In the first Part of this paper Property Systems are investigated in order to define intensional and extensional operators fulfilling adjointness properties. On this basis a set of operators are defined which are able to determine non-classical upper and lower approximations of subsets of objects or properties. But in order to bypass "discontinuity" of such operators we introduce, in the second Part, the higher order notion of an "Information Quantum". This way we can account for Attribute Systems as well as Property Systems by transforming them into new structures called "Information Quantum Relational Systems" in which adjointness makes operators fulfill continuity and makes it possible to define a class of Generalised Approximation Spaces. ©2005 IEEE.

P PAGLIANI

M K CHAKRABORTY

University of Calcutta (informally known as Calcutta University or CU) is a collegiate public state university located in Kolkata, West Bengal, India.&nbsp;Within India it is recognized as a &quot;Five-Star University&quot; and accredited &quot;A&quot; Grade by National Assessment and Accreditation Council.

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The University of Calcutta has secured the Fifth position among the Universities of India in the prestigious &quot;Indian University Ranking 2019&quot; list, released by the NIRF of the Ministry of Human Resource Development, Government of India.

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It was established on 24 January 1857, and was one of the first institutions in Asia to be established as a multidisciplinary and Western-style university. Its alumni and faculty include several heads of state, heads of government, social reformers, prominent artists, only academy award winner and Dirac medal winner in India, many Fellows of the Royal Society and five Nobel laureates as of 2019 which is highest in South Asia.

University Of Calcutta

Information quanta and approximation spaces. I. Non-classical approximation operators

2005 IEEE International Conference on Granular Computing

Rough Set Theory may be considered as a formal interpretation of observation of phenomena. On one side we have objects and on the other side we have properties. This is what we call a Property System. Observing is then the act of perceiving and then interpreting the binary relation (of satisfaction) between the two sides. Of course, the set of properties can be given a particular structure. However, from a pure " phenomenological" point of view, a structure is given by the satisfaction relation we observe. So it is a result and not a precondition. Phenomena, in general, do not give rise to topological systems but to pre-topological systems. In particular, "interior" and "closure" operators are not continuous with respect to joins, so that they can "miss" information. To obtain continuous operators we have to lift the abstraction level of Property Systems by synthesizing relations between objects and properties into systems of relations between objects and objects. Such relations are based on the notion of a minimal amount of information that is carried by an item. This way we can also account for Attribute Systems, that is, systems in which we have attributes instead of properties and items are evaluated by means of attribute values. But in order to apply our mathematical machinery to Attribute Systems we have to transform them into Property Systems in an appropriate manner. © Springer-Verlag Berlin Heidelberg 2007.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Formal topology and information systems

In the first Part we have introduced non-classical upper and lower approximations of subsets of objects or properties, on the basis of the properties featured by Galois adjunctions between intensional and extensionnal operators. In the present Part we introduce 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. ©2005 IEEE.

Information quanta and approximation spaces. II: Generalised approximation spaces

Two agents Ag1 and Ag2 confront each other with their own perspectives represented by approximation spaces (U, R1) and (U, R2). They enter into a dialogue (negotiation) over either the extension of the same 'concept' or over two pieces of information or beliefs, A and B, the first for Ag1 and the second for Ag2 respectively, which are subsets of U. A combined approximation space (U, R) emerges out of the superimposition of the equivalence classes due to R 1 and R2. Each agent performs some specified operations one at a time. After an operation by an agent the turn comes to the co-agent. Rounds and effects of rounds are then defined. A dialogue is a sequence of rounds. There are certain rules of the game that depend on the three approximation spaces. The result of a dialogue after n rounds starting with the initial sets A, B is a pair (An, Bn), An,B n being supersets of A and B respectively. A dialogue is characterised depending on the various kinds of overlap of the sets A n and Bn and their lower and upper approximations. It is satisfactory if the sets An and Bn turn out to be roughly equal with respect to the approximation space (U, R). Dialogues of lower satisfaction are not altogether rejected. This latter type generalizes the notion of Belief-Merging, Some preliminary observations are made and future directions of work are indicated.

Journal	2005 IEEE International Conference on Granular Computing
Publisher	-