Credibility Space Research Articles

Exploring strongly almost λ-convergence of fuzzy variable sequences via Orlicz functions in credibility space

Exploring strongly almost λ-convergence of fuzzy variable sequences via Orlicz functions in credibility space

Some Results on Statistically Pre-Cauchy Sequences of Fuzzy Variables Defined by Orlicz Functions in Credibility Space

This study introduces the concept of statistically pre-Cauchy sequences of fuzzy variables in five directions of credibility theory: almost surely, in measure, in mean, in distribution, and uniformly almost surely. However, the main focus is kept on statistically pre-Cauchy sequences in measure, in mean, and in distribution. Furthermore, a correlation between statistically pre-Cauchy sequences and statistically convergent sequences is established using fuzzy variables. Additionally, the exploration of statistically pre-Cauchy sequences of fuzzy variables is initiated through the application of Orlicz functions. The objective is to enhance the understanding of the statistical behavior and convergence properties of fuzzy variables in various credibility scenarios.

Characterization of lacunary ℐ-convergent sequences in credibility space

Abstract This research paper aims to introduce the concept of lacunary ideal Cauchy sequences of fuzzy variables in a credibility space. We establish the interrelationships between this notion with lacunary ideal convergent sequences in the same structure from several aspects of credibility. Furthermore, we explore the concepts of strongly lacunary Cauchy, strongly ℐ {\mathcal{I}} -lacunary Cauchy, and strongly ℐ ∗ {\mathcal{I}^{\ast}} -lacunary Cauchy sequences of fuzzy variables within the context of credibility. We also examine the interconnections between these concepts and analyze their relationships.

Certain aspects of deferred statistical convergence of fuzzy variables in credibility space

Certain aspects of deferred statistical convergence of fuzzy variables in credibility space

Some results on lacunary statistical convergence of order $$\alpha$$ in credibility space

Some results on lacunary statistical convergence of order $$\alpha$$ in credibility space

Conflict, epidemic and faith communities: church-state relations during the fight against Covid-19 in north-eastern DR Congo

BackgroundUnderstanding and improving access to essential services in (post)-conflict settings requires paying particular attention to the actors who occupy the space left ‘empty’ by weak or deficient State institutions. Religious institutions often play a fundamental role among these actors and typically benefit from high trust capital, a rare resource in so-called ‘fragile’ states. While there is a literature looking at the role faith organisations play to mobilise and sensitise communities during emergencies, our focus is on a different dimension: the reconfiguration of the relationship between religion and health authorities impelled by health crises.MethodsWe analyse observations, interviews, and focus group discussions with 21 leaders from eight different religious groups in Ituri province in 2020–2021.ResultsFaith institutions handled the Covid-19 lockdown period by using and redeploying structures at the grassroots level but also by responding to health authorities’ call for support. New actors usually not associated with the health system, such as revivalist churches, became involved. The interviewed religious leaders, especially those whose congregations were not previously involved in healthcare provision, felt that they were doing a favour to the State and the health authorities by engaging in community-level awareness-raising, but also, crucially, by ‘depoliticising’ Covid-19 through their public commitment against Covid-19 and work with the authorities in a context where the public response to epidemics has been highly contentious in recent years (particularly during the Ebola outbreak). The closure of places of worship during the lockdown shocked all faith leaders but, ultimately, most were inclined to follow and support health authorities. Such experience was, however, often one of frustration and of feeling unheard.ConclusionIn the short run, depoliticization may help address health emergencies, but in the longer run and in the absence of a credible space for discussion, it may affect the constructive criticism of health system responses and health system strengthening. The faith leaders are putting forward the desire for a relationship that is not just subordination of the religious to the imperatives of health care but a dialogue that allows the experiences of the faithful in conflict zones to be brought to the fore.

Existence Results of Fuzzy Delay Impulsive Fractional Differential Equation by Fixed Point Theory Approach

The main aim of this article is to study controllability and existence of solution of fuzzy delay impulsive fractional nonlocal integro-differential equation in the sense of Caputo operator. The existence and uniqueness of the solution have been carried out with the help of the Banach fixed point theorem. Moreover, for fuzzy fractional differential equations (FFDEs) driven by the Liu process, this present work introduced a concept of stability in credibility space. Finally, efficient examples are presented to demonstrate the main theoretical findings.

On Statistical Convergence in Credibility Space

In this paper, we present the notions of statistically convergent sequence for fuzzy variables, statistically Cauchy sequence in credibility space, and present a kind of statistical completeness for credibility space. Furthermore, the conditions of statistical convergence almost surely (a.s.), statistical convergence in credibility, statistical convergence in mean, statistical convergence in distribution and statistical convergence uniformly almost surely (u.a.s.) of fuzzy variable sequences are examined. We have proved relations between these notions.

