First we introduce some basic theoretical issues that set the stage for subsequent accounts. Seco... more First we introduce some basic theoretical issues that set the stage for subsequent accounts. Secondly, we touch upon some important issues: Set-theory vs. category theory, various conceptions of sets, the problem of universals, combining set-theory and category theory, structuralism, and finally category theory as an application tool. We argue that in the present time, the categorical holistic way of structuring is much needed. Also we would like to see a kind of unification, not only to mathematics but to structuralism as well.
Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems, 2014
In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-parti... more In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-partitions together with a notion of refinement is tantamount a construction of an MV-power, analogous to Boolean power construction (Mansfield, 1971). Using this new notion we introduce the corresponding theory of MV-powers.
In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and e... more In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and equi-varL1nt· ·proper\: ies • . l:l. plausibility confidence interval based on n inimum distance estimator is introduced using relational orde r systems. Th e properties which are used to characterize distances in metric spaces are main ly dictated from convergence purposes. For example, uniqueness 6f limits are very important in analy-sis .IIm· mver r in Statistics and in the case v;here no asym.rtot:!-c meth~ds are used and thus no limits are involved, the tern udis-tance" is used in a broader sense. What is essential is the non-negativerwss of the distance function and its being zero v:hen and only when the arguments are indentical. It is known, also , (see p.32 in (14)) that in passing frorn metric spaces to gene-ral topoloqical spaces · we lose ·the syrmnetry property of ou1:· no-tion of closeness in addition to other properties. If y is close to x in a ~etric space, then x is c...
First we introduce some basic theoretical issues that set the stage for subsequent accounts. Seco... more First we introduce some basic theoretical issues that set the stage for subsequent accounts. Secondly, we touch upon some important issues: Set-theory vs. category theory, various conceptions of sets, the problem of universals, combining set-theory and category theory, structuralism, and finally category theory as an application tool. We argue that in the present time, the categorical holistic way of structuring is much needed. Also we would like to see a kind of unification, not only to mathematics but to structuralism as well.
Mathematics of Uncertainty Modeling in the Analysis of Engineering and Science Problems, 2014
In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-parti... more In this chapter, the authors generalize the Boolean partition to semisimple MV-algebras. MV-partitions together with a notion of refinement is tantamount a construction of an MV-power, analogous to Boolean power construction (Mansfield, 1971). Using this new notion we introduce the corresponding theory of MV-powers.
In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and e... more In this paper the minimurn. distance esti m~ tor is proved that it possesses both invariant and equi-varL1nt· ·proper\: ies • . l:l. plausibility confidence interval based on n inimum distance estimator is introduced using relational orde r systems. Th e properties which are used to characterize distances in metric spaces are main ly dictated from convergence purposes. For example, uniqueness 6f limits are very important in analy-sis .IIm· mver r in Statistics and in the case v;here no asym.rtot:!-c meth~ds are used and thus no limits are involved, the tern udis-tance" is used in a broader sense. What is essential is the non-negativerwss of the distance function and its being zero v:hen and only when the arguments are indentical. It is known, also , (see p.32 in (14)) that in passing frorn metric spaces to gene-ral topoloqical spaces · we lose ·the syrmnetry property of ou1:· no-tion of closeness in addition to other properties. If y is close to x in a ~etric space, then x is c...
Uploads
Papers by Costas Drossos