scholarly journals Algebraic Structure of Union of Fuzzy (Anti-Fuzzy) Normal Sub - Groups Fuzzy (Anti-Fuzzy) Normal Sub ch Bigroups And Soon Fuzzy (Anti-Fuzzy) Normal Sub - N Groups

2019 ◽  
pp. 312-322 ◽  
Author(s):  
S. Chandrasekaran ◽  
N. Deepica
Keyword(s):  
Normal Subgroup ◽  
Algebraic Structure ◽  
Definition Of ◽  
Quadratic Group ◽  
Fuzzy Subsets

In this paper, union of Fuzzy subsets, definition of Fuzzy normal subgroup, definition of Fuzzy normal sub bi-group, definition of Fuzzy normal sub tri-group, definition of Fuzzy normal sub – Quadratic group, definition of fuzzy normal sub- Pentant group and definition of Fuzzy normal sub–N groups are derived. Moreover, some properties and theorems of union in fuzzy normal based on these have been derived.

scholarly journals Union of Fuzzy Sub - Quadradic Groups Fuzzy Sub - Pendant Groups and Fuzzy Sub - N Groups

2019 ◽  
pp. 303-311
Author(s):  
S. Chandrasekaran ◽  
N. Deepica
Keyword(s):  
Pendant Group ◽  
Definition Of ◽  
Quadratic Group ◽  
Fuzzy Subsets

In this paper, union of Fuzzy subsets, Fuzzy sub – Quadratic group, fuzzy sub - Pendant group and Fuzzy sub–N groups are discussed. Moreover, some properties and theorems based on these have been derived and derive the definitions of Union of Fuzzy sub – Quadratic group, definitions of Union of fuzzy sub- Pendant group and soon definitions of Union of Fuzzy sub–N groups, and derive the definitions of Fuzzy Quadratic group, definitions of fuzzy Pendant group and soon definitions of Fuzzy N group and definition of Quadratic group, definitions of Pendant group and soon definitions of N group.

On EMV-Semirings

2019 ◽  
Vol 69 (4) ◽  
pp. 739-752 ◽  
Author(s):  
R. A. Borzooei ◽  
M. Shenavaei ◽  
A. Di Nola ◽  
O. Zahiri
Keyword(s):  
Distributive Lattice ◽  
Algebraic Structure ◽  
Maximal Ideal ◽  
Boolean Algebras ◽  
Algebraic Extension ◽  
Theoretic Approach ◽  
Basic Properties ◽  
Mv Algebra ◽  
Definition Of ◽  
Generalized Boolean Algebras

Abstract The paper deals with an algebraic extension of MV-semirings based on the definition of generalized Boolean algebras. We propose a semiring-theoretic approach to EMV-algebras based on the connections between such algebras and idempotent semirings. We introduce a new algebraic structure, not necessarily with a top element, which is called an EMV-semiring and we get some examples and basic properties of EMV-semiring. We show that every EMV-semiring is an EMV-algebra and every EMV-semiring contains an MV-semiring and an MV-algebra. Then, we study EMV-semiring as a lattice and prove that any EMV-semiring is a distributive lattice. Moreover, we define an EMV-semiring homomorphism and show that the categories of EMV-semirings and the category of EMV-algebras are isomorphic. We also define the concepts of GI-simple and DLO-semiring and prove that every EMV-semiring is a GI-simple and a DLO-semiring. Finally, we propose a representation for EMV-semirings, which proves that any EMV-semiring is either an MV-semiring or can be embedded into an MV-semiring as a maximal ideal.

scholarly journals On Frattini-like subgroups

1993 ◽  
Vol 35 (1) ◽  
pp. 95-98 ◽  
Author(s):  
James C. Beidleman ◽  
Howard Smith
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Maximal Subgroups ◽  
Property A ◽  
Arbitrary Group ◽  
Close Relationship ◽  
Similar Vein ◽  
Definition Of ◽  
A Finite Group

