In this paper, missing attribute values in incomplete data sets have three possible interpretations: lost values, attribute-concept values and ‘do not care’ conditions. For rule induction, we use characteristic sets and generalized maximal consistent blocks. Therefore, we apply six different approaches for data mining. As follows from our previous experiments, where we used an error rate evaluated by ten-fold cross validation as the main criterion of quality, no approach is universally the best. Thus, we decided to compare our six approaches (...) using complexity of rule sets induced from incomplete data sets. We show that the smallest rule sets are induced from incomplete data sets with attribute-concept values, while the most complicated rule sets are induced from data sets with lost values. The choice between interpretations of missing attribute values is more important than the choice between characteristic sets and generalized maximal consistent blocks. (shrink)

Descriptive set theory and computability theory are closely-related fields of logic; both are oriented around a notion of descriptive complexity. However, the two fields typically consider objects of very different sizes; computability theory is principally concerned with subsets of the naturals, while descriptive set theory is interested primarily in subsets of the reals. In this paper, we apply a generalization of computability theory, admissible recursion theory, to consider the relative complexity of notions that are of interest in descriptive (...) set theory. In particular, we examine the perfect set property, determinacy, the Baire property, and Lebesgue measurability. We demonstrate that there is a separation of descriptive complexity between the perfect set property and determinacy for analytic sets of reals; we also show that the Baire property and Lebesgue measurability are both equivalent in complexity to the property of simply being a Borel set, for $\boldsymbol {\Sigma ^{1}_{2}}$ sets of reals. (shrink)

We consider the possible complexity of the set of reals belonging to an inner model M of set theory. We show that if this set is analytic then either 1M is countable or else all reals are in M. We also show that if an inner model contains a superperfect set of reals as a subset then it contains all reals. On the other hand, it is possible to have an inner model M whose reals are an uncountable Fσ (...) set and which does not have all reals. A similar construction shows that there can be an inner model M which computes correctly 1, contains a perfect set of reals as a subset and yet not all reals are in M. These results were motivated by questions of H. Friedman and K. Prikry. (shrink)

As a generation of fuzzy set, the notion of complex fuzzy set which is an innovative concept is introduced by Ramot, Milo, Friedman and Kandel. The purpose of this article is to apply complex fuzzy set to BCK/BCI-algebras. The notions of a complex subalgebra and a complex left reduced ideal in a BCK/BCI- algebra are introduced, and related properties are investigated. Characterizations of a complex subalgebra are provided, and the homomorphic image of a complex subalgebra and a complex left reduced (...) ideal. (shrink)

This study explores the experiences of nurses that provide ‘complex’, generalist healthcare in hospital settings. Complex care is described as care for patients experiencing acute issues additional to multimorbidity, ageing or psychosocial complexity. Nurses are the largest professional group of frontline healthcare workers and patients experiencing chronic conditions are overrepresented in acute care settings. Research exploring nurses’ experiences of hospital‐based complex care is limited, however. This study aims to add to what is known currently. Four ‘complex care’ nurses undertook (...) in‐depth semistructured interviews and their narratives were analysed using the conceptual framework of complex adaptive phenomenology. Two overarching themes constituting the ‘essence’ of complex care nursing were identified: Contextual factors and attribute/value‐based elements. Creating meaningful patient outcomes and feeling part of a team were experienced as fulfilling, whereas time constraints, institutional settings and systemic barriers to comprehensive caregiving diminished the experience of providing complex care. Overall, work meaning presented as a dynamic phenomenon, shaped by personal and professional values, local settings and systemic factors. It is recommended that more expansive research be undertaken to explore the experience of complex care for nurses. Such knowledge can contribute to initiatives that draw a skilled, effective and engaged hospital‐based complex care nursing workforce. (shrink)

We introduce the set of definable restricted complex powers for expansions of the real field and calculate it explicitly for expansions of the real field itself by collections of restricted complex powers. We apply this computation to establish a classification theorem for expansions of the real field by families of locally closed trajectories of linear vector fields.