Controllability for Fuzzy Fractional Evolution Equations in Credibility Space

This article addresses exact controllability for Caputo fuzzy fractional evolution equations in the credibility space from the perspective of the Liu process. The class or problems considered here are Caputo fuzzy differential equations with Caputo derivatives of order β∈(1,2), 0CDtβu(t,ζ)=Au(t,ζ)+f(t,u(t,ζ))dCt+Bx(t)Cx(t)dt with initial conditions u(0)=u0,u′(0)=u1, where u(t,ζ) takes values from U(⊂EN),V(⊂EN) is the other bounded space, and EN represents the set of all upper semi-continuously convex fuzzy numbers on R. In addition, several numerical solutions have been provided to verify the correctness and effectiveness of the main result. Finally, an example is given, which expresses the fuzzy fractional differential equations.

The Scalar Mean Chance and Expected Value of Regular Bifuzzy Variables

As a natural extension of the fuzzy variable, a bifuzzy variable is defined as a mapping from a credibility space to the collection of fuzzy variables, which is an appropriate tool to model the two-fold fuzzy phenomena. In order to enrich its theoretical foundation, this paper explores some important measures for regular bifuzzy variables, the most commonly used type of bifuzzy variables. Firstly, we introduce the regular bifuzzy variables’ mean chance measure and some properties, including self-duality and its calculation formulas. Furthermore, we also investigate the mean chance distribution for strictly monotone functions of regular bifuzzy variables based on the proposed operational law. Finally, we present the expected value operator as well as equivalent analytical formulas of the expected value of regular bifuzzy variables and their strictly monotone functions.

Surrounded by science: The Researchers' Gallery at Malmö University Library

The Researchers' Gallery at Malmö University Library shows current research in exhibitions, co-created by librarians and researchers. The library invites all visitors to take part in and learn more about the research process and outcome. In an academic yet informal setting, the library offers a credible space for research communication. The Researchers' Gallery is a space for students, researchers and the society to meet, and encourage cross-border knowledge creation. The Researchers’ Gallery has become a platform for continuing collaboration between researchers and between researchers and librarians. Exhibited research now has a natural and an integrated place in the learning environment of the library and at the university.

Una recreación inédita y desconocida del <em>Quijote: El último Quijote</em> (1902) de Jesús de Amber y José Montero

Estudiamos y editamos en este trabajo una recreación teatral desconocida e inédita de Don Quijote: El último Quijote (1902), sainete lírico de Jesús de Amber y José Montero Iglesias, periodistas afincados en Santander en el comienzo del siglo XX. Se trata de una de las primeras parodias de la novela cervantina en la centuria pasada, escrita en momento de especial intensidad a este respecto, tiempo propicio para aquellas y de consolidación del mito quijotesco. La obra que nos ocupa añade, en tanto que recreación, la novedad de situar la acción en un tiempo contemporáneo (aunque nunca concretado de forma explícita), en un espacio inventado pero verosímil, y de acudir a los registros y procedimientos del Género chico para desarrollar la parodia del personaje y libro cervantino.

Pan-integral on credibility space and its properties

Pan-integral on credibility space and its properties

A new bi-matrix game model with fuzzy payoffs in credibility space

Uncertain theory based on expert's evaluation and non-additive measure is introduced to explore the bi-matrix game with the uncertain payoffs. The uncertainty space based on the axiom of the uncertain measures is presented. Some basic characteristics of uncertain events are described and the expected value of the uncertain variables is given in uncertainty space. A new model of bi-matrix game with uncertain payoffs is established and its equivalent strategy is given. Then, we develop an expected model of uncertain bi-matrix games and define the uncertain equilibrium strategy of uncertain bi-matrix games. By using the expected value of uncertain variable, we transform the model into a linear programming, the expected equilibrium strategy of the uncertain bi-matrix games is identified through solving linear equations.

The application of heliospheric imaging to space weather operations: Lessons learned from published studies

AbstractThe field of heliospheric imaging has matured significantly over the last 10 years—corresponding, in particular, to the launch of NASA's STEREO mission and the successful operation of the heliospheric imager (HI) instruments thereon. In parallel, this decade has borne witness to a marked increase in concern over the potentially damaging effects of space weather on space and ground‐based technological assets, and the corresponding potential threat to human health, such that it is now under serious consideration at governmental level in many countries worldwide. Hence, in a political climate that recognizes the pressing need for enhanced operational space weather monitoring capabilities most appropriately stationed, it is widely accepted, at the Lagrangian L1 and L5 points, it is timely to assess the value of heliospheric imaging observations in the context of space weather operations. To this end, we review a cross section of the scientific analyses that have exploited heliospheric imagery—particularly from STEREO/HI—and discuss their relevance to operational predictions of, in particular, coronal mass ejection (CME) arrival at Earth and elsewhere. We believe that the potential benefit of heliospheric images to the provision of accurate CME arrival predictions on an operational basis, although as yet not fully realized, is significant and we assert that heliospheric imagery is central to any credible space weather mission, particularly one located at a vantage point off the Sun‐Earth line.

