A review of the relationships between implication, negation and aggregation functions from the point of view of material implication

Implication and aggregation functions play important complementary roles in the field of fuzzy logic. Both have been intensively investigated since the early 1980s, revealing a tight relationship between them. However, the main results regarding this relationship, published by Fodor and Demirli DeBaets in the 1990s, have been poorly disseminated and are nowadays somewhat obsolete due to the subsequent advances in the field. The present paper deals with the translation of the classical logical equivalence p → q = ¬pvq, often called material implication, to the fuzzy framework, which establishes a one-to-one correspondence between implication functions and disjunctors (the class of aggregation functions that extend the Boolean disjunction to the unit interval). The construction of implication functions from disjunctors via negation functions, and vice versa, is reviewed, stressing the properties of disjunctors (respectively, implication functions) that ensure certain properties of implication functions (disjunctors).

Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such a system, which appears in an astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity in the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved non-normal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this answers the question of the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of the origin of turbulence therein.

Conjugacy invariant pseudo-norms, representability and RNA secondary structures

To a reasonable approximation, a secondary structures of RNA is determined by Watson-Crick pairing without pseudo-knots in such a way as to minimise the number of unpaired bases: We show that this minimal number is determined by the maximal conjugacy-invariant pseudo-norm on the free group on two generators subject to bounds on the generators. This allows us to construct lower bounds on the minimal number of unpaired bases by constructing conjugacy invariant pseudo-norms. We show that one such construction, based on isometric actions on metric spaces, gives a sharp lower bound. A major goal here is to formulate a purely mathematical question, based on considering orthogonal representations, which we believe is of some interest independent of its biological roots.

Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

The interactions of consumption characteristics on social norms

Purpose: An extended Theory of Planned Behavior (TPB) model tests how customer loyalty intentions may relate to subjective and descriptive norms. The study further determines whether consumption characteristics – product enjoyment and importance – moderate norms-loyalty relationships.----- Methodology: Using a two-study approach focusing on youth, an Australian study (n = 244) first augmented TPB with descriptive norm. A Singapore study (n = 415) followed up with how consumption characteristics might moderate norms-loyalty relationships. With both studies, linear regressions tested the relationships among the variables.----- Findings: Extending TPB with descriptive norm improved TPB’s predictive ability across studies. Further, product enjoyment and importance moderated the norms-loyalty relationships differently. Subjective norm related to loyalty intentions significantly with high enjoyment, whereas descriptive norm was significant with low enjoyment. Only subjective norm was significant with low importance.----- Research limitations: Single-item variables, self-reported questionnaires on intended rather than actual behavior, and not controlling for cultural differences between the two samples limit generalizablity.----- Practical implications: The significance of both norms suggests that mobile firms should reach youth through their peers. With youth, social pressure may be influential particularly with hedonic products. However, the different moderations of product enjoyment and importance imply that a blanket marketing strategy targeting youth may not work.----- Originality/Value: This study extends academic knowledge on the relationships between norms and customer loyalty, particularly with consumption characteristics as moderators. The findings highlight the importance of considering different norms with consumer behavior. The study should help mobile firms understand how social influences impact customer loyalty.

Willingness to trial functional foods and vitamin supplements: the role of attitudes, subjective norms, and dread of risks

Australian non-users of vitamin supplements (N = 162) and functional foods (N = 226) responded to a questionnaire examining their attitudes, subjective norms, and perceived behavioural control from the Theory of Planned Behaviour (TPB), risk dread and risk familiarity, and willingness to engage in free product trials. The impact of participants’ gender and age was also examined. Attitude and subjective norms were significant determinants of non-users willingness to trial each of the health products. Participants’ dread of the risk associated with the product was also a determinant of willingness to use functional foods. The overall models predicted between 25% and 30% of the variance in people’s willingness to trial the products. The findings provided some support for the TPB in predicting people’s willingness to trial functional foods and vitamin supplements and suggested, for willingness to trial functional foods, that non-users are also influenced by their dread of the risk associated with product use.

Protective behavior in adolescent friendships : the influence of attitudes toward the consequences, friendship norms and perceived control

The current study sought to understand adolescent protective behavior in friendship using a Theory of Planned Behavior framework. In particular, the study sought to consider a young persons’ direct and active intervention to inhibit their friends’ risky behavior or to assist them when the behavior leads to injury. The role of attitudes regarding the consequences, norms and control about protective behavior were examined both qualitatively through focus groups (n= 50) and quantitatively through surveys from a sample of 540 Year 9 students (13-14 years old). There was some support for the theory with attitudes regarding the consequences of the behavior and norms predicting intended protective behavior. A path analysis was conducted with a sub-sample of 140 students which showed that intentions to be protective and perceived control to undertake protective behavior directly predicted such behavior after a 3 month interval. Attitudes towards the consequences and norms only indirectly predicted protective behavior via intention. The findings provide important applied information for interventions designed to increase adolescent protective behavior in their friendships.

Environmental and pro-social norms : evidence on littering

The paper investigates the relationship between pro-social norms and its implications for improved environmentsl outcomes. This is an area, which has been neglected in the environmental economic literature. We provide empirical evidence to demonstrate a small but significant positive impact between perceived environmental cooperation (reduced public littering) and increased voluntary environmental morale. For this purpose we use European Value Survey (EVS) data for 30 European countries. We also demonstrate that Western European countries are more sensitive to perceived environmental cooperation than the public in Eastern Europe. Interestingly, the results also demonstrate that environmental morale is strongly correlated with several socio-economic and environmental variables. Several robustness tests are conducted to check the validity of the results.

