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Disjointness of fuzzy coalitions

Milan Mareš, Milan Vlach (2008)

Kybernetika

The cooperative games with fuzzy coalitions in which some players act in a coalition only with a fraction of their total “power” (endeavor, investments, material, etc.) or in which they can distribute their “power” in more coalitions, are connected with some formal or interpretational problems. Some of these problems can be avoided if we interpret each fuzzy coalition as a fuzzy class of crisp coalitions, as shown by Mareš and Vlach in [9,10,11]. The relation between this model of fuzziness and...

Distributive implication groupoids

Ivan Chajda, Radomir Halaš (2007)

Open Mathematics

We introduce a concept of implication groupoid which is an essential generalization of the implication reduct of intuitionistic logic, i.e. a Hilbert algebra. We prove several connections among ideals, deductive systems and congruence kernels which even coincide whenever our implication groupoid is distributive.

Distributivity of ordinal sum implications over overlap and grouping functions

Deng Pan, Hongjun Zhou (2021)

Kybernetika

In 2015, a new class of fuzzy implications, called ordinal sum implications, was proposed by Su et al. They then discussed the distributivity of such ordinal sum implications with respect to t-norms and t-conorms. In this paper, we continue the study of distributivity of such ordinal sum implications over two newly-born classes of aggregation operators, namely overlap and grouping functions, respectively. The main results of this paper are characterizations of the overlap and/or grouping function...

Distributivity of strong implications over conjunctive and disjunctive uninorms

Daniel Ruiz-Aguilera, Joan Torrens (2006)

Kybernetika

This paper deals with implications defined from disjunctive uninorms U by the expression I ( x , y ) = U ( N ( x ) , y ) where N is a strong negation. The main goal is to solve the functional equation derived from the distributivity condition of these implications over conjunctive and disjunctive uninorms. Special cases are considered when the conjunctive and disjunctive uninorm are a t -norm or a t -conorm respectively. The obtained results show a lot of new solutions generalyzing those obtained in previous works when the implications...

Divergence measure between fuzzy sets using cardinality

Vladimír Kobza (2017)

Kybernetika

In this paper we extend the concept of measuring difference between two fuzzy subsets defined on a finite universe. The first main section is devoted to the local divergence measures. We propose a divergence measure based on the scalar cardinalities of fuzzy sets with respect to the basic axioms. In the next step we introduce the divergence based on the generating function and the appropriate distances. The other approach to the divergence measure is motivated by class of the rational similarity...

Divisible ℤ-modules

Yuichi Futa, Yasunari Shidama (2016)

Formalized Mathematics

In this article, we formalize the definition of divisible ℤ-module and its properties in the Mizar system [3]. We formally prove that any non-trivial divisible ℤ-modules are not finitely-generated.We introduce a divisible ℤ-module, equivalent to a vector space of a torsion-free ℤ-module with a coefficient ring ℚ. ℤ-modules are important for lattice problems, LLL (Lenstra, Lenstra and Lovász) base reduction algorithm [15], cryptographic systems with lattices [16] and coding theory [8].

Division schemes under uncertainty of claims

Xianghui Li, Yang Li, Wei Zheng (2021)

Kybernetika

In some economic or social division problems, we may encounter uncertainty of claims, that is, a certain amount of estate has to be divided among some claimants who have individual claims on the estate, and the corresponding claim of each claimant can vary within a closed interval or fuzzy interval. In this paper, we classify the division problems under uncertainty of claims into three subclasses and present several division schemes from the perspective of axiomatizations, which are consistent with...

DMF-algebras: representation and topological characterization

Maurizio Negri (1998)

Bollettino dell'Unione Matematica Italiana

Gli insiemi parziali sono coppie A , B di sottoinsiemi di X , dove A ∩ B ≠ 0 . Gli insiemi parziali su X costituiscono una DMF-algebra, ossia un'algebra di De Morgan in cui la negazione ha un solo punto fisso. Dimostriamo che ogni DMF-algebra è isomorfa a un campo di insiemi parziali. Utilizzando gli insiemi parziali su X come aperti, introduciamo il concetto di spazio topologico parziale su X . Infine associamo ad ogni DMF-algebra A uno spazio topologico parziale i cui clopen compatti costituiscono un campo d'insiemi...

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