For any group G, denote by φf(G respectively L(G)) the intersection of all maximal subgroups of finite index (respectively finite nonprime index) in G, with the usual provision that the subgroup concerned equals Gif no such maximals exist. The subgroup φf(G) was discussed in [1] in connection with a property v possessed by certain groups: a group G has v if and only if every nonnilpotent, normal subgroup of G has a finite, nonnilpotent G-image. It was shown there, for instance, that G/φf(G) has v for all groups G. The subgroup L(G), in the case where G is finite, was investigated at some length in [3], one of the main results being that L(G) is supersoluble. (A published proof of this result appears as Theorem 3 of [4]). The present paper is concerned with the role of L(G) in groups G having property v or a related property a, the definition of which is obtained by replacing “nonnilpotent” by “nonsupersoluble” in the definition of v. We also present a result (namely Theorem 4) which displays a close relationship between the subgroups L(G) and φf(G) in an arbitrary group G. Some of the results for finite groups in [3] are found to hold with rather weaker hypotheses and, in fact, remain true for groups with v or a. We recall that if a group has a it also has v ([2]Theorem 2) but not conversely. For example, G = (x, y: y-1xy = x2)has v but not a. It is a well-known result of Gaschütz ([8], 5.2.15) that, in a finite group G, if His a normal subgroup containing φ(G) such that H/φ(G) is nilpotent than His nilpotent. This remains true in the case where G is any group with v [1, Proposition 1]. Our first result is in a similar vein and is a generalization of Theorem 9 of [7] and Theorem 1.2.9 of [3], the latter of which states that, for a finite group G, if G/L(G) is supersoluble, then so is G.

scholarly journals Translation, modulation and dilation systems in set-valued signal processing

2018 ◽  
Vol 10 (1) ◽  
pp. 143-164 ◽  
Author(s):  
H. Levent ◽  
Y. Yilmaz
Keyword(s):  
Signal Processing ◽  
Linear Space ◽  
Algebraic Structure ◽  
Compact Convex ◽  
Inner Product ◽  
Complex Numbers ◽  
Real Numbers ◽  
Aumann Integral ◽  
Definition Of ◽  
Interval Valued

In this paper, we investigate a very important function space consists of set-valued functions defined on the set of real numbers with values on the space of all compact-convex subsets of complex numbers for which the $p$th power of their norm is integrable. In general, this space is denoted by $L^{p}% (\mathbb{R},\Omega(\mathbb{C}))$ for $1\leq p<\infty$ and it has an algebraic structure named as a quasilinear space which is a generalization of a classical linear space. Further, we introduce an inner-product (set-valued inner product) on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ and we think it is especially important to manage interval-valued data and interval-based signal processing. This also can be used in imprecise expectations. The definition of inner-product on $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is based on Aumann integral which is ready for use integration of set-valued functions and we show that the space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$ is a Hilbert quasilinear space. Finally, we give translation, modulation and dilation operators which are three fundational set-valued operators on Hilbert quasilinear space $L^{2}(\mathbb{R},\Omega(\mathbb{C}))$.

scholarly journals Convex preferences: A new definition

2019 ◽  
Vol 14 (4) ◽  
pp. 1169-1183 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Decision Maker ◽  
Algebraic Structure ◽  
Preference Relation ◽  
Evaluation Criteria ◽  
Convex Preferences ◽  
Definition Of ◽  
General Conditions

We suggest a concept of convexity of preferences that does not rely on any algebraic structure. A decision maker has in mind a set of orderings interpreted as evaluation criteria. A preference relation is defined to be convex when it satisfies the following condition: If, for each criterion, there is an element that is both inferior to b by the criterion and superior to a by the preference relation, then b is preferred to a. This definition generalizes the standard Euclidean definition of convex preferences. It is shown that under general conditions, any strict convex preference relation is represented by a maxmin of utility representations of the criteria. Some economic examples are provided.

scholarly journals FUZZY RINGS AND ITS PROPERTIES

2017 ◽  
Vol 5 (1) ◽  
pp. 32
Author(s):  
Karyati Karyati ◽  
Rifki Chandra Utama
Keyword(s):  
Normal Subgroup ◽  
Fuzzy Sets ◽  
Algebraic Structure ◽  
Binary Operation ◽  
Quotient Ring ◽  
Ring Homomorphism ◽  
Factor Group ◽  
Semi Group ◽  
Fuzzy Ideal ◽  
Fuzzy Ring

Abstract One of algebraic structure that involves a binary operation is a group that is defined  an un empty set (classical) with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level  and strong level  as well as image and pre-image homomorphism fuzzy ring. Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring

scholarly journals PARABOSE-PARAFERMI SUPERSYMMETRY

1996 ◽  
Vol 11 (16) ◽  
pp. 2957-2975 ◽  
Author(s):  
ALI MOSTAFAZADEH
Keyword(s):  
Quantum Mechanics ◽  
Quantum System ◽  
Algebraic Structure ◽  
Central Charge ◽  
Supersymmetric Quantum Mechanics ◽  
Eigenvalues And Eigenvectors ◽  
Energy Eigenvalues ◽  
General Terms ◽  
Symmetry Transformations ◽  
Definition Of

