A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

Demographic category membership and leadership in small groups : a social identity analysis

Developing the social identity theory of leadership (e.g., [Hogg, M. A. (2001). A social identity theory of leadership. Personality and Social Psychology Review, 5, 184–200]), an experiment (N=257) tested the hypothesis that as group members identify more strongly with their group (salience) their evaluations of leadership effectiveness become more strongly influenced by the extent to which their demographic stereotype-based impressions of their leader match the norm of the group (prototypicality). Participants, with more or less traditional gender attitudes (orientation), were members, under high or low group salience conditions (salience), of non-interactive laboratory groups that had “instrumental” or “expressive” group norms (norm), and a male or female leader (leader gender). As predicted, these four variables interacted significantly to affect perceptions of leadership effectiveness. Reconfiguration of the eight conditions formed by orientation, norm and leader gender produced a single prototypicality variable. Irrespective of participant gender, prototypical leaders were considered more effective in high then low salience groups, and in high salience groups prototypical leaders were more effective than less prototypical leaders. Alternative explanations based on status characteristics and role incongruity theory do not account well for the findings. Implications of these results for the glass ceiling effect and for a wider social identity analysis of the impact of demographic group membership on leadership in small groups are discussed.

Communication and essentialism: Grounding the shared reality of a social category

Essentialism is an ontological belief that there exists an underlying essence to a category. This article advances and tests in three studies the hypothesis that communication about a social category, and expected or actual mutual validation, promotes essentialism about a social category. In Study 1, people who wrote communications about a social category to their ingroup audiences essentialized it more strongly than those who simply memorized about it. In Study 2, communicators whose messages about a novel social category were more elaborately discussed with a confederate showed a stronger tendency to essentialize it. In Study 3, communicators who elaborately talked about a social category with a naive conversant also essentialized the social category. A meta-analysis of the results supported the hypothesis that communication promotes essentialism. Although essentialism has been discussed primarily in perceptual and cognitive domains, the role of social processes as its antecedent deserves greater attention.

Probabilistic orthographic cues to grammatical category in the brain

What helps us determine whether a word is a noun or a verb, without conscious awareness? We report on cues in the way individual English words are spelled, and, for the first time, identify their neural correlates via functional magnetic resonance imaging (fMRI). We used a lexical decision task with trisyllabic nouns and verbs containing orthographic cues that are either consistent or inconsistent with the spelling patterns of words from that grammatical category. Significant linear increases in response times and error rates were observed as orthography became less consistent, paralleled by significant linear decreases in blood oxygen level dependent (BOLD) signal in the left supramarginal gyrus of the left inferior parietal lobule, a brain region implicated in visual word recognition. A similar pattern was observed in the left superior parietal lobule. These findings align with an emergentist view of grammatical category processing which results from sensitivity to multiple probabilistic cues.

Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Violencia en el deporte en edad escolar en la Comunidad Aut??noma del Pa??s Vasco

El presente trabajo informa sobre qu?? es la violencia en el deporte y analiza el proyecto que realiz?? el Comit?? Vasco Contra la Violencia en el deporte en edad escolar en la Comunidad Aut??noma del Pa??s Vasco en el que finalmente se proponen unas ??reas de mejora.