuzzy metric space called algebra fuzzy metric space after that some examples is introduced to illustrate this notion. Then basic properties of algebra fuzzy metric space is proved.
International Journal of Mathematics and Computer Science, 2023
In this article, we introduce the notion of a-fuzzy normed algebra by using two binary operations... more In this article, we introduce the notion of a-fuzzy normed algebra by using two binary operations: the t−conorm ⊛ defined as µ ⊛ ω = µ + ω − µω for all µ, ω ∈ [0, 1] and the t−norm ⊙ defined as η ⊙ θ = η.θ for all η, θ ∈ [0, 1]. Moreover, we give some examples to show the existence of such a notion. Furthermore, we introduce basic properties of a fuzzy complete a-fuzzy normed algebra and prove that ⊙ is a fuzzy continuous function and that every a-fuzzy normed algebra Z can be embedded in af b(Z, Z) as a closed subalgebra.
A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this... more A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this name is the continuous t-norm used here is binary operation usually product between number in [0, 1]. To show that this type of spaces is exists we give some examples, then some important basic properties, of this space are introduced with its proves. Moreover we study fuzzy continuous and uniformly fuzzy continuous function by proving basic properties of these notions. Furthermore the prove of cross product of finite number of p-FMS is again a p-FMS is introduced.
In this article we recall the definition of algebra fuzzy metric space and its basic properties. ... more In this article we recall the definition of algebra fuzzy metric space and its basic properties. In order to introduced the Hausdorff algebra fuzzy metric from fuzzy compact set to another fuzzy compact set we define the algebra fuzzy distance between two fuzzy compact sets after that basic properties of the Hausdorff algebra fuzzy metric between two fuzzy compact sets are proved. Finally the main result in this paper is proved that is if (S, m, ) is a fuzzy complete algebra fuzzy metric space then (AFH(S), h, ) is a fuzzy complete algebra fuzzy metric space.
Journal of Applied Sciences and Nanotechnology, 2022
The idea of generalizing quasi injective by employing a new term is introduced in this paper. The... more The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, the idea of strongly mainly self-pure submodules was added, which is similar to strongly primarily self-injective sub-modules. Some characteristics of injective, quasi-injective, principally self-injective, principally injective, absolutely self-pure, absolutely pure, and finitely R-injective modules being lengthened to strongly principally self-injective modules. So, in the present work, some properties are added to the concept in a manner similar to the absolutely self-neatness. The fundamental features of these concepts and their interrelationships are linked to the conceptions of some rings. (Von Neumann) regular, left SF-ring, and left pp-ring rings are described via such concept. For instance, the homomorphic picture of every principally injective module be strongly principally self-injective if R being left pp-ring, and another example for a commutative ring R of every strongly principally self-injective module be flat if R being (Von Neumann) regular. Also, a ring R be (Von Neumann) regular if and only if each R-module being strongly principally self-injective module.
we introduce the definition of afuzzy inner product space and discuss some properties of this spa... more we introduce the definition of afuzzy inner product space and discuss some properties of this space,and we use the definition of fuzzy inner product space to introduced anew definitions such that the definition of fuzzy Hilbert space ,Fuzzy convergence, ,Fuzzy complete,and we studied the relation between ordinary inner product space and fuzzy inner product space. Keywords: fuzzy set,fuzzy inner product space ﺍﻟﻀﺒﺎﺒﻴﺔ ﻫﻠﺒﺭﺕ ﻓﻀﺎﺀﺍﺕ ﺍﻟﺨﻼﺼﺔ ﺍﻟﻔﻀـﺎﺀ ﺒﻬﺫﺍ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺍﻟﺨﺼﺎﺌﺹ ﺒﻌﺽ ﻭﻨﺎﻗﺸﻨﺎ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﺘﻌﺭﻴﻑ ﻗﺩﻤﻨﺎ ﻫﻠﺒـﺭﺕ ﻓﻀـﺎﺀ ﺘﻌﺭﻴﻑ ﻤﺜﻶ ﺠﺩﻴﺩﺓ ﺘﻌﺎﺭﻴﻑ ﻟﺘﻘﺩﻴﻡ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﺘﻌﺭﻴﻑ ﻭﺍﺴﺘﺨﺩﻤﻨﺎ ﺍﻟﻀﺒﺎﺒﻲ , ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺘﻘﺎﺭﺏ , ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺘﺎﻡ ﻭ ﺒﺩﺭﺍﺴﺔ ﻗﻤﻨﺎ ﺍﻟـﺩﺍﺨﻠﻲ ﺍﻟﻀـﺭﺏ ﻓﻀﺎﺀ ﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﻭﻓﻀﺎﺀ ﺍﻻﻋﺘﻴﺎﺩﻱ .
