scholarly journals Construction of Fuzzy Measures over Product Spaces

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1605 ◽  
Author(s):  
Fernando Reche ◽  
María Morales ◽  
Antonio Salmerón
Keyword(s):  
Product Space ◽  
Fuzzy Measure ◽  
Product Measure ◽  
Product Spaces ◽  
Joint Function ◽  
Single Product ◽  
Fuzzy Measures ◽  
Statistical Indices ◽  
Product Measures ◽  
Definition Of

In this paper, we study the problem of constructing a fuzzy measure over a product space when fuzzy measures over the marginal spaces are available. We propose a definition of independence of fuzzy measures and introduce different ways of constructing product measures, analyzing their properties. We derive bounds for the measure on the product space and show that it is possible to construct a single product measure when the marginal measures are capacities of order 2. We also study the combination of real functions over the marginal spaces in order to produce a joint function over the product space, compatible with the concept of marginalization, paving the way for the definition of statistical indices based on fuzzy measures.

scholarly journals Statistical Parameters Based on Fuzzy Measures

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2015
Author(s):  
Fernando Reche ◽  
María Morales ◽  
Antonio Salmerón
Keyword(s):  
Product Space ◽  
Fuzzy Measure ◽  
Joint Analysis ◽  
Product Spaces ◽  
Statistical Parameters ◽  
Fuzzy Measures ◽  
Reference Set

In this paper, we study the problem of defining statistical parameters when the uncertainty is expressed using a fuzzy measure. We extend the concept of monotone expectation in order to define a monotone variance and monotone moments. We also study parameters that allow the joint analysis of two functions defined over the same reference set. Finally, we propose some parameters over product spaces, considering the case in which a function over the product space is available and also the case in which such function is obtained by combining those in the marginal spaces.

Fuzzy Measures: A solution to deal with community detection problems for networks with additional information

2020 ◽  
Vol 39 (5) ◽  
pp. 6217-6230
Author(s):  
Inmaculada Gutiérrez ◽  
Daniel Gómez ◽  
Javier Castro ◽  
Rosa Espínola
Keyword(s):  
Community Detection ◽  
Weighted Graph ◽  
Fuzzy Relation ◽  
Fuzzy Measure ◽  
Fuzzy Measures ◽  
Additional Information ◽  
Fuzzy Graphs ◽  
Finite Set ◽  
Definition Of ◽  
Community Detection Problems

In this work we introduce the notion of the weighted graph associated with a fuzzy measure. Having a finite set of elements between which there exists an affinity fuzzy relation, we propose the definition of a group based on that affinity fuzzy relation between the individuals. Then, we propose an algorithm based on the Louvain’s method to deal with community detection problems with additional information independent of the graph. We also provide a particular method to solve community detection problems over extended fuzzy graphs. Finally, we test the performance of our proposal by means of some detailed computational tests calculated in several benchmark models.

scholarly journals Some Properties of Fuzzy Anti-Inner Product Spaces

2020 ◽  
pp. 3042-3047
Author(s):  
Radhi I. M. Ali ◽  
Esraa A. Hussein
Keyword(s):  
Linear Space ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Definition Of

In this paper, the definition of fuzzy anti-inner product in a linear space is introduced. Some results of fuzzy anti-inner product spaces are given, such as the relation between fuzzy inner product space and fuzzy anti-inner product. The notion of minimizing vector is introduced in fuzzy anti-inner product settings.

scholarly journals Fuzzy Inner Product Space: Literature Review and a New Approach

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 765
Author(s):  
Lorena Popa ◽  
Lavinia Sida
Keyword(s):  
Literature Review ◽  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Comprehensive Overview ◽  
New Approach ◽  
Inner Product Spaces ◽  
Product Function ◽  
Suitable Definition

The aim of this paper is to provide a suitable definition for the concept of fuzzy inner product space. In order to achieve this, we firstly focused on various approaches from the already-existent literature. Due to the emergence of various studies on fuzzy inner product spaces, it is necessary to make a comprehensive overview of the published papers on the aforementioned subject in order to facilitate subsequent research. Then we considered another approach to the notion of fuzzy inner product starting from P. Majundar and S.K. Samanta’s definition. In fact, we changed their definition and we proved some new properties of the fuzzy inner product function. We also proved that this fuzzy inner product generates a fuzzy norm of the type Nădăban-Dzitac. Finally, some challenges are given.

