Boolean Filters Research Articles

Some Types of Neutrosophic Filters in Basic Logic Algebras


 The purpose of this article is to study the neutrosophication of prime and Boolean filters in Basic Logic (BL) algebras. We establish the notions of the neutrosophic prime and Boolean filters of BL-algebras with suitable examples and examine a few of their properties. As a result, we can determine the necessary and sufficient conditions and extension properties of both the neutrosophic prime and Boolean filters of BL-algebras. In addition, by combining both filters we instigate the concept of the neutrosophic prime Boolean filter of BL-algebras with illustration. In the future, the above study can be extended to soft multiset. Moreover, these filters can be applied to various digital image processing techniques.

Integral prefilters and integral Eq-algebras

Abstract In this paper, the notion of some new classes of EQ-algebras which are called integral, O-local, and locally finite EQ-algebras are introduced, and relationships between locally finite EQ-algebras and maximal prefilters are described. Also, the notion of integral prefilters are introduced and several characteristics of them are presented. Moreover, relation among integral prefilters and some type of other prefilter such as positive implicative, maximal, prime, and fantastic prefilters in EQ-algebras are studied. Finally, Boolean prefilters in bounded lattice EQ-algebras are introduced, and it is proved that a filter of a prelinear involutive EQ-algebra L is a Boolean filter if and only if L/F is a Boolean algebra.

An investigation of Boolean filter and Boolean pseudofilter over a residuated lattice in multiset and anti-multiset contexts

In this paper, the concepts of multiset Boolean filter, multiset Boolean pseudofilter, anti-multiset Boolean filter, and anti-multiset Boolean pseudofilter are introduced. Also, the relation between multiset Boolean filter(pseudofilter) and some other types of multiset filters(pseudofilters) are given.

Several types of hesitant fuzzy filters on residuated lattices

The present paper investigates the hesitant fuzzy filters on residuated lattices. A one-to-one correspondence between the set of all hesitant fuzzy filters and the set of all hesitant fuzzy congruences is established and a quotient residuated lattice with respect to a hesitant fuzzy filter is induced. Furthermore, several special types of hesitant fuzzy filters such as hesitant fuzzy implicative, regular and Boolean filters are introduced, and some alternative definitions of them are obtained, then some typical logical algebras are characterized by these identity forms.

DatView: a graphical user interface for visualizing and querying large data sets in serial femtosecond crystallography.

DatView is a new graphical user interface (GUI) for plotting parameters to explore correlations, identify outliers and export subsets of data. It was designed to simplify and expedite analysis of very large unmerged serial femtosecond crystallography (SFX) data sets composed of indexing results from hundreds of thousands of microcrystal diffraction patterns. However, DatView works with any tabulated data, offering its functionality to many applications outside serial crystallography. In DatView's user-friendly GUI, selections are drawn onto plots and synchronized across all other plots, so correlations between multiple parameters in large multi-parameter data sets can be rapidly identified. It also includes an item viewer for displaying images in the current selection alongside the associated metadata. For serial crystallography data processed by indexamajig from CrystFEL [White, Kirian, Martin, Aquila, Nass, Barty & Chapman (2012 ▸). J. Appl. Cryst. 45, 335-341], DatView generates a table of parameters and metadata from stream files and, optionally, the associated HDF5 files. By combining the functionality of several commonly needed tools for SFX in a single GUI that operates on tabulated data, the time needed to load and calculate statistics from large data sets is reduced. This paper describes how DatView facilitates (i) efficient feedback during data collection by examining trends in time, sample position or any parameter, (ii) determination of optimal indexing and integration parameters via the comparison mode, (iii) identification of systematic errors in unmerged SFX data sets, and (iv) sorting and highly flexible data filtering (plot selections, Boolean filters and more), including direct export of subset CrystFEL stream files for further processing.

Geological assessment for tunnel excavation under river with shallow overburden using surface site investigation data and electrical resistivity tomography

Tunnelling is a challenging task as many geotechnical uncertainties involved during construction, especially under a river crossing with shallow overburden. This study focussed on geological assessment for the New Austrian Tunneling Method excavation that crosses under Kerau River with shallow overburden. 3D filtered tunnel models using Boolean filter for rock mass weathering grade, rock quality designation, and Lugeon value are developed. Results predict that 53.3% of the tunnel excavation under the Kerau River crossing are highly weathered rocks (Grades III and IV), and 64.51% are in the moderately to highly fractured zone (0%–75% RQD) along the roof of the tunnel granitic bedrock. The Lugeon value models show that 71.64% of the excavating rocks possess a Lugeon value of 5–50 (6–60 × 10−5 cm/s), which denotes considerably high permeability. 2D electrical resistivity tomography is used to verify the permeability results from the Lugeon test.