In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall ... more In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall basic definitions and properties of this space. Then we introduce the notion pseudo fuzzy length space on a fuzzy set to prove that the fuzzy completion of pseudo fuzzy length is a fuzzy length space. Finally we defined the quotient of a fuzzy length space then we defined the fuzzy length to the quotient space. Keywords: Fuzzy length space on fuzzy set; Pseudo fuzzy length space on a fuzzy set; Fuzzy continuous operator.
In this paper we introduce a new definition of a fuzzy normed space (to the best of our knowledge... more In this paper we introduce a new definition of a fuzzy normed space (to the best of our knowledge) then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.
In the present paper first we recall the definition of algebra fuzzy metric space and some basic ... more In the present paper first we recall the definition of algebra fuzzy metric space and some basic properties of algebra fuzzy metric space are introduced. Our goal is to prove the fixed point theorem in fuzzy complete algebra fuzzy metric space. Finally, the application to this theorem introduced.
In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the... more In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.
The first step of this study is to recall the definition and basic theorems for convex fuzzy metr... more The first step of this study is to recall the definition and basic theorems for convex fuzzy metric space (Z, M). Then, the definition of the convex fuzzy distance between two sets F and Y as well as the convex fuzzy distance from a point z to a set Y are introduced. Furthermore, the set of all nonempty convex fuzzy compact sets CFC(Z) are proved as a convex fuzzy complete when the convex fuzzy metric space (Z, M) is convex fuzzy complete.
In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduce... more In this paper further properties of the fuzzy complete a-fuzzy normed algebra have been introduced. Then we found the relation between the maximal ideals of fuzzy complete a-fuzzy normed algebra and the associated multiplicative linear function space. In this direction we proved that if ℓ is character on Z then kerℓ is a maximal ideal in Z. After this we introduce the notion structure of the a-fuzzy normed algebra then we prove that the structure, st(Z) is ω *-fuzzy closed subset of fb(Z, ℂ) when (Z, , ⊛, ⊙) is a commutative fuzzy complete a-fuzzy normed algebra with identity e.
International Journal of Mathematics and Computer Science,, 2024
The main goal here is to introduce another type of fuzzy normed space which we call a convex fuzz... more The main goal here is to introduce another type of fuzzy normed space which we call a convex fuzzy normed space. Moreover, we give important properties of such a space.
Journal of Al-Qadisiyah for Computer Science and Mathematics
Our goal in the present paper is to introduce new type of fuzzy metric space called algebra fuzzy... more Our goal in the present paper is to introduce new type of fuzzy metric space called algebra fuzzy metric space after that some examples is introduced to illustrate this notion. Then basic properties of algebra fuzzy metric space is proved.
International Journal of Mathematics and Computer Science, 2023
In this article, we introduce the notion of a-fuzzy normed algebra by using two binary operations... more In this article, we introduce the notion of a-fuzzy normed algebra by using two binary operations: the t−conorm ⊛ defined as µ ⊛ ω = µ + ω − µω for all µ, ω ∈ [0, 1] and the t−norm ⊙ defined as η ⊙ θ = η.θ for all η, θ ∈ [0, 1]. Moreover, we give some examples to show the existence of such a notion. Furthermore, we introduce basic properties of a fuzzy complete a-fuzzy normed algebra and prove that ⊙ is a fuzzy continuous function and that every a-fuzzy normed algebra Z can be embedded in af b(Z, Z) as a closed subalgebra.
A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this... more A new type of FMS, known as a product FMS (or simply p-FMS) is introduced, the reason behind this name is the continuous t-norm used here is binary operation usually product between number in [0, 1]. To show that this type of spaces is exists we give some examples, then some important basic properties, of this space are introduced with its proves. Moreover we study fuzzy continuous and uniformly fuzzy continuous function by proving basic properties of these notions. Furthermore the prove of cross product of finite number of p-FMS is again a p-FMS is introduced.
In this article we recall the definition of algebra fuzzy metric space and its basic properties. ... more In this article we recall the definition of algebra fuzzy metric space and its basic properties. In order to introduced the Hausdorff algebra fuzzy metric from fuzzy compact set to another fuzzy compact set we define the algebra fuzzy distance between two fuzzy compact sets after that basic properties of the Hausdorff algebra fuzzy metric between two fuzzy compact sets are proved. Finally the main result in this paper is proved that is if (S, m, ) is a fuzzy complete algebra fuzzy metric space then (AFH(S), h, ) is a fuzzy complete algebra fuzzy metric space.
