23,745 research outputs found
Vagueness and Roughness
The paper proposes a new formal approach to vagueness and vague sets taking inspirations from Pawlakās rough set theory. Following a brief introduction to the problem of vagueness, an approach to conceptualization and representation of vague knowledge is presented from a number of diļ¬erent perspectives: those of logic, set theory, algebra, and computer science. The central notion of the vague set, in relation to the rough set, is deļ¬ned as a family of sets approximated by the so called lower and upper limits. The family is simultaneously considered as a family of all denotations of sharp terms representing a suitable vague term, from the agentās point of view. Some algebraic operations on vague sets and their properties are deļ¬ned. Some important conditions concerning the membership relation for vague sets, in connection to Blizardās multisets and Zadehās fuzzy sets, are established as well. A classical outlook on a logic of vague sentences (vague logic) based on vague sets is also discussed
A unified theory of granularity, vagueness and approximation
Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more
familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations
Improving circuit miniaturization and its efficiency using Rough Set Theory
High-speed, accuracy, meticulousness and quick response are notion of the
vital necessities for modern digital world. An efficient electronic circuit
unswervingly affects the maneuver of the whole system. Different tools are
required to unravel different types of engineering tribulations. Improving the
efficiency, accuracy and low power consumption in an electronic circuit is
always been a bottle neck problem. So the need of circuit miniaturization is
always there. It saves a lot of time and power that is wasted in switching of
gates, the wiring-crises is reduced, cross-sectional area of chip is reduced,
the number of transistors that can implemented in chip is multiplied many
folds. Therefore to trounce with this problem we have proposed an Artificial
intelligence (AI) based approach that make use of Rough Set Theory for its
implementation. Theory of rough set has been proposed by Z Pawlak in the year
1982. Rough set theory is a new mathematical tool which deals with uncertainty
and vagueness. Decisions can be generated using rough set theory by reducing
the unwanted and superfluous data. We have condensed the number of gates
without upsetting the productivity of the given circuit. This paper proposes an
approach with the help of rough set theory which basically lessens the number
of gates in the circuit, based on decision rules.Comment: The International Conference on Machine Intelligence Research and
Advancement,ICMIRA-201
Uncertainty behind the veil of ignorance
This paper argues that the decision problem in the original position should be characterized as a decision problem under uncertainty even when it is assumed that the denizens of the original position know that they have an equal chance of ending up in any given individual's place. It argues for this claim by arguing that (a) the continuity axiom of decision theory does not hold between all of the outcomes the denizens of the original position face and that (b) neither us nor the denizens of the original position can know the exact point where discontinuity sets in, because the language we employ in comparing different outcomes is ineradicably vague. It is also argued that the account underlying (b) can help proponents of superiority in value theory defend their view against arguments offered by Norcross and Griffin
On Vague Computers
Vagueness is something everyone is familiar with. In fact, most people think
that vagueness is closely related to language and exists only there. However,
vagueness is a property of the physical world. Quantum computers harness
superposition and entanglement to perform their computational tasks. Both
superposition and entanglement are vague processes. Thus quantum computers,
which process exact data without "exploiting" vagueness, are actually vague
computers
Epistemicism and modality
What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamsonās Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics from that model theory, one of which I will find to be more plausible than the other
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