Involutive filters of pseudo-hoops

In this paper, we introduce the notion of involutive filters of pseudo-hoops, and we emphasize their role in the probability theory on these structures. Characterizations of involutive pseudo-hoops are given, and their properties are investigated. We give a characterization of involutive filters of a good pseudo-hoop, and we prove that in the case of good pseudo-hoops, the sets of fantastic and involutive filters are equal. One of the main results consists of proving that a normal filter F of a bounded pseudo-hoop A is involutive if and only if A / F is an involutive pseudo-hoop. It is also proved that any implicative filter of a bounded pseudo-hoop is involutive and that any Boolean filter of a bounded Wajsberg pseudo-hoop is involutive. The notions of state operators and state-morphism operators on pseudo-hoops are introduced, and the relationship between these operators is investigated. For a bounded Wajsberg pseudo-hoop, we prove that the kernel of any state operator is an involutive filter.

On weak implication algebra

In this paper, we introduce the notion of implication filter as a generalization of Boolean filter of first kind in Hilbert algebra and study it in detail. Also, we prove that F is an implication filter of a Hilbert algebra H if and only if every implicative filter of quotient algebra H / F is an implication filter. Finally, we generalized Boolean algebra and introduced a weak implication algebra, we prove that F is an implication filter of a Hilbert algebra H if and only if the quotient algebra H / F is a weak implication algebra. By suitable diagrams, we summarize the results of this paper and the previous results in these fields.

N-Fold Heyting, Boolean and pseudo-MV filters in residuated lattices

This paper is devoted to introduce the notions of n-fold left-(right-)Heyting, n-fold left-(right-)Boolean and n-fold left-(right-)MV filters in residuated lattices and to investigate their properties. Several characterizations of these notions are derived. The relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)Heyting filters are investigated and we prove that an n-fold left-(right-)Boolean filter is an n-fold left-(right-)Heyting filter, respectively, and this implication is strict. Also, the relations between n-fold left-(right-)Boolean filters and n-fold left-(right-)MV filters are investigated and we show that a normal n-fold left-(right-)Boolean filter is a normal n-fold left-(right-)MV filter and each n-fold left-(right-)Heyting and n-fold left-(right-)MV filter is an n-fold left-(right-)Boolean filter.

Rough approximations in non-commutative residuated lattices

Based on Pawlak’s rough set theory, we study and investigate the roughness in non-commutative residuated lattices, which are generalizations of non-commutative fuzzy structures such as MV-algebras and BL-algebras. We give many theorems and examples to describe the rough approximations. Also, to investigate the properties of roughness of subsets (and of course filters) more closely, we consider some different kinds of filters such as Boolean filters and prime filters. Especially, we prove that with respect to some certain filters, the obtained approximations form a Boolean algebra or a pseudo MTL-algebra.

Some results in local Hilbert algebras

Abstract In this paper, we study local Hilbert algebras and give some theorems that characterize local Hilbert algebras. Also, we prove that, (i) H is a local Hilbert algebra if and only if the set of all dense elements of H is H ∖ {0}. (ii) H is a local Hilbert algebra if and only if the set of all regular elements of H is a local Boolean algebra. In a local Hilbert algebra H with supremum, we prove that: (i) If F is a Boolean filter of H, then F is a prime filter. (ii) F is a Boolean filter iff F is a maximal filter iff F = H ∖ {0}.

N-Fold integral ideals and n-fold Boolean ideals in BL-algebras

In this paper, we introduce the concepts of n-fold integral ideals and n-fold Boolean ideals in BL-algebras. With respect to concepts, we give some related results. In particular, we prove that an ideal is an n-fold integral ideal if and only if is an n-fold Boolean and (prime)maximal ideal. Also, we prove that a BL-algebra is an n-fold integral BL-algebra if and only if trivial ideal $$\{0\}$$ is an n-fold integral ideal. Moreover, we study relation between n-fold integral ideals and n-fold obstinate filters in BL-algebras by using the set of complement elements. Also, we describe relationship between n-fold Boolean ideals and n-fold positive implicative filters in BL-algebras.

