The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector spaces are also Intuitionistic fuzzy hypervector space. Lastly, the notion of a linear transformation on a hypervector space is introduced and established an important theorem relative to Intuitionistic fuzzy hypervector spaces.
In this study different types of intuitionistic fuzzy continuities (IFCs) and intuitionistic fuzzy boundedness (IFBs) in intuitionistic fuzzy pseudo normed linear spaces are studied. Relations (intra and inter) on intuitionistic fuzzy continuities and intuitionistic fuzzy boundedness are investigated.
A complex intuitionistic fuzzy Lie superalgebra is a generalization of intuitionistic fuzzy Lie super-algebra whose membership function takes values in the unit disk in the complex plane. In [4], we introduced and studied the concepts of complex intuitionistic fuzzy Lie sub-superalgebras and complex intuitionistic fuzzy ideals of Lie superalgebras. Moreover, we also, in [4], defined the image and preimage of complex intuitionistic fuzzy Lie sub-superalgebra under Lie superalgebra anti-homomorphism, and he investigated the properties of anti-complex intuitionistic fuzzy Lie sub-superalgebras an…
A Note on Generalized Intuitionistic Fuzzy $ψ$ Normed Linear Space
针对直觉模糊n-范数\cite{Vijayabalaji}的定义，在线性空间上引入了广义直觉模糊$ψ$范数（简称GIF $ψ$ N \）的定义，并在此基础上得到了广义直觉模糊$ψ$赋范线性空间和有限维广义直觉模糊$ψ$赋范线性空间的一些结果.最后，引入了广义直觉模糊$ψ$连续性和序列直觉模糊$ψ$连续性的定义，并证明了它们是等价的。
The idea of rough statistical convergence for double sequences was studied by Ozcan and Or[29] in a intuitionistic fuzzy normed space. Recently the same has been generalized in the ideal context by Hossain and Banerjee[15] for sequences. Here in this paper we have discussed the idea of rough ideal convergence of double sequences in intuitionistic fuzzy normed spaces generalizing the idea of rough statistical convergence of double sequences. Also we have defined rough I2-cluster points for a double sequence and also investigated some of the basic properties associated with rough I2-limit set of…
We define weighted mean summability method of double sequences in intuitionistic fuzzy normed spaces($IFNS$), and obtain necessary and sufficient Tauberian conditions under which convergence of double sequences in $IFNS$ follows from their weighted mean summability. This study reveals also Tauberian results for some known summation methods in the special cases.
Being a pair of dual concepts, the normalized distance and similarity measures are very important tools for decision-making and pattern recognition under intuitionistic fuzzy sets framework. To be more effective for decision-making and pattern recognition applications, a good normalized distance measure should ensure that its dual similarity measure satisfies the axiomatic definition. In this paper, we first construct some examples to illustrate that the dual similarity measures of two nonlinear distance measures introduced in [A distance measure for intuitionistic fuzzy sets and its applicati…
Total Ordering Defined on the set of all Intuitionistic Fuzzy Numbers
L. A. Zadeh在1965年提出了模糊集合论的概念，作为经典集合论的推广，Atanassov在1983年进一步将其推广到直觉模糊集（IFS），用隶属度、非隶属度和犹豫度比模糊逻辑理论更精确地建模信息。直觉模糊数的概念在不同的情况下，在文献中进行了研究，并在现实生活中的应用。在涉及定性、定量和不确定信息的不同领域中的问题可以使用[17]中引入的直觉模糊数来更好地建模，该直觉模糊数推广了直觉模糊值[1，7，17]，区间值直觉模糊数（IVIFN）[10]，而不是通常的IFN [5，11，21]。模糊数的排序始于上个世纪七十年代初，直到2014年，W.Wang和Z.Wang才完成了模糊数类的完整排序。Geetha等人利用公理化的隶属度、非隶属度、模糊度和精确度评分函数，对IVIFNs类进行了完整的排序。[10]第10段。本文利用区间[0; 1]上的双上稠密序列给出了一类干扰素网络[17]的全序，推广了模糊数的全序，并举例说明.实例表明，该方法对这种类型的干扰素是优于现有的方法，本文将更好地理解这种新类型的干扰素。
We define statistical Cesàro and statistical logarithmic summability methods of sequences in intuitionistic fuzzy normed spaces($IFNS$) and give slowly oscillating type and Hardy type Tauberian conditions under which statistical Cesàro summability and statistical logarithmic summability imply convergence in $IFNS$. Besides, we obtain analogous results for the higher order summability methods as corollaries. Also, two theorems concerning the convergence of statically convergent sequences in $IFNS$ are proved in the paper.
All intuitionistic fuzzy TOPSIS methods contain two key elements: (1) the order structure, which can affect the choices of positive ideal-points and negative ideal-points, and construction of admissible distance/similarity measures; (2) the distance/similarity measure, which is closely related to the values of the relative closeness degrees and determines the accuracy and rationality of decision-making. For the order structure, many efforts are devoted to constructing some score functions, which can strictly distinguish different intuitionistic fuzzy values (IFVs) and preserve the natural part…
A complex intuitionistic fuzzy Lie superalgebra is a generalization of intuitionistic fuzzy Lie superalgebra whose membership function takes values in the unit disk in the complex plane. In this research, the concepts of complex intuitionistic fuzzy sets are introduced to Lie superalgebras. We define the complex intuitionistic fuzzy Lie sub superalgebras and complex intuitionistic fuzzy ideals of Lie superalgebras. Then, we study some related properties of complex intuitionistic fuzzy Lie sub-superalgebras and complex intuitionistic fuzzy ideals. Finally, we define the image and preimage of co…
We define weighted geometric mean method of convergence for sequences in $\mathbb{R}^+$ by using multiplicative calculus and obtain necessary and sufficient conditions under which convergence of sequences in $\mathbb{R}^+$ follows from convergence of their weighted geometric means. We also obtain multiplicative analogues of Schmidt type slow oscillation condition and Landau type two-sided condition for the convergence in particular. Besides, we introduce the concepts of $^{\oplus}$convergence, $^{\otimes}$convergence, $(\bar{N},p)-^{\oplus}$convergence, $(\bar{G},p)-^{\otimes}$convergence for …
