Foundations of Vagueness: a Category-theoretic Approach
Reads0
Chats0
TLDR
This paper has tried to establish the thesis that vagueness has its origin in indiscernibility on a category-theoretic basis and some other related notions, e.g. property, have been clarified.About:
This article is published in Electronic Notes in Theoretical Computer Science.The article was published on 2003-03-01 and is currently open access. It has received 17 citations till now. The article focuses on the topics: Vagueness & Property (philosophy).read more
Citations
More filters
Book ChapterDOI
Dialectics of counting and the mathematics of vagueness
TL;DR: In this paper, the authors introduce rough natural number systems from both formal and less formal perspectives, which are used to improve most rough set-theoretical measures in general Rough Set theory and to represent rough semantics.
Book ChapterDOI
A Categorial Basis for Granular Computing
Mohua Banerjee,Yiyu Yao +1 more
TL;DR: It is shown how two main operations between granulations can be expressed in terms of $cal C_G$-morphisms, the theory of granular computing's main features using category-theoretic language.
Proceedings ArticleDOI
Information quanta and approximation spaces II: generalised approximation spaces
TL;DR: The higher order notions of an " information quantum" an "information quantum relational system" which make adjoint operators into continuous approximation operators and make it possible to define a class of topological approximation spaces are introduced.
Book ChapterDOI
Formal topology and information systems
TL;DR: Rough Set Theory may be considered as a formal interpretation of observation of phenomena by synthesizing relations between objects and properties into systems of relations betweenObjects and objects and objects.
Journal ArticleDOI
Fuzzy relation and fuzzy function over fuzzy sets: a retrospective
Soma Dutta,Mihir K. Chakraborty +1 more
TL;DR: The presentation is uniform and integrated in the sense that every concept is developed on fuzzy set as base and is organized from the angle of foundational aspects of fuzzy set theory.
References
More filters
Journal ArticleDOI
Similarity relations and fuzzy orderings
TL;DR: An extended version of Szpilrajn's theorem is proved and various properties of similarity relations and fuzzy orderings are investigated and, as an illustration, a fuzzy preordering is investigated which is reflexive and antisymmetric.
Book
Topoi: The Categorial Analysis of Logic
TL;DR: In this article, the authors introduce the concept of topoi, a topos structure for algebra of subobjects, and introduce a set theory of set concepts and its logic, namely, set concepts, set theory, set notions, and set concepts.
Book ChapterDOI
An Inquiry into Indistinguishability Operators
Enric Trillas,L. Valverde +1 more
TL;DR: The problem of individuation is a long-standing phi1osophical preoccupation (Munitz,1971); because though things are, themselves, what they are, a human or artificial observer aided by intelligence or instruments "reads" things and sees in them just what can be seen, what the discriminating power of the instrument allows, this being true for physical as well as intellectual instruments as mentioned in this paper.
BookDOI
Aspects of vagueness
TL;DR: The Alternative Set Theory and its approach to Cantor's Set Theory as mentioned in this paper is a general framework for fuzzy set theory, and it is based on the notion of Fuzzy Probability Measures.