On minimal sets of graded attribute implications

Vychodil, Vilém

doi:10.1016/j.ins.2014.09.059

Cited by 4 publications

(2 citation statements)

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“…In fact, for * being the globalization, (17) translates into (14). In [53], a criterion for minimality of a general set of FAIs for * being the globalization is described.…”

Section: Preliminariesmentioning

confidence: 99%

On sets of graded attribute implications with witnessed non-redundancy

Vychodil

2016

Information Sciences

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We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications are show that bases of graded attribute implications given by systems of pseudo-intents correspond to non-redundant sets of graded attribute implications with saturated consequents where the non-redundancy is witnessed by antecedents of the contained graded attribute implications. We introduce an algorithm which transforms any complete set of graded attribute implications parameterized by globalization into a base given by pseudo-intents. Experimental evaluation is provided to compare the method of obtaining bases for general parameterizations by hedges with earlier graph-based approaches

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“…In fact, for * being the globalization, (17) translates into (14). In [53], a criterion for minimality of a general set of FAIs for * being the globalization is described.…”

Section: Preliminariesmentioning

confidence: 99%

On sets of graded attribute implications with witnessed non-redundancy

Vychodil

2016

Information Sciences

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“…Theory is called redundant whenever there is ⊂ such that ≡ ; otherwise is called non-redundant. Theory is called minimal [42] whenever for each such that ≡ , we have | | ≤ | |. One of the basic properties of non-redundant sets of graded attribute implications is the following: is…”

Section: Remarkmentioning

confidence: 99%

Computing sets of graded attribute implications with witnessed non-redundancy

Vychodil

2016

Information Sciences

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a b s t r a c tIn this paper we extend our previous results on sets of graded attribute implications with witnessed non-redundancy. We assume finite residuated lattices as structures of truth degrees and use arbitrary idempotent truth-stressing linguistic hedges as parameters which influence the semantics of graded attribute implications. In this setting, we introduce algorithm which transforms any set of graded attribute implications into an equivalent nonredundant set of graded attribute implications with saturated consequents whose nonredundancy is witnessed by antecedents of the formulas. As a consequence, we solve the open problem regarding the existence of general systems of pseudo-intents which appear in formal concept analysis of object-attribute data with graded attributes and linguistic hedges. Furthermore, we show a polynomial-time procedure for determining bases given by general systems of pseudo-intents from sets of graded attribute implications which are complete in data.

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