(Fuzzy) Ideals of BN-Algebras.
Ontology highlight
ABSTRACT:
SUBMITTER: Dymek G
PROVIDER: S-EPMC4466498 | biostudies-other | 2015
REPOSITORIES: biostudies-other
Similar Datasets
Project description:In this paper we investigate further properties of fuzzy ideals of a BL-algebra. The notions of fuzzy prime ideals, fuzzy irreducible ideals, and fuzzy Gödel ideals of a BL-algebra are introduced and their several properties are investigated. We give a procedure to generate a fuzzy ideal by a fuzzy set. We prove that every fuzzy irreducible ideal is a fuzzy prime ideal but a fuzzy prime ideal may not be a fuzzy irreducible ideal and prove that a fuzzy prime ideal ω is a fuzzy irreducible ideal if and only if ω(0) = 1 and |Im(ω)| = 2. We give the Krull-Stone representation theorem of fuzzy ideals in BL-algebras. Furthermore, we prove that the lattice of all fuzzy ideals of a BL-algebra is a complete distributive lattice. Finally, it is proved that every fuzzy Boolean ideal is a fuzzy Gödel ideal, but the converse implication is not true.
| S-EPMC4032761 | biostudies-other
Project description:As a link between classical soft sets and hesitant fuzzy sets, the notion of hesitant fuzzy soft sets is introduced and applied to a decision making problem in the papers by Babitha and John (2013) and Wang et al. (2014). The aim of this paper is to apply hesitant fuzzy soft set for dealing with several kinds of theories in BCK/BCI-algebras. The notions of hesitant fuzzy soft subalgebras and (closed) hesitant fuzzy soft ideals are introduced, and related properties are investigated. Relations between a hesitant fuzzy soft subalgebra and a (closed) hesitant fuzzy soft ideal are discussed. Conditions for a hesitant fuzzy soft set to be a hesitant fuzzy soft subalgebra are given, and conditions for a hesitant fuzzy soft subalgebra to be a hesitant fuzzy soft ideal are provided. Characterizations of a (closed) hesitant fuzzy soft ideal are considered.
| S-EPMC4212623 | biostudies-other
Project description:The aim of this paper is to introduce the concepts of fuzzy strong h-ideals and fuzzy congruences of hemirings. The quotient hemirings via fuzzy strong h-ideals are investigated. The relationships between fuzzy congruences and fuzzy strong h-ideals of hemirings are discussed. Pay attention to an open question on fuzzy congruences. Finally, the normal fuzzy strong h-ideals of hemirings are explored.
| S-EPMC4127294 | biostudies-other
Project description:Some new properties of fuzzy associative filters (also known as fuzzy associative pseudo-filters), fuzzy p-filter (also known as fuzzy pseudo-p-filters), and fuzzy a-filter (also known as fuzzy pseudo-a-filters) in pseudo-BCI algebras are investigated. By these properties, the following important results are proved: (1) a fuzzy filter (also known as fuzzy pseudo-filters) of a pseudo-BCI algebra is a fuzzy associative filter if and only if it is a fuzzy a-filter; (2) a filter (also known as pseudo-filter) of a pseudo-BCI algebra is associative if and only if it is an a-filter (also call it pseudo-a filter); (3) a fuzzy filter of a pseudo-BCI algebra is fuzzy a-filter if and only if it is both a fuzzy p-filter and a fuzzy q-filter.
| S-EPMC4000979 | biostudies-other
Project description:We study several degrees in defining a fuzzy positive implicative filter, which is a generalization of a fuzzy filter in BE-algebras.
| S-EPMC4058197 | biostudies-other
Project description:Research on young-adult sexuality in sub-Saharan Africa typically conceptualizes sex as an individual-level risk behavior. We introduce a new approach that connects the conditions surrounding the initiation of sex with subsequent relationship well-being, examines relationships as sequences of interdependent events, and indexes relationship experiences to individually held ideals. New card-sort data from southern Malawi capture young women's relationship experiences and their ideals in a sequential framework. Using optimal matching, we measure the distance between ideal and experienced relationship sequences to (1) assess the associations between ideological congruence and perceived relationship well-being, (2) compare this ideal-based approach to other experience-based alternatives, and (3) identify individual- and couple-level correlates of congruence between ideals and experiences in the romantic realm. We show that congruence between ideals and experiences conveys relationship well-being along four dimensions: expressions of love and support, robust communication habits, perceived biological safety, and perceived relationship stability. We further show that congruence is patterned by socioeconomic status and supported by shared ideals within romantic dyads. We argue that conceiving of ideals as anchors for how sexual experiences are manifest advances current understandings of romantic relationships, and we suggest that this approach has applications for other domains of life.