Intuitionistic fuzzy variables: Concepts and applications in decision making

The present paper aims at advancing the well-recognized uncertainty theory built upon the credibility measure. In face of the increasing level of uncertainty embedded within the real world problem solving, it is discovered that the fuzzy variables defined in the credibility space are far from adequate to reflect the hesitance incurred during decision making. Although more complex fuzzy quantities are introduced, such as the fuzzy possibility space based type-2 fuzzy variables, the area of intuitionistic fuzzy variables is still a largely unexplored territory. Therefore, a novel concept of intuitionistic fuzzy variable is introduced hereby as an attempt to extend the uncertainty theory, which possesses a decent self-dual property compared with the fuzzy set theory. Unlike the intuitionistic fuzzy set theory, which has been widely implemented in various application fields, the intuitionistic fuzzy variables have hardly been employed in practices, especially the decision making sector. To bridge the gap, three outranking methods are developed to help evaluate intuitionistic fuzzy variables. The sufficient conditions of the three methods in distinguishing different fuzzy variables are also proved in the present work. The benefits of ranking with the three methods include the minimum amount of defuzzification, which prevents the information loss to a significant extent. Furthermore, in order to validate the proposed methods, a numerical study is performed. And the consistency of the ranking outputs from the three proposed methods is analyzed afterward. Besides, several managerial insights are presented regarding the sensitivity analysis of each ranking method.

Exact Controllability for Fuzzy Differential Equations in Credibility Space

With reasonable control selections on the space of functions, various application models can take the shape of a well-defined control system on mathematics. In the credibility space, controlability management of fuzzy differential equation is as much important issue as stability. This paper addresses exact controllability for abstract fuzzy differential equations in the credibility space in the perspective of Liu process. This is an extension of the controllability results of Park et al. (Controllability for the semilinear fuzzy integro-differential equations with nonlocal conditions) to fuzzy differential equations driven by Liu process.

A new support vector machine based on type-2 fuzzy samples

Classical support vector machine is based on the real valued random samples and established on the probability space. It is hard to deal with classification problems based on type-2 fuzzy samples established on non-probability space. The existing algorithm, type-2 fuzzy support vector machine established on generalized credibility space, transforms the classification problems based on type-2 fuzzy samples to general fuzzy optimization problems and expands the application range of traditional support vector machine. However, nonnegativeness of the decision variables of general fuzzy optimization problems is too strict to be satisfied in some practical applications. Motivated by this, the concept of expected fuzzy possibility measure is proposed. Then type-2 fuzzy support vector machine on expected fuzzy possibility space is established, and the second-order cone programming of type-2 fuzzy support vector machine on expected fuzzy possibility space is given. The results of numerical experiments show the effectiveness of the type-2 fuzzy support vector machine established on expected fuzzy possibility space.

A new method for mining area ecological environment assessment based on credibility measure

PurposeThe purpose of this paper is to present a more objective evaluation method for a mining area ecological environment. It proposes the weight of indices with respect to the total goal, and provides a new evaluation method which generalizes the weighted‐average method.Design/methodology/approachFirst, the authors describe the evaluation grades by fuzzy variables in credibility space, and the degree of an index belonging to a grade is transformed to be the credibility measure of a fuzzy event by the credibility inversion theorem. Second, a new algorithm which generalizes the weighted‐average method is proposed to realize the transformation from the credibility degree of the underlying indices to the credibility degree of the total target.FindingsThe method proposed in this paper can obtain the correct results illustrated with a numerical evaluation example. The comparison with two other methods shows that the proposed method has stronger classification ability.Originality/valueThe new method presented in this paper generalizes the weighted‐average method, and provides methods for other evaluation systems with a hierarchical structure.

Support Vector Machine Based on Type-2 Fuzzy Training Samples

In order to deal with the classification problems of type-2 fuzzy training samples on generalized credibility space. Firstly the type-2 fuzzy training samples are reduced to ordinary fuzzy samples by the mean reduction method. Secondly the definition of strong fuzzy linear separable data for type-2 fuzzy samples on generalized credibility space is introduced. Further, by utilizing fuzzy chance-constrained programming and classic support vector machine, a support vector machine based on type-2 fuzzy training samples and established on generalized credibility space is given. An example shows the efficiency of the support vector machine.