• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.85-98
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• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• Korean Journal of Logic
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• v.17 no.1
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• pp.33-70
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• 2014

We still do not know against what histocial/philosophical background and motivation was Tarski's definition of logical consequence introduced, even if it has had such a strong influence. In view of the centrality of the notion of logical consequence in logic and philosophy of logic, it is rather shocking. There must be various intertwined reasons to blame for this uncomfortable situation. There has been remarkable progress achieved recently on the history of analytic philosophy and modern logic. In view of the recent developments of the controversies involved, however, we will have to wait years to resolve all this uneasiness. In this gloomy situation, Douglas Patterson's recent study of Tarski's philosophy of language and logic seems to have the potential to turn out to be a ground breaking achievement. [Patterson (2012)] This article aims at reporting the state-of-the-art in this problem area, and fathoming the future directions of research by examining critically some unclear components of Patterson's study.