We prove two sets of results concerning computational complexity classes. First, we propose a new variation of the random oracle hypothesis, originally posed by Bennett and Gill after they showed that relative to a randomly chosen oracle, with probability 1. Their original hypothesis was quickly disproven in several ways, most famously in 1992 with the result that, in spite of the classes being shown unequal with probability 1. Here we propose a variation of what it means to be “large” (...) using the Ellentuck topology. In this new context, we demonstrate that the set of oracles separating and is not small, and obtain similar results for the separation of from along with the separation of from. We also show that the set of oracles equating with is large in this new sense. We demonstrate that this version of the hypothesis provides a sufficient condition for unrelativized relationships, at least in the cases considered here. Second, we examine the descriptive complexity of the classes of oracles providing the separations for these various classes, and determine their exact placement in the Borel hierarchy. (shrink)

The powerset operator, [MATHEMATICAL SCRIPT CAPITAL P], is compared with other operators of similar type and logical complexity. Namely we examine positive operators whose defining formula has a canonical form containing at most a string of universal quantifiers. We call them ∀-operators. The question we address in this paper is: How is the class of ∀-operators generated ? It is shown that every positive ∀-operator Γ such that Γ ≠ ∅, is finitely generated from [MATHEMATICAL SCRIPT CAPITAL P], the (...) identity operator Id, constant operators and certain trivial ones by composition, ∪ and ∩. This extends results of [3] concerning bounded positive operators. (shrink)

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly $\Delta (...) _\alpha ^0 $ orbit (from the proof). (shrink)

We reconsider some classical natural semantics of integers in the perspective of Kolmogorov complexity. To each such semantics one can attach a simple representation of integers that we suitably effectivize in order to develop an associated Kolmogorov theory. Such effectivizations are particular instances of a general notion of “self-enumerated system” that we introduce in this paper. Our main result asserts that, with such effectivizations, Kolmogorov theory allows to quantitatively distinguish the underlying semantics. We characterize the families obtained by such (...) effectivizations and prove that the associated Kolmogorov complexities constitute a hierarchy which coincides with that of Kolmogorov complexities defined via jump oracles and/or infinite computations . This contrasts with the well-known fact that usual Kolmogorov complexity does not depend on the chosen arithmetic representation of integers, let it be in any base n ≥ 2 or in unary. Also, in a conceptual point of view, our result can be seen as a mean to measure the degree of abstraction of these diverse semantics. (shrink)

Let$ \le _c $be computable the reducibility on computably enumerable equivalence relations. We show that for every ceerRwith infinitely many equivalence classes, the index sets$\left\{ {i:R_i \le _c R} \right\}$,$\left\{ {i:R_i \ge _c R} \right\}$, and$\left\{ {i:R_i \equiv _c R} \right\}$are${\rm{\Sigma }}_3^0$complete, whereas in caseRhas only finitely many equivalence classes, we have that$\left\{ {i:R_i \le _c R} \right\}$is${\rm{\Pi }}_2^0$complete, and$\left\{ {i:R \ge _c R} \right\}$ is${\rm{\Sigma }}_2^0$complete. Next, solving an open problem from [1], we prove that the index set of (...) the effectively inseparable ceers is${\rm{\Pi }}_4^0$complete. Finally, we prove that the 1-reducibility preordering on c.e. sets is a${\rm{\Sigma }}_3^0$complete preordering relation, a fact that is used to show that the preordering relation$ \le _c $on ceers is a${\rm{\Sigma }}_3^0$complete preordering relation. (shrink)

Social choice rules are often evaluated and compared by inquiring whether they satisfy certain desirable criteria such as the Condorcet criterion, which states that an alternative should always be chosen when more than half of the voters prefer it over any other alternative. Many of these criteria can be formulated in terms of choice sets that single out reasonable alternatives based on the preferences of the voters. In this paper, we consider choice sets whose definition merely relies on the pairwise (...) majority relation. These sets include the Copeland set, the Smith set, the Schwartz set, von Neumann-Morgenstern stable sets, the Banks set, and the Slater set. We investigate the relationships between these sets and completely characterize their computational complexity, which allows us to obtain hardness results for entire classes of social choice rules. (shrink)

We suggest some new ways to effectivize the definitions of several classes of simple sets. On this basis, new completeness criterions for simple sets are obtained. In particular, we give descriptions of the class of complete maximal sets.

