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A Mathematical Study of Tripolar Intuitionistic Fuzzy Graphs
AbstractGraph-based models provide a fundamental mathematical framework for representing relational systems in terms of vertices and their connections. Fuzzy sets extend classical set theory by assigning each element a membership degree in the interval [0,1], thereby allowing partial membership rather than restricting membership to binary values.
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Decidability and Specker sequences in intuitionistic mathematics
Mathematical Logic Quarterly, 2009AbstractA bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit.
Rasoul Ramezanian, Mohammad Ardeshir
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Mathematics of Intuitionistic Fuzzy Sets
Studies in Fuzziness and Soft Computing, 2016Short firsthand remarks on the history and theory of Intuitionistic Fuzzy Sets (IFSs) are given. Influences of other areas of mathematics for development of the IFSs theory are discussed. On the basis of results in IFSs theory, some ideas for development of other mathematical areas are offered.
Krassimir Atanassov
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Temporal and atemporal truth in intuitionistic mathematics
Topoi, 1994In Sect. 11.2, we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of the classical meaning of the logical constants and consequently is incompatible with the antirealism of orthodox Intuitionism. In Sect.
Martino, Enrico, Usberti, Gabriele
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Intuitionistic mathematics does not needex falso quodlibet
Topoi, 1994We define a system IR of first-order intuitionistic relevant logic. We show that intuitionistic mathematics (on the assumption that it is consistent) can be relevantized, by virtue of the following metatheorem: any intuitionistic proof of A from a setX of premisses can be converted into a proof in IR of eitherA or absurdity from some subset ofX.
Neil Tennant
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Intuitionistic mathematics and wittgenstein
History and Philosophy of Logic, 1991The relation between Wittgenstein's philosophy of mathematics and mathematical Intuitionism has raised a considerable debate. My attempt is to analyse if there is a commitment in Wittgenstein to themes characteristic of the intuitionist movement in Mathematics and if that commitment is one important strain that runs through his Remarks on the ...
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Solipsism and philosophy of mathematics: intuitionists compared
2022This paper will consider L. E. J. Brouwer, A. Heyting and G. F. C. Griss as the first generation of Dutch intuitionists to look at the interrelationship between solipsism and mathematics. In particular, our focus will be on Heyting, on the basis of the existence of some unpublished material (and also some difficult to find published material) revealing
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Elementary Intuitionistic Mathematics
2000Abstract The name ‘intuitionism’ is due to Brouwer’s acceptance of the Kantian thesis that our concept of the natural number series is derived from temporal intuition, our apprehension of the passage of time; not, indeed, from any particular details of our experience, but from the a priori form of that experience as involving temporal ...
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