Related papers: Rules and Algorithms for Objective Construction of…
In this article, we introduce a differentiability concept for fuzzy functions $\tilde{f}: F(\mathbb{R}) \to F(\mathbb{R})$, where $F(\mathbb{R})$ is the set of all fuzzy numbers. With the help of the proposed differentiability notion, we…
The approach described here allows using membership function to represent imprecise and uncertain knowledge by learning in Fuzzy Semantic Networks. This representation has a great practical interest due to the possibility to realize on the…
In this article, we have introdued D-fuzzy sets. We have discussed the notions of inclusion, union, intersection, complementation and convexity of such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy sets.
In this work we propose a formal system for fuzzy algebraic reasoning. The sequent calculus we define is based on two kinds of propositions, capturing equality and existence of terms as members of a fuzzy set. We provide a sound semantics…
Fuzzy rule-based systems have been mostly used in interpretable decision-making because of their interpretable linguistic rules. However, interpretability requires both sensible linguistic partitions and small rule-base sizes, which are not…
In this paper, we give a constructive method for linear extensions of Zadeh's fuzzy orders. We also characterize Zadeh's fuzzy orders by their linear extensions.
This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular…
In this paper we establish a link between fuzzy and preferential semantics for description logics and Self-Organising Maps, which have been proposed as possible candidates to explain the psychological mechanisms underlying category…
After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying…
For any fixed dimension $d \geq 3$ we construct a Nikodym set in $F_q^d$ of cardinality $q^d - (\frac{d-2}{\log 2} +1+o(1)) q^{d-1} \log q$ in the limit $q \to \infty$, when $q$ is an odd prime power. This improves upon the naive random…
In a previous article the authors determined the best-known upper bound for the cardinality of the image set for several classes of functions, including planar functions. Here, we show that the upper bound cannot be tight for planar…
Maji et al. introduced in 2002 a method of parametric decision making using soft sets as tools and representing their tabular form as a binary matrix. In cases, however, where some or all of the parameters used for the characterization of…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
Interpretability is the next frontier in machine learning research. In the search for white box models - as opposed to black box models, like random forests or neural networks - rule induction algorithms are a logical and promising option,…
Four constructions result from a desire to create enhancements to Cantor's infinite real set cardinality. Each continues to keep Cantor's cardinality formulation in place while providing new comparisons of arbitrary infinite sets. To…
Time series clustering is a central machine learning task with applications in many fields. While the majority of the methods focus on real-valued time series, very few works consider series with discrete response. In this paper, the…
Fuzzy implication functions are one of the most important operators used in the fuzzy logic framework. While their flexible definition allows for diverse families with distinct properties, this variety needs a deeper theoretical…
This is a major update of the previous version. The methods of the paper are now fully constructive and the style is "formalization ready" with the emphasis on the possibility of formalization both in type theory and in constructive set…
The combination of higher-order theories and fuzzy logic can be useful in decision-making tasks that involve reasoning across abstract functions and predicates, where exact matches are often rare or unnecessary. Developing efficient…