Hylomorphically complex objects are things that change their parts or matter or that might have, or have had, different parts or matter. Often ontologists analyze such objects in terms of sets (or functions, understood set-theoretically) or other extensional entities such as mereological fusions or quantities of matter. I urge two reasons for being wary of any such analyses. First, being extensional, such things as sets are ill-suited to capture the characteristic modal and temporal flexibility of hylomorphically complex objects. Secondly, sets (...) are often appealed to because they seem to contain their members. But the idea that sets do contain their members, in the ordinary sense of containment, is a substantive metaphysical position that makes analyses that rely on that idea for their plausibility much more metaphysically committing than is generally thought. (shrink)

Let [Formula: see text] be an integer. We show that the set of real numbers that are Poisson generic in base [Formula: see text] is [Formula: see text]-complete in the Borel hierarchy of subsets of the real line. Furthermore, the set of real numbers that are Borel normal in base [Formula: see text] and not Poisson generic in base [Formula: see text] is complete for the class given by the differences between [Formula: see text] sets. We also show that the (...) effective versions of these results hold in the effective Borel hierarchy. (shrink)

In this paper, one extends the single-valued complex neutrosophic set to the subsetvalued complex neutrosophic set, and afterwards to the subset-valued complex refined neutrosophic set.

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α, δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which (...) one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ. (shrink)

In this paper, we bring together research on complex problem solving with that on motivational psychology about goal setting. Complex problems require motivational effort because of their inherent difficulties. Goal Setting Theory has shown with simple tasks that high, specific performance goals lead to better performance outcome than do-your-best goals. However, in complex tasks, learning goals have proven more effective than performance goals. Based on the Zurich Resource Model, so-called motto-goals should activate a person’s resources through positive affect. It was (...) found that motto-goals are effective with unpleasant duties. Therefore, we tested the hypothesis that motto-goals outperform learning and performance goals in the case of complex problems. A total of N = 123 subject participated in the experiment. In dependence of their goal condition, subjects developed a personal motto, learning, or performance goal. This goal was adapted for the computer-simulated complex scenario Tailorshop, where subjects worked as managers in a small fictional company. Other than expected, there was no main effect of goal condition for the management performance. An unexpected gender effect revealed better performance for men than women, pointing to a potential stereotype threat. As hypothesized, motto goals led to higher positive and lower negative affect than the other two goal types. Even though positive affect decreased and negative affect increased in all three groups during Tailorshop completion, participants with motto goals reported the lowest rates of negative affect. Exploratory analyses investigated the role of affect in complex problem solving via mediational analyses and the influence of goal type on perceived goal attainment. (shrink)

Aleksandar Ignjatović. Delineating Classes of Computational Complexity via Second Order Theories with Weak Set Existence Principles (I).

We prove that any speedable computably enumerable set may be split into a disjoint pair of speedable computably enumerable sets. This solves a longstanding question of J.B. Remmel concerning the behavior of computably enumerable sets in Blum's machine independent complexity theory. We specify dynamic requirements and implement a novel way of detecting speedability-by embedding the relevant measurements into the substage structure of the tree construction. Technical difficulties in satisfying the dynamic requirements lead us to implement "local" strategies that only (...) look down the tree. The (obvious) problems with locality are then resolved by placing an isomorphic copy of the entire priority tree below each strategy (yielding a self-similar tree). This part of the construction could be replaced by an application of the Recursion Theorem, but shows how to achieve the same effect with a more direct construction. (shrink)

