Fuzzy Sets and Systems

As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let Y be a non-degenerate compact convex subset of the n-dimensional Euclidean space, and let FS z 0 ( Y ) be the family consisting ...

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. In this paper, we extend monadic MV-algebras with a state operator that describes ...

In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, G, as well as its extension G Δ associated with first-order relational languages enjoy the Craig interpolation property. These results partially ...

Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture ...

• 2D language is a collection of all rectangular pictures.
• 2D FCFL reduces the uncertainty of color scale of the pixel in pictures.
• Presented closure properties of 2D FCFLs.
• Discussed applications of 2D FCFL in formation of ...

In this article, we modify the product structure and turn it into the so-called ε-truncated product structure I ε, for any ε ∈ ( 0 , 1 ). The new structure keeps the property of being a complete residuated lattice, and additionally, its semiring ...

In this note we show that pseudo-analysis tools can be effective in obtaining results in a distorted probability framework. More precisely, we introduce the notion of pseudo-independence and that of pseudo-moment generating function, the latter ...

Fuzzy implications and coimplications play important roles in both theoretic and applied communities of fuzzy set theory. In this paper, we provide a unified framework for fuzzy implications and coimplications. Specifically, firstly, we introduce ...

Effective communication among autonomous agents is crucial for coordination and solving complex tasks within multi-agent systems. To formalize interactions between agents, social accessibility relations are often utilized. Current research ...

In the first part of this paper, we have considered: a) generalized credal sets on the powerset of a finite set X; b) their general definition allowing a generalized credal set to be not convex; c) the justification of basic aggregation rules on ...

Explicit formulas for t-conorms constructed by the sum of ranges of discrete additive generators of t-conorms are introduced.