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Fuzzy weighted average as a fuzzified aggregation operator and its properties

Ondřej Pavlačka, Martina Pavlačková, Vladislav Hetfleiš (2017)

Kybernetika

The weighted average is a well-known aggregation operator that is widely applied in various mathematical models. It possesses some important properties defined for aggregation operators, like monotonicity, continuity, idempotency, etc., that play an important role in practical applications. In the paper, we reveal whether and in which way such properties can be observed also for the fuzzy weighted average operator where the weights as well as the weighted values are expressed by noninteractive fuzzy...

Fuzzy-valued integrals based on a constructive methodology

Hsien-Chung Wu (2007)

Applications of Mathematics

The procedures for constructing a fuzzy number and a fuzzy-valued function from a family of closed intervals and two families of real-valued functions, respectively, are proposed in this paper. The constructive methodology follows from the form of the well-known “Resolution Identity” (decomposition theorem) in fuzzy sets theory. The fuzzy-valued measure is also proposed by introducing the notion of convergence for a sequence of fuzzy numbers. Under this setting, we develop the fuzzy-valued integral...

G δ -separation axioms in ordered fuzzy topological spaces

Elango Roja, Mallasamudram Kuppusamy Uma, Ganesan Balasubramanian (2007)

Kybernetika

G δ -separation axioms are introduced in ordered fuzzy topological spaces and some of their basic properties are investigated besides establishing an analogue of Urysohn’s lemma.

Games with creatures

Saharon Shelah, Jindřich Zapletal (2003)

Commentationes Mathematicae Universitatis Carolinae

Many forcing notions obtained using the creature technology are naturally connected with certain integer games.

Gaps in analytic quotients

Stevo Todorčević (1998)

Fundamenta Mathematicae

We prove that the quotient algebra P(ℕ)/I over any analytic ideal I on ℕ contains a Hausdorff gap.

Generalized Choquet spaces

Samuel Coskey, Philipp Schlicht (2016)

Fundamenta Mathematicae

We introduce an analog to the notion of Polish space for spaces of weight ≤ κ, where κ is an uncountable regular cardinal such that κ < κ = κ . Specifically, we consider spaces in which player II has a winning strategy in a variant of the strong Choquet game which runs for κ many rounds. After discussing the basic theory of these games and spaces, we prove that there is a surjectively universal such space and that there are exactly 2 κ many such spaces up to homeomorphism. We also establish a Kuratowski-like...

Generalized convexities related to aggregation operators of fuzzy sets

Susana Díaz, Esteban Induráin, Vladimír Janiš, Juan Vicente Llinares, Susana Montes (2017)

Kybernetika

We analyze the existence of fuzzy sets of a universe that are convex with respect to certain particular classes of fusion operators that merge two fuzzy sets. In addition, we study aggregation operators that preserve various classes of generalized convexity on fuzzy sets. We focus our study on fuzzy subsets of the real line, so that given a mapping F : [ 0 , 1 ] × [ 0 , 1 ] [ 0 , 1 ] , a fuzzy subset, say X , of the real line is said to be F -convex if for any x , y , z such that x y z , it holds that μ X ( y ) F ( μ X ( x ) , μ X ( z ) ) , where μ X : [ 0 , 1 ] stands here for the membership function...

Generalized E-algebras via λ-calculus I

Rüdiger Göbel, Saharon Shelah (2006)

Fundamenta Mathematicae

An R-algebra A is called an E(R)-algebra if the canonical homomorphism from A to the endomorphism algebra E n d R A of the R-module R A , taking any a ∈ A to the right multiplication a r E n d R A by a, is an isomorphism of algebras. In this case R A is called an E(R)-module. There is a proper class of examples constructed in [4]. E(R)-algebras arise naturally in various topics of algebra. So it is not surprising that they were investigated thoroughly in the last decades; see [3, 5, 7, 8, 10, 13, 14, 15, 18, 19]. Despite...

Generalized projections of Borel and analytic sets

Marek Balcerzak (1996)

Colloquium Mathematicae

For a σ-ideal I of sets in a Polish space X and for A ⊆ X 2 , we consider the generalized projection (A) of A given by (A) = x ∈ X: Ax ∉ I, where A x =y ∈ X: 〈x,y〉∈ A. We study the behaviour of with respect to Borel and analytic sets in the case when I is a 2 0 -supported σ-ideal. In particular, we give an alternative proof of the recent result of Kechris showing that [ 1 1 ( X 2 ) ] = 1 1 ( X ) for a wide class of 2 0 -supported σ-ideals.

Generalized version of the compatibility theorem. Two examples.

Carlo Bertoluzza, Antonella Bodini (1996)

Mathware and Soft Computing

In a previous work ([3]) we proved that the Nguyen's condition for [f(tilde-A)]α to be equal to f(Aα) also holds for the most general class of the L-fuzzy subsets, where L is an arbitrary lattice. Here we recall the main points of the proof ad present some examples ralated to non-linear lattices.

Generated triangular norms

Erich Peter Klement, Radko Mesiar, Endre Pap (2000)

Kybernetika

An overview of generated triangular norms and their applications is presented. Several properties of generated t -norms are investigated by means of the corresponding generators, including convergence properties. Some applications are given. An exhaustive list of relevant references is included.

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