On open problems based on fuzzy filters of pseudo BCK-algebras

We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the notion of implicative pseudo-filter equivalent to the notion of Boolean filter? and Prove or negate the following conclusion: A pseudo-BCK algebra is an implicative pseudo-BCK algebra if and only if every pseudo-filter of it is a Boolean filter(or an implicative pseudo-filter) are partly solved.

Facilitating the iterative design of informatics tools to advance the science of autism.

This paper describes a usability evaluation study of an innovative first generation system (Data Dig) designed to retrieve phenotypic data from the large SFARI data set of 2700 families each of which has one child affected with autism spectrum disorder. The usability methods included a cognitive walkthrough and usability testing. Although the subjects were able to learn to use the system, more than 50 usability problems of varying severity were noted. The problems with the greatest frequency resulted from users being unable to understand meanings of variables, filter categories correctly, use the Boolean filter, and correctly interpret the feedback provided by the system. Subjects had difficulty forming a mental model of the organizational system underlying the database. This precluded them from making informed navigation choices while formulating queries. Clinical research informatics is a new and immensely promising discipline. However in its nascent stage, it lacks a stable interaction paradigm to support a range of users on pertinent tasks. This presents great opportunity for researchers to further this science by harnessing the powers of user-centered iterative design.

Boolean filters in pseudo-complemented almost distributive lattices

Boolean filters in pseudo-complemented almost distributive lattices

Vague Filters of Residuated Lattices

Notions of vague filters, subpositive implicative vague filters, and Boolean vague filters of a residuated lattice are introduced and some related properties are investigated. The characterizations of (subpositive implicative, Boolean) vague filters is obtained. We prove that the set of all vague filters of a residuated lattice forms a complete lattice and we find its distributive sublattices. The relation among subpositive implicative vague filters and Boolean vague filters are obtained and it is proved that subpositive implicative vague filters are equivalent to Boolean vague filters.

¿DÓNDE Y CÓMO BUSCAR EVIDENCIA CIENTÍFICA EN MEDICINA?

Where and how to search scientific medical evidence? The practice of evidence based medicine requires strategies to efficiently search relevant medical infor mation. This paper provides tools to optimize literature searches and access the best papers available. There are several electronic databases that can be consulted such as MEDLINE, LILACS, Web of Knowledge, The Cochrane Library, TRIP database, EMBASE and Google Scholar. Prior to the search, a research question must be formulated, structured according to the mnemonic rule PICO (Patient, Intervention, Comparator and Outcome). The question must be adapted to the language of the search engine with the help of Boolean operators, MeSH terms, keywords and methodological filters such as type of study, type of population, clinical category and sensitivity. These techniques will allow the performance of an efficient literature search in a shorter lapse.

A new approach for classification of filters in residuated lattices

In the mathematical literature, many types of filters in residuated lattices or in special classes of residuated lattices (BL-algebras, MTL-algebras, etc.) have been studied. Consequently many names have been proposed for these types of filters: Boolean filters, Heyting filters, implicative filters, positive implicative filters, fantastic filters, easy filters, etc. This multiplicity of names for the filters makes it very difficult to study them and the connections between them. To avoid this inconvenience, in this paper we propose a new approach for the study of these filters in residuated lattices, in order to be easily accessible to the readers. We also present a unified treatment of some particular results about filters in residuated lattices (Theorem 16, Corollary 17).

Fuzzy Weak Regular, Strong and Preassociative Filters in Residuated Lattices

In this paper, the notions of fuzzy weak regular, strong and preassociative filters are introduced with some properties of them investigated. In particular, under the context of Glivenko algebras, fuzzy weak regular filters and regular ones are equivalent and characterizations of Glivenko algebras are concluded by characterizations of fuzzy strong filters. At last the notion of fuzzy preassociative filters are defined, which are proved to coincide with fuzzy Boolean filters, and then some new alternative definitions of Boolean algebras are obtained by this type of filters.

A new filter in BL-algebras

In this paper we introduce the notion of obstinate filter in BL-algebra A and we state and prove some theorems which determine the relationship between this notion and other types of filters of a BL-algebra and by some examples we show that this notion is different. Also, we prove that if F is an obstinate filter, then F is a Boolean filter hence A/F is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and filters in finite BL-algebras.