Interaction of natural survival instincts and internalized social norms exploring the Titanic and Lusitania disasters

To understand human behavior, it is important to know under what conditions people deviate from selfish rationality. This study explores the interaction of natural survival instincts and internalized social norms using data on the sinking of the Titanic and the Lusitania. We show that time pressure appears to be crucial when explaining behavior under extreme conditions of life and death. Even though the two vessels and the composition of their passengers were quite similar, the behavior of the individuals on board was dramatically different. On the Lusitania, selfish behavior dominated (which corresponds to the classical homo oeconomicus); on the Titanic, social norms and social status (class) dominated, which contradicts standard economics. This difference could be attributed to the fact that the Lusitania sank in 18 minutes, creating a situation in which the short-run flight impulse dominates behavior. On the slowly sinking Titanic (2 hours, 40 minutes), there was time for socially determined behavioral patterns to re-emerge. To our knowledge, this is the first time that these shipping disasters have been analyzed in a comparative manner with advanced statistical (econometric) techniques using individual data of the passengers and crew. Knowing human behavior under extreme conditions allows us to gain insights about how varied human behavior can be depending on differing external conditions.

The role of non-factorizability in determining "pseudo-classical" non-separability

This article introduces a “pseudo classical” notion of modelling non-separability. This form of non-separability can be viewed as lying between separability and quantum-like non-separability. Non-separability is formalized in terms of the non-factorizabilty of the underlying joint probability distribution. A decision criterium for determining the non-factorizability of the joint distribution is related to determining the rank of a matrix as well as another approach based on the chi-square-goodness-of-fit test. This pseudo-classical notion of non-separability is discussed in terms of quantum games and concept combinations in human cognition.

The international search for ethics norms : which consumer behaviors do consumers consider (un)acceptable?

Purpose: Businesses cannot rely on their customers to always do the right thing. To help researchers and service providers better understand the dark (and light) side of customer behavior, this study aims to aggregate and investigate perceptions of consumer ethics from young consumers on five continents. The study seeks to present a profile of consumer behavioral norms, how ethical inclinations have evolved over time, and country differences. ---------- Design/methodology/approach: Data were collected from ten countries across five continents between 1997 and 2007. A self-administered questionnaire containing 14 consumer scenarios asked respondents to rate acceptability of questionable consumer actions. ---------- Findings: Overall, consumers found four of the 14 questionable consumer actions acceptable. Illegal activities were mostly viewed as unethical, while some legal actions that were against company policy were viewed less harshly. Differences across continents emerged, with Europeans being the least critical, while Asians and Africans shared duties as most critical of consumer actions. Over time, consumers have become less tolerant of questionable behaviors. ---------- Practical implications: Service providers should use the findings of this study to better understand the service customer. Knowing what customers in general believe is ethical or unethical can help service designers focus on the aspects of the technology or design most vulnerable to customer deviance. ---------- Multinationals already know they must adapt their business practices to the market in which they are operating, but they must also adapt their expectations as to the behavior of the corresponding consumer base. Originality/value: This investigation into consumer ethics helps businesses understand what their customer base believes is the right thing in their role as customer. This is a large-scale study of consumer ethics including 3,739 respondents on five continents offering an evolving view of the ethical inclinations of young consumers.

Pseudo-merohedral twinning in the structure of the hydrated 1:1 proton-transfer compound of 5-sulfosalicylic acid with 4-aminopyridine

The structure of the pseudo-merohedrally twinned crystal of the 1:1 proton-transfer compound of 5-sulfosalicylic acid (3-carboxy-4-hydroxybenzenesulfonic acid) with 4-aminopyridine: 4-aminopyridinium 3-carboxy-4-hydroxybenzenesulfonate sesquihydrate has been determined at 180 K and the hydrogen-bonding pattern is described. Crystals of the compound are monoclinic with space group P21/c, with unit cell dimensions a = 35.2589(8), b = 7.1948(1), c = 24.5851(5) Å, β = 110.373(2)o, and Z = 16. The monoclinic asymmetric unit comprises four cation-anion pairs and six water molecules of solvation with only the pyridinium cations having pseudo-symmetry as a result of inter-cation aromatic ring π-π stacking effects. Extensive hydrogen bonding gives a three-dimensional framework structure.

Order supported by law : the enforcement of norms in virtual communities

As online social spaces continue to grow in importance, the complex relationship between users and the private providers of the platforms continues to raise increasingly difficult questions about legitimacy in online governance. This article examines two issues that go to the core of egitimate governance in online communities: how are rules enforced and punishments imposed, and how should the law support legitimate governance and protect participants from the illegitimate exercise of power? Because the rules of online communities are generally ultimately backed by contractual terms of service, the imposition of punishment for the breach of internal rules exists in a difficult conceptual gap between criminal law and the predominantly compensatory remedies of contractual doctrine. When theorists have addressed the need for the rules of virtual communities to be enforced, a dichotomy has generally emerged between the appropriate role of criminal law for 'real' crimes, and the private, internal resolution of 'virtual' or 'fantasy' crimes. In this structure, the punitive effect of internal measures is downplayed and the harm that can be caused to participants by internal sanctions is systemically undervalued.