Rough Approximation Based on Weak q-RIFs

Gomolińska, Anna

doi:10.1007/978-3-642-03281-3_4

Cited by 12 publications

(10 citation statements)

References 30 publications

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“…Therefore graded inclusions of which rough inclusion is a prominent representative are of use [6,7,19,26,27]. Rough mereology by Polkowski and Skowron [21], extending Leśniewski's mereology, may be viewed as a formal theory of rough inclusion.…”

Section: Rough Inclusionmentioning

confidence: 98%

“…In such an approach, we need a method to compute membership values for objects of U in extensions of descriptors first. Next, a triangular norm f , a triangular co-norm g, and a complementation function h should be chosen suitably 7 . Finally, the induced fuzzy semantics for compound formulas can be derived, generalizing the crisp semantics:…”

Section: Rough Satisfiability: a Fuzzy Perspectivementioning

confidence: 99%

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A Fuzzy View on Rough Satisfiability

Gomolińska

2010

Rough Sets and Current Trends in Computing

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Section: Rough Inclusionmentioning

confidence: 98%

Section: Rough Satisfiability: a Fuzzy Perspectivementioning

confidence: 99%

A Fuzzy View on Rough Satisfiability

Gomolińska

2010

Rough Sets and Current Trends in Computing

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“…RIFs and variants thereof are defined over power sets in [43,41]. For rewriting them in the set HGOS way, it is necessary to assume that S = ℘(⊤), ⊤ being a finite set, ⊥ = ∅, P = =⊆, ∨ = ∪ and ∧ = ∩.…”

Section: Specific Weak Quasi-rifsmentioning

confidence: 99%

Algebraic Semantics of Generalized RIFs

Mani

2021

Preprint

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A number of numeric measures like rough inclusion functions (RIFs) are used in general rough sets and soft computing. But these are often intrusive by definition, and amount to making unjustified assumptions about the data. The contamination problem is also about recognizing the domains of discourses involved in this, specifying errors and reducing data intrusion relative to them. In this research, weak quasi rough inclusion functions (wqRIFs) are generalized to general granular operator spaces with scope for limiting contamination. New algebraic operations are defined over collections of such functions, and are studied by the present author. It is shown by her that the algebras formed by the generalized wqRIFs are ordered hemirings with additional operators. By contrast the generalized rough inclusion functions lack similar structure. This potentially contributes to improving the selection (possibly automatic) of such functions, training methods, and reducing contamination (and data intrusion) in applications. The underlying framework and associated concepts are explained in some detail as they are relatively new.

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“…The usual set-theoretical inclusion may be viewed as a special case of rough inclusion. Apart from the literature on rough mereology there are several papers where the problem of graded inclusion and, in particular, rough inclusion is addressed (see, e.g., [93,94,95,96,97,87,98]). …”

Section: Rough Inclusionmentioning

confidence: 99%

Satisfiability Judgement under Incomplete Information

Gomolińska

2010

Lecture Notes in Computer Science

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Abstract. In this paper we keep on discussing satisfiability of conditions by objects when information about the situation considered, including objects of some sort and concepts comprised of them, is incomplete. Our approach to satisfiability is that of concept modelling and we have a rough granular view on the problem. Objects considered are known partially, in terms of values of attributes of Pawlak information systems. An additional knowledge (domain knowledge) is assumed to be available. We choose descriptor languages for Pawlak information systems as specification languages in which we will express conditions about objects and concepts.

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Rough Approximation Based on Weak q-RIFs

Cited by 12 publications

References 30 publications

A Fuzzy View on Rough Satisfiability

A Fuzzy View on Rough Satisfiability

Algebraic Semantics of Generalized RIFs

Satisfiability Judgement under Incomplete Information

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