We show that if κ is a weakly compact cardinal then the embeddability relation on trees of size κ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space View the MathML source there is an Lκ+κ-sentence φ such that the embeddability relation on its models of size κ, which are all trees, is Borel bi-reducible to R. In particular, this implies that the relation of embeddability on trees of size κ is complete for (...) analytic quasi-orders on View the MathML source. These facts generalize analogous results for κ=ω obtained in Louveau and Rosendal [17] and Friedman and Motto Ros [6], and it also partially extends a result from Baumgartner [3] concerning the structure of the embeddability relation on linear orders of size κ. (shrink)

The clinical relevance of whole-exome sequencing is unquestionable. In the prenatal setting, the standard testing process of reflexing from karyotype to microarray to single-gene disorders may take several weeks, leaving a family in prolonged turmoil and often without answers in time to make a decision about the pregnancy. WES provides a powerful amount of data more quickly and with a higher yield of diagnostic results, allowing a timelier plan for medical management and decision-making. However, while results that pertain specifically to (...) the testing indication can be isolated, the potential for incidental findings or results that are unrelated to the original testing indication is significant. In 2013, ACMG published recommendations for reporting incidental or secondary findings, providing a list of 57 clinically actionable genes for which reporting should be obligatory. These recommendations were updated in 2015 to include the option to opt out of receiving all secondary findings. The list includes childhood-onset conditions, for which medical management would be immediately impacted. However, the list also includes adult-onset conditions such as hereditary breast and ovarian cancer and Lynch syndrome. Historically, decisions regarding genetic testing for these conditions have been left up to the individual until they reach the age of consent. While the 2015 recommendations are an improvement over the 2013 recommendations insofar as they allow an option to opt out of receiving secondary findings, the recommendations continue to have potentially troubling ethical consequences. (shrink)

To survive in a competitive environment, small and medium enterprises have had to adapt to the digital environment in order to adjust to customer needs globally, particularly in the post-COVID-19 world. The advantages of cloud computing provide opportunities for SMEs with a restricted budget and limited resources. To understand how SMEs adopt cloud computing in a complex digital environment, this study examines how antecedents combine with each other to explain the high adoption of cloud computing. From the perspectives of holism (...) and set theory, we draw on complexity and configuration theories, present a conceptual model including seven antecedents based on the technology-organization-environment framework, and conduct an asymmetric fuzzy-set qualitative comparative analysis. Through an empirical study with 123 Chinese companies, we identify nine combinations of determinant antecedents that lead to the high adoption of cloud computing. The results show that none of the factors are indispensable to explain a high adoption on their own; instead, they are insufficient but necessary parts of the causal combinations that explain a high adoption. This study contributes to the literature on cloud computing adoption by extending current knowledge on how antecedents combine to increase the adoption and identify specific patterns of SMEs for whom these factors are essential and greatly influence their adoption. (shrink)

Video‐recording healthcare interactions provides important opportunities for research and service improvement. However, this method brings about tensions, especially when recording sensitive topics. Subsequent reflection may compel the researcher to engage in ethical and moral deliberations. This paper presents experiences from a South African genetic counselling study which made use of video‐recordings to understand communicative processes in routine practice. Video‐recording as a research method, as well as contextual and process considerations are discussed, such as researching one's own field, issues of trust (...) and anonymity, the challenge of providing true informed consent and capturing details which may cause psychological harm. Several recommendations for research practice in diverse healthcare settings are made. This includes the value of reflective pieces, the importance of retrospective consent, disclosure of the limitations to anonymity, as well as the collective responsibility of those involved to produce ethical research. These recommendations have value for genetic counselling and other healthcare fields. (shrink)

According to physicalism, everything is physical or metaphysically connected to the physical. If physicalism were true, it seems that we should – in principle – be able to reduce the descriptions and explanations of special sciences to physical ones, for example, explaining biological regularities, via chemistry, by the laws of particle physics. The multiple realization of the property types of the special sciences is often seen to be an obstacle to such epistemic reductions. Here, we introduce another, new argument against (...) epistemic reduction. Based on mathematical complexity, we show that, under certain conditions, there can be “complexity barriers” that make epistemic reduction – in principle – unachievable even if physicalism were true. (shrink)