Journal of Applied Sciences and Nanotechnology, 2022
The idea of generalizing quasi injective by employing a new term is introduced in this paper. The... more The idea of generalizing quasi injective by employing a new term is introduced in this paper. The introduction of principally self-injective modules, which are principally self-injective modules. A number of characteristics and characterizations of such modules have been established. In addition, the idea of strongly mainly self-pure submodules was added, which is similar to strongly primarily self-injective sub-modules. Some characteristics of injective, quasi-injective, principally self-injective, principally injective, absolutely self-pure, absolutely pure, and finitely R-injective modules being lengthened to strongly principally self-injective modules. So, in the present work, some properties are added to the concept in a manner similar to the absolutely self-neatness. The fundamental features of these concepts and their interrelationships are linked to the conceptions of some rings. (Von Neumann) regular, left SF-ring, and left pp-ring rings are described via such concept. For instance, the homomorphic picture of every principally injective module be strongly principally self-injective if R being left pp-ring, and another example for a commutative ring R of every strongly principally self-injective module be flat if R being (Von Neumann) regular. Also, a ring R be (Von Neumann) regular if and only if each R-module being strongly principally self-injective module.
we introduce the definition of afuzzy inner product space and discuss some properties of this spa... more we introduce the definition of afuzzy inner product space and discuss some properties of this space,and we use the definition of fuzzy inner product space to introduced anew definitions such that the definition of fuzzy Hilbert space ,Fuzzy convergence, ,Fuzzy complete,and we studied the relation between ordinary inner product space and fuzzy inner product space. Keywords: fuzzy set,fuzzy inner product space ﺍﻟﻀﺒﺎﺒﻴﺔ ﻫﻠﺒﺭﺕ ﻓﻀﺎﺀﺍﺕ ﺍﻟﺨﻼﺼﺔ ﺍﻟﻔﻀـﺎﺀ ﺒﻬﺫﺍ ﺍﻟﻤﺘﻌﻠﻘﺔ ﺍﻟﺨﺼﺎﺌﺹ ﺒﻌﺽ ﻭﻨﺎﻗﺸﻨﺎ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﺘﻌﺭﻴﻑ ﻗﺩﻤﻨﺎ ﻫﻠﺒـﺭﺕ ﻓﻀـﺎﺀ ﺘﻌﺭﻴﻑ ﻤﺜﻶ ﺠﺩﻴﺩﺓ ﺘﻌﺎﺭﻴﻑ ﻟﺘﻘﺩﻴﻡ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﺘﻌﺭﻴﻑ ﻭﺍﺴﺘﺨﺩﻤﻨﺎ ﺍﻟﻀﺒﺎﺒﻲ , ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺘﻘﺎﺭﺏ , ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺘﺎﻡ ﻭ ﺒﺩﺭﺍﺴﺔ ﻗﻤﻨﺎ ﺍﻟـﺩﺍﺨﻠﻲ ﺍﻟﻀـﺭﺏ ﻓﻀﺎﺀ ﺒﻴﻥ ﺍﻟﻌﻼﻗﺔ ﺍﻟﻀﺒﺎﺒﻲ ﺍﻟﺩﺍﺨﻠﻲ ﺍﻟﻀﺭﺏ ﻭﻓﻀﺎﺀ ﺍﻻﻋﺘﻴﺎﺩﻱ .
In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall ... more In this paper we recall the definition of fuzzy length space on a fuzzy set after that we recall basic definitions and properties of this space. Then we introduce the notion pseudo fuzzy length space on a fuzzy set to prove that the fuzzy completion of pseudo fuzzy length is a fuzzy length space. Finally we defined the quotient of a fuzzy length space then we defined the fuzzy length to the quotient space. Keywords: Fuzzy length space on fuzzy set; Pseudo fuzzy length space on a fuzzy set; Fuzzy continuous operator.
In this paper we introduce a new definition of a fuzzy normed space (to the best of our knowledge... more In this paper we introduce a new definition of a fuzzy normed space (to the best of our knowledge) then the related concepts such as fuzzy continuous, convergence of sequence of fuzzy points and Cauchy sequence of fuzzy points are discussed in details.
In the present paper first we recall the definition of algebra fuzzy metric space and some basic ... more In the present paper first we recall the definition of algebra fuzzy metric space and some basic properties of algebra fuzzy metric space are introduced. Our goal is to prove the fixed point theorem in fuzzy complete algebra fuzzy metric space. Finally, the application to this theorem introduced.
In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the... more In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact operators. Finally, if T belongs to FC(V,U) and dimension of V is finite then T is fuzzy compact is proved.
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