The (p=2) parabose–parafermi supersymmetry is studied in general terms. It is shown that the algebraic structure of the (p=2) parastatistical dynamical variables allows for (symmetry) transformations which mix the parabose and parafermi coordinate variables. The example of a simple parabose-parafermi oscillator is discussed and its symmetries investigated. It turns out that this oscillator possesses two parabose-parafermi supersymmetries. The combined set of generators of the symmetries forms the algebra of supersymmetric quantum mechanics supplemented with an additional central charge. In this sense there is no relation between the parabose–parafermi supersymmetry and the parasupersymmetric quantum mechanics. A precise definition of a quantum system involving this type of parabose-parafermi supersymmetry is offered, thus introducing (p=2) supersymmetric paraquantum mechanics. The spectrum degeneracy structure of general (p=2) supersymmetric paraquantum mechanics is analyzed in detail. The energy eigenvalues and eigenvectors for the parabose–parafermi oscillator are then obtained explicitly. The latter confirms the validity of the results obtained for general supersymmetric paraquantum mechanics.

AN AXIOMATIC DEFINITION OF FUZZY DIVERGENCE MEASURES

2008 ◽  
Vol 16 (01) ◽  
pp. 1-17 ◽  
Author(s):  
INÉS COUSO ◽  
SUSANA MONTES
Keyword(s):  
Real Number ◽  
Divergence Measure ◽  
Essential Information ◽  
Divergence Measures ◽  
Axiomatic Definition ◽  
One To One ◽  
Definition Of ◽  
Fuzzy Divergence ◽  
Fuzzy Subsets

The representation of the degree of difference between two fuzzy subsets by means of a real number has been proposed in previous papers, and it seems to be useful in some situations. However, the requirement of assigning a precise number may lead us to the loss of essential information about this difference. Thus, (crisp) divergence measures studied in previous papers may not distinguish whether the differences between two fuzzy subsets are in low or high membership degrees. In this paper we propose a way of measuring these differences by means of a fuzzy valued function which we will call fuzzy divergence measure. We formulate a list of natural axioms that these measures should satisfy. We derive additional properties from these axioms, some of them are related to the properties required to crisp divergence measures. We finish the paper by establishing a one-to-one correspondence between families of crisp and fuzzy divergence measures. This result provides us with a method to build a fuzzy divergence measure from a crisp valued one.

Fuzzy Adjacency between Image Objects

1997 ◽  
Vol 05 (06) ◽  
pp. 615-653 ◽  
Author(s):  
Isabelle Bloch ◽  
Henri Maître ◽  
Morteza Anvari
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Relation ◽  
Adjacency Relation ◽  
Image Objects ◽  
Model Based ◽  
Important Relationship ◽  
Definition Of ◽  
Fuzzy Subsets

The notion of adjacency has a strong interest for image processing and pattern recognition, since it denotes an important relationship between objects or regions in an image, widely used as a feature in model-based pattern recognition. A crisp definition of adjacency often leads to low robustness in the presence of noise, imprecision, or segmentation errors. We propose two approaches to cope with spatial imprecision in image processing applications, both based on the framework of fuzzy sets. These approaches lead to two completely different classes of definitions of a degree of adjacency. In the first approach, we introduce imprecision as a property of the adjacency relation, and consider adjacency between two (crisp) objects to be a matter of degree. We represent adjacency by a fuzzy relation whose value depends on the distance between the objects. In the second approach, we introduce imprecision (in particular spatial imprecision) as a property of the objects, and consider objects to be fuzzy subsets of the image space. We then represent adjacency by a relation between fuzzy sets. This approach is, in our opinion, more powerful and general. We propose several ways for extending adjacency to fuzzy sets, either by using α-cuts, or by using a formal translation of binary equations into fuzzy ones. Since set equations are more easily translated into fuzzy terms, we shall privilege set representations of adjacency, particularly in the framework of fuzzy mathematical morphology. Finally, we give some hints on how to compare degrees of adjacency, typically for applications in model-based pattern recognition.

Recognizable sets of graphs: equivalent definitions and closure properties

1994 ◽  
Vol 4 (1) ◽  
pp. 1-32 ◽  
Author(s):  
Bruno Courcelle
Keyword(s):  
Algebraic Structure ◽  
Algebraic Structures ◽  
Closure Properties ◽  
Definition Of ◽  
Standard Consequence

The notion of a recognizable set of words, trees or graphs is relative to an algebraic structure on the set of words, trees or graphs respectively. We establish that several algebraic structures yield the same notion of a recognizable set of graphs. This notion is equivalent to that of a fully cutset-regular set of graphs introduced by Fellows and Abrahamson. We also establish that the class of recognizable sets of graphs is closed under the operations considered in these various equivalent definitions. This fact is not a standard consequence of the definition of recognizability.

Sign in / Sign up

Export Citation Format

Share Document