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A study of universal algebras in fuzzy set theory

  • Authors: Murali, V
  • Date: 1988
  • Subjects: Fuzzy sets Algebra, Universal
  • Language: English
  • Type: Thesis , Doctoral , PhD
  • Identifier: vital:5394 , http://hdl.handle.net/10962/d1001983
  • Description: This thesis attempts a synthesis of two important and fast developing branches of mathematics, namely universal algebra and fuzzy set theory. Given an abstract algebra [X,F] where X is a non-empty set and F is a set of finitary operations on X, a fuzzy algebra [I×,F] is constructed by extending operations on X to that on I×, the set of fuzzy subsets of X (I denotes the unit interval), using Zadeh's extension principle. Homomorphisms between fuzzy algebras are defined and discussed. Fuzzy subalgebras of an algebra are defined to be elements of a fuzzy algebra which respect the extended algebra operations under inclusion of fuzzy subsets. The family of fuzzy subalgebras of an algebra is an algebraic closure system in I×. Thus the set of fuzzy subalgebras is a complete lattice. A fuzzy equivalence relation on a set is defined and a partition of such a relation into a class of fuzzy subsets is derived. Using these ideas, fuzzy functions between sets, fuzzy congruence relations, and fuzzy homomorphisms are defined. The kernels of fuzzy homomorphisms are proved to be fuzzy congruence relations, paving the way for the fuzzy isomorphism theorem. Finally, we sketch some ideas on free fuzzy subalgebras and polynomial algebras. In a nutshell, we can say that this thesis treats the central ideas of universal algebras, namely subalgebras, homomorphisms, equivalence and congruence relations, isomorphism theorems and free algebra in the fuzzy set theory setting
  • Full Text:
  • Date Issued: 1988

A survey of San paintings from the southern Natal Drakensberg

  • Authors: Steynberg, Peter John
  • Date: 1988
  • Subjects: Art, San Rock paintings -- Drakensberg Mountains Cave paintings -- Drakensberg Mountains Art, Prehistoric -- Drakensberg Mountains Art, Prehistoric -- South Africa
  • Language: English
  • Type: Thesis , Masters , MFA
  • Identifier: vital:2437 , http://hdl.handle.net/10962/d1004918
  • Description: From Introduction: The study of San rock art has undergone several different phases in approach to the interpretation of art. Two approaches are currently in use. The first emphasises the art as narrative or literal representations of San life and its proponents may be called the "art for art's sake" school. Adherents to the second approach make detailed use of the San ethnography on the belief system of these people and are highly critical of the literalists because they provide no such context. The second approach has rapidly gained ascendancy and replaced the "art for art's sake" school over the last twenty years. The watershed came with the researches of Vinnicombe (1967) in the southern Drakensberg and Maggs (1967) in the Western Cape who both embarked upon programs of research which had quantification and numerical analysis at their core, so that they could present "...some objective observations on a given sample of rock paintings in a particular area..." in order to compare and contrast paintings from geographically different areas. What Vinnicombe's numerical analyses clearly showed was that the eland was the most frequently depicted antelope and that it must have played a fundamental role "...in both the economy and the rellgious beliefs of the painters...", which opened up the search for what those beliefs might be and how they could be related to the rock art itself. In order to understand what the rock art was all about it was recognised that researchers had to meaningfully contextualise the art within the social and religious framework of the artists themselves. Without the provision of such a relevant context, as many different interpretations of the paintings could be made as there were people with imaginations. Such a piecemeal approach provides a meaningless jumble of subjective fancy which tells us something about the interpreters but nothing about the rock art. It is unfortunate that the advent of this explicitly social and anthropological approach marks the end of the amateur as a serious interpreter of San rock art, for the juxtaposition of the ethnography with the rock art requires a proper training in which the intricacies of symbol and metaphor can be recognised.
  • Full Text:
  • Date Issued: 1988

Abahhlezi phansi ngek'bathwal

Abahlezi

Abahlezi phansi

Abo ti Elo

  • Authors: St Mary's Choir , Haoseb, H , Dargie, Dave
  • Date: 1988
  • Subjects: Folk music , Field recordings , Africa, Sub-Saharan , Africa Namibia Gobabis f-sx
  • Language: Khoekhoegowab
  • Type: sound recordings , field recordings , sound recording-musical
  • Identifier: http://hdl.handle.net/10962/309337 , vital:59026 , International Library of African Music, Rhodes University, Makhanda, South Africa , Dave Dargie Field Tapes, Rhodes University, Makhanda, South Africa , DD117-80
  • Description: Recording Session of Catholic Choirs.
  • Full Text: false
  • Date Issued: 1988

Acclamation

Acclamation: Thiser smile

Agnus Dei

Agnus Dei

Agnus Dei

Agnus Dei

Agnus Dei

Albany Rugby Football Club 1st XV, 1988

  • Date: 1988
  • Subjects: Rugby football -- South Africa -- Eastern Cape -- Photographs , Albany Rugby Football Club -- Photographs
  • Type: still image
  • Identifier: http://hdl.handle.net/10962/50807 , vital:26029 , This image is held at the Cory Library for Humanities Research at Rhodes University. For further information contact cory@ru.ac.za. The digitisation of this image was made possible through a generous grant received from the Andrew W. Mellon Foundation 2014-2017. , PIC/M 6707
  • Description: Albany Rugby Football Club 1st XV 1988, Winners of the “Frans Geldenhuys Cup”, “Goodyear 7 a side” and “UCT Cup”, Team photograph with rugby/football players, in rugby uniform, Group photograph, Black and white photograph, Outdoor photograph, Vice President, President and Manager wearing suits, Players standing have arms behind their backs, Players sitting have arms in their laps, Back Row (left to right): M. Calitz, J. de Beer, J Waugh, L. Claasen, J. Spies, Middle Row (left to right): J. Vos, J. du Toit, N. Swart, D. Ferriara, P. Henderson, G. Maas, Front Row (left to right): B. Beneke, J. Moolman (Vice President), D. Meyer (Captain), R. Liddiard (President), W. Currie (Vice Captain), L. Wolmarans (Manager), J. Jacobs, Absent: B. Peterson (Coach), M. Koen.
  • Full Text: false
  • Date Issued: 1988

Aleluya

Aleluya

Aleluya

Aleluya

Aleluya

Aleluya

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