On the Fusion of Multiple Measure Based Belief Structures

2018 ◽  
Vol 26 (Suppl. 2) ◽  
pp. 63-88 ◽  
Author(s):  
Ronald R. Yager
Keyword(s):  
Fuzzy Measure ◽  
Uncertain Information ◽  
Fuzzy Measures ◽  
Belief Structures ◽  
Multiple Measure

We introduce the concept of a fuzzy measure and describe the process of combining fuzzy measures to form new measures. We discuss the role of fuzzy measures in modeling uncertain information and its use in modeling granular uncertain information with the aid of measure based belief structures. We turn to the problem of fusing multiple measure based belief structures. First we look at the case when the belief structures being fused have the same focal elements. Then we turn to case where the structures being fused have different focal elements. Finally we compare measure-based fusion with Dempster’s rule.

MEASURES OF LOCAL ENTROPIES FOR COMPOSITIVE FUZZY PARTITIONS

2011 ◽  
Vol 19 (04) ◽  
pp. 717-728 ◽  
Author(s):  
DORETTA VIVONA ◽  
MARIA DIVARI
Keyword(s):  
Functional Equations ◽  
Fuzzy Measure ◽  
System Of Functional Equations ◽  
Locality Property ◽  
Fuzzy Measures ◽  
Fuzzy Partitions

The aim of this paper is to characterize of the measures of entropies without probability or fuzzy measure for compositive fuzzy partitions, taking into account the so-called locality property. We propose a system of functional equations, whose solutions give some forms of entropies without probability or fuzzy measures.

A Brownian Agent Model for Analyzing Changes in a Nation's Product Space Structure

2015 ◽  
Vol 11 (1) ◽  
pp. 52-71
Author(s):  
Bin Jiang ◽  
Chao Yang ◽  
Takashi Yamada ◽  
Takao Terano
Keyword(s):  
Product Space ◽  
Initial Distribution ◽  
Space Structure ◽  
Product Spaces ◽  
Qualitative And Quantitative Analysis ◽  
Agent Model ◽  
Self Organized ◽  
Cooperative Production ◽  
Labor Resources ◽  
Agent Migration

This paper proposes a Brownian agent model for simulating and analyzing changes in a nation's product space structure. A measurement of proximity has been employed to quantify a relationship between two products and proved to be useful in product space analysis. This study employs such proximity measurement, and estimates a continued structure transformation of a nation's product space through feedback between agent movements and network evolutions. Labor resources of an enterprise or a firm are regarded as Brownian agents; they move through different product spaces for higher economic rewards. The simulation results show that trade areas were self-organized through Brownian agent migration and cooperative production with a random initial distribution. Furthermore, we have verified the applicability and efficiency of the model in analyzing changes in Chinese product space structure with empirical data. Main contributions of this paper are: 1) it provides a bottom-up model for analyzing changes of a nation's product space structure; and 2) it also provides both qualitative and quantitative analysis methods for a nation's product space structure.

scholarly journals On Bessel and Grüss inequalities for orthonormal families in inner product spaces

2004 ◽  
Vol 69 (2) ◽  
pp. 327-340 ◽  
Author(s):  
S. S. Dragomir
Keyword(s):  
Product Space ◽  
Inner Product Space ◽  
Inner Product ◽  
Product Spaces ◽  
Inner Product Spaces

A new reverse of Bessel's inequality for orthornormal families in real or complex inner product space is obtained. Applications for some Grüss type results are also provided.

Rigidity of entire graphs in weighted product spaces with nonnegative Bakry–Émery–Ricci tensor

2017 ◽  
Vol 17 (1) ◽  
Author(s):  
Henrique F. de Lima ◽  
Arlandson M. S. Oliveira ◽  
Márcio S. Santos
Keyword(s):  
Smooth Function ◽  
Mean Curvature ◽  
Ricci Tensor ◽  
Product Space ◽  
Product Spaces ◽  
Weighted Mean ◽  
Weighted Mean Curvature ◽  
Entire Graphs

AbstractWe study the rigidity of entire graphs defined over the fiber of a weighted product space whose Bakry–Émery–Ricci tensor is nonnegative. Supposing that the weighted mean curvature is constant and assuming appropriated constraints on the norm of the gradient of the smooth function

scholarly journals Characterizations of inner product spaces by means of norm one points

2005 ◽  
Vol 97 (1) ◽  
pp. 104
Author(s):  
José Mendoza ◽  
Tijani Pakhrou
Keyword(s):  
Convex Hull ◽  
Unit Sphere ◽  
Product Space ◽  
Normed Linear Space ◽  
Inner Product ◽  
Chebyshev Center ◽  
Product Spaces ◽  
Inner Product Spaces ◽  
Point Subset ◽  
Real Normed Linear Space

Let $X$ be a a real normed linear space of dimension at least three, with unit sphere $S_X$. In this paper we prove that $X$ is an inner product space if and only if every three point subset of $S_X$ has a Chebyshev center in its convex hull. We also give other characterizations expressed in terms of centers of three point subsets of $S_X$ only. We use in these characterizations Chebyshev centers as well as Fermat centers and $p$-centers.

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