| S-EPMC4838189 | biostudies-literature
Project description:Taking stock of individuals' perceived family ideals is particularly important in the current moment given unprecedented fertility declines and the diversification of households in advanced industrial societies. Study participants in urban China, Japan, South Korea, Singapore, the United States, Italy, Spain, and Norway were asked to evaluate vignettes describing families whose characteristics vary on ten dimensions. In contrast to previous studies that focused on a single dimension, such as fertility ideals or gender roles, this holistic vignette approach identifies the relative importance of each dimension. Multilevel regression analysis reveals both expected and unexpected findings. Parenthood remains a positive ideal, but the number of children does not matter once other family dimensions are considered, a potentially important finding in light of conventional wisdom regarding the two-children ideal. When evaluating families with at least one child, respondents tend to positively evaluate more traditional arrangements, including valuing marriage relative to cohabitation and, particularly, divorce. Also, in addition to financial resources, good communication between immediate and extended family members, as well as maintaining respect in the larger community, are highly salient attributes of an ideal family. Notwithstanding some important cross-national differences, egalitarian gender roles and avoiding work-family conflict are also valued positively. Overall, even as the study reveals some notable variations between societies, respondents across countries identify similar components of an ideal family.
| S-EPMC10861923 | biostudies-literature
Project description:Human cognitive capacity includes recursively definable concepts, which are prevalent in domains involving lists, numbers, and languages. Cognitive science currently lacks a satisfactory explanation for the systematic nature of such capacities (i.e., why the capacity for some recursive cognitive abilities-e.g., finding the smallest number in a list-implies the capacity for certain others-finding the largest number, given knowledge of number order). The category-theoretic constructs of initial F-algebra, catamorphism, and their duals, final coalgebra and anamorphism provide a formal, systematic treatment of recursion in computer science. Here, we use this formalism to explain the systematicity of recursive cognitive capacities without ad hoc assumptions (i.e., to the same explanatory standard used in our account of systematicity for non-recursive capacities). The presence of an initial algebra/final coalgebra explains systematicity because all recursive cognitive capacities, in the domain of interest, factor through (are composed of) the same component process. Moreover, this factorization is unique, hence no further (ad hoc) assumptions are required to establish the intrinsic connection between members of a group of systematically-related capacities. This formulation also provides a new perspective on the relationship between recursive cognitive capacities. In particular, the link between number and language does not depend on recursion, as such, but on the underlying functor on which the group of recursive capacities is based. Thus, many species (and infants) can employ recursive processes without having a full-blown capacity for number and language.
| S-EPMC3325926 | biostudies-literature
Project description:Interpretability is the dominant feature of a fuzzy model in security-oriented fields. Traditionally fuzzy models based on expert knowledge have obtained well interpretation innately but imprecisely. Numerical data based fuzzy models perform well in precision but not necessarily in interpretation. To utilize the expert knowledge and numerical data in a fuzzy model synchronously, this paper proposed a hybrid fuzzy c-means (FCM) clustering algorithm and Fuzzy Network (FN) method-based model for prediction. The Mamdani rule-based structure of the proposed model is identified based on FCM algorithm from data and by expert-system method from expert knowledge, both of which are combined by FN method. Particle swarm optimization (PSO) algorithm is utilized to optimize the fuzzy set parameters. We tested the proposed model on 6 real datasets comparing the results with the ones obtained by using FCM algorithm. The results showed that our model performed best in interpretability, transparency, and accuracy.
| S-EPMC9523042 | biostudies-literature
Project description:Transition metal catalyzed coupling reaction strategy has been utilized in the synthesis of two novel BN-perylenes starting from halogenated BN-naphthalene derivatives. The molecular structures and packing modes of BN-perylenes were confirmed by NMR spectroscopy and X-ray single-crystal diffraction experiments. Their photophysical properties were further investigated using UV-vis and fluorescence spectroscopy and DFT calculations. Interestingly, the isosteric BN-insertion in perylene system resulted in stronger π-π stacking interaction both in solid and solution phases. The synthesized BN-perylenes are proved to be highly stable and thus provide a new valuable platform for novel organic materials applications which is otherwise inaccessible to date.
| S-EPMC8658878 | biostudies-literature