Fuzzy Relations and Fuzzy Functions in Partial Fuzzy Set Theory

Daňková, Martina

doi:10.1007/978-3-319-66830-7_50

Cited by 8 publications

(11 citation statements)

References 9 publications

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“…This paper extends the conference paper [12], which contains a few preliminary results without proofs. It is organized as follows: Sections 2 and 3 briefly summarize basic notions of VFST, most of which have been introduced in [4,17].…”

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confidence: 66%

“…The Sobociński-style family, which treats * as the neutral element. It turns out that these families are rich enough to describe intuitive behaviors of basic partial fuzzy relational and set operations and their properties [12] and consequently also functional partial fuzzy relations. Our notion of functionality (Definition 12 below) stems from the functionality property of fuzzy relations studied by many authors [1, [13][14][15][16].…”

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confidence: 99%

“…A generalization thereof is proposed in agreement with our intuitive expectations, namely, that only defined membership values are important for checking the functionality property and undefined parts are ignored. We also recall the notion of functionality for partial fuzzy relations given in [12] and compare them. The next issue addressed in the area of functional partial fuzzy relations is the study of functionality transmission under set operations and relational compositions.…”

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confidence: 99%

“…Let us identify the lattice order ≤ and the identity = on L with their {0, 1}-valued characteristic functions. Then, we define the following crisp binary relations on L * [12]: = sub subidentity.…”

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confidence: 99%

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Functional Partial Fuzzy Relations

Daňková

2021

Mathematics

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We study fuzzy relations that satisfy the functionality property and that their membership functions can be partial functions. Such fuzzy relations are called partial fuzzy relations, and the variable-domain fuzzy set theory is a framework that provides powerful tools for handling these objects. There, the special operations based on connectives and quantifiers of a partial fuzzy logic are in use. The undefined degrees of membership are carried via those special operations. Furthermore, we show that a suitable combination of these operations leads to a meaningful definition of the functionality property, and we investigate its basic characteristics.

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Functional Partial Fuzzy Relations

Daňková

2021

Mathematics

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“…Recently, investigations of the systems of fuzzy relational equations allowing the appearance of undefined values in the involved fuzzy sets were initiated [4,7]. Partial fuzzy logic which is considered as a generalization of the threevalued logic, and the related partial fuzzy set theory has been established [1][2][3]11]. Several well-known algebras were already generalized in partial fuzzy set theory such as the Bochvar algebra, the Sobociński algebra, the Kleene algebra, or Nelson algebra [2].…”

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confidence: 99%

Sufficient Solvability Conditions for Systems of Partial Fuzzy Relational Equations

Cao

Štěpnička

2020

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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This paper focuses on searching sufficient conditions for the solvability of systems of partial fuzzy relational equations. In the case of solvable systems, we provide solutions of the systems. Two standard systems of fuzzy relational equations -namely the systems built on the basic composition and on the Bandler-Kohout subproduct -are considered under the assumption of partiality. Such an extension requires to employ partial algebras of operations for dealing with undefined values. In this investigation, we consider seven most-known algebras of undefined values in partial fuzzy set theory such as the Bochvar, Bochvar external, Sobociński, McCarthy, Nelson, Kleene, and the Lukasiewicz algebra. Conditions that are sufficient for the solvability of the systems are provided. The crucial role will be played by the so-called boundary condition.

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