Some notes on the category of fuzzy implications on bounded lattices

Amin Yousefi; Mashaallah Mashinchi; Radko Mesiar

Displaying similar documents to “Some notes on the category of fuzzy implications on bounded lattices”

Complete subobjects of fuzzy sets over $M V$ -algebras

Jiří Močkoř (2004)

Czechoslovak Mathematical Journal

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A subobjects structure of the category $Ω$ - of $Ω$ -fuzzy sets over a complete $M V$ -algebra $Ω = (L, \land, \lor, \otimes, \to)$ is investigated, where an $Ω$ -fuzzy set is a pair $𝐀 = (A, δ)$ such that $A$ is a set and $δ A \times A \to Ω$ is a special map. Special subobjects (called complete) of an $Ω$ -fuzzy set $𝐀$ which can be identified with some characteristic morphisms $𝐀 \to Ω^{*} = (L \times L, μ)$ are then investigated. It is proved that some truth-valued morphisms $\neg_{Ω} Ω^{*} \to Ω^{*}, \cap_{Ω}$ , $\cup_{Ω} Ω^{*} \times Ω^{*} \to Ω^{*}$ are characteristic morphisms of complete subobjects.

Some Remarks on the Category Set(l), Part II

Sergey. A. Solovyov (2003)

Matematički Vesnik

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Information systems in categories of valued relations.

Vladimir B. Gisin (1994)

Mathware and Soft Computing

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The paper presents a categorical version of the notion of information system due to D. Scott. The notion of information system is determined in the framework of ordered categories with involution and division and the category of information systems is constructed. The essential role in all definitions and constructions play correlations between inclusion relations and entailment relations.

Extensional subobjects in categories of $Ω$ -fuzzy sets

Jiří Močkoř (2007)

Czechoslovak Mathematical Journal

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Two categories $𝕊𝕖𝕥 (Ω)$ and $𝕊𝕖𝕥𝔽 (Ω)$ of fuzzy sets over an $M V$ -algebra $Ω$ are investigated. Full subcategories of these categories are introduced consisting of objects $(s u b (A, δ)$ , $σ)$ , where $s u b (A, δ)$ is a subset of all extensional subobjects of an object $(A, δ)$ . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

The study on semicopula based implications

Zuming Peng (2020)

Kybernetika

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Recently, Baczyński et al. (2017) proposed a new family of implication operators called semicopula based implications, which combines a given a priori fuzzy implication and a semicopula. In this paper, firstly, the relationship between the basic properties of the priori fuzzy implication and the semicopula based implication are analyzed. Secondly, the conditions such that the semicopula based implication is a fuzzy implication are studied, the study is carried out mainly in the case...

The convergence of the core of a fuzzy exchange economy

Xia Zhang, Hao Sun, Moses Olabhele Esangbedo, Xuanzhu Jin (2021)

Kybernetika

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This paper focuses on a new model called fuzzy exchange economy (FXE), which integrates fuzzy consumption, fuzzy initial endowment and the agent’s fuzzy preference (vague attitude) in the fuzzy consumption set. Also, the existence of the fuzzy competitive equilibrium for the FXE is verified through a related pure exchange economy. We define a core-like concept (called weak fuzzy core) of the FXE and prove that any fuzzy competitive allocation belongs to the weak fuzzy core. The fuzzy...

Intuitionistic $H$ -fuzzy relations.

Hur, Kul, Jang, Su Youn, Kang, Hee Won (2005)

International Journal of Mathematics and Mathematical Sciences

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Extensions of fuzzy connectives on ACDL

Hui Liu, Bin Zhao (2019)

Kybernetika

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The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend...