Related papers: On lattice-ordered $t_{r}$-norms for type-2 fuzzy …
This paper studies t-norms on the space $\mathbf{L}$ of all normal and convex fuzzy truth values. We first prove that the only non-convolution form type-2 t-norm constructed by Wu et al. satisfies the distributivity law for meet-convolution…
In Type-2 rule-based fuzzy systems (T2 RFