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  • Any fuzzy set X in a classical set A with values in a complete (residuated) lattice Q can be identified with a system of alpha- cuts. Analogical results were proved for sets with similarity relations with values in Q (e.g. Q-sets) which are objects of two special categories of Q-sets and for fuzzy sets defined as special morphisms in these categories. These fuzzy sets can be defined equivalently as special cut systems, called f-cuts. In the paper we are interested in relationships between sets of fuzzy sets and sets of f-cuts in an Q-set in corresponding categories, which are endowed with binary operations extended either from Binary operations in the lattice Q, or from binary operations defined in a set A by the generalized Zadeh extension principle. We prove that the resulting binary structures are (under some conditions) isomorphic.
  • Any fuzzy set X in a classical set A with values in a complete (residuated) lattice Q can be identified with a system of alpha- cuts. Analogical results were proved for sets with similarity relations with values in Q (e.g. Q-sets) which are objects of two special categories of Q-sets and for fuzzy sets defined as special morphisms in these categories. These fuzzy sets can be defined equivalently as special cut systems, called f-cuts. In the paper we are interested in relationships between sets of fuzzy sets and sets of f-cuts in an Q-set in corresponding categories, which are endowed with binary operations extended either from Binary operations in the lattice Q, or from binary operations defined in a set A by the generalized Zadeh extension principle. We prove that the resulting binary structures are (under some conditions) isomorphic. (en)
Title
  • Operations in Fuzzy Sets and Cut Systems
  • Operations in Fuzzy Sets and Cut Systems (en)
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  • Operations in Fuzzy Sets and Cut Systems
  • Operations in Fuzzy Sets and Cut Systems (en)
skos:notation
  • RIV/61988987:17610/14:A14019BI!RIV14-MSM-17610___
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  • P(ED1.1.00/02.0070)
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  • 34683
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  • RIV/61988987:17610/14:A14019BI
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  • fuzzy set; residuated lattice; set with similarity relation; cut system (en)
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  • [0DA9AB25BA67]
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  • Las Vegas, USA
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  • Los Alamitos, California
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  • Proceedings of the International Conference on Computational Science and Computational Intelligence (CSCI 2014)
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  • Močkoř, Jiří
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  • IEEE Computer Society
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  • 978-1-4799-3009-8
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  • 17610
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