From Lattice Valued Theories to Lattice Valued Analysis
We claim and justify that the future of a fuzzy logic is in the interconnection of various well-developed theories. We are focused on a lattice valued analysis that unifies the treatments of atomic elements, sets of atomic elements, functions between sets of atomic elements and their properties. We clarify the relationship between a fuzzy function and its ordinary core. We discuss the property of continuity of a fuzzy function in a lattice valued topology.
KeywordsFuzzy Logic Residuated Lattice Fuzzy Relation Fuzzy Function Extension Principle
The support of the two projects is kindly announced: ESF project 2013/0024/1DP/184.108.40.206.0/13/APIA/VIAA/045, European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070).
- 7.Klawonn, F.: Fuzzy points, fuzzy relations and fuzzy functions. In: Novák, V., Perfilieva, I. (eds.) Discovering the World with Fuzzy Logic, pp. 431–453. Springer, Berlin (2000)Google Scholar
- 12.Perfilieva, I.: Fuzzy function: theoretical and practical point of view. In: Proceedings of 7th Conference European Society for Fuzzy Logic and Technology, EUSFLAT 2011, Aix-Les-Bains, France, 18–22 July 2011, pp. 480–486, Atlantis Press (2011)Google Scholar
- 14.Šostak, A.: Fuzzy functions and an extension of the category L-top of Chang-Goguen L-Topological spaces. In: Proceedings of 9th Prague Topological Symposium, Czech Republic, 19–25 August 2001, pp. 271–294 (2001)Google Scholar
- 15.Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning I, II, III. Inf. Sci. 8–9, 199–257, 301–357, 43–80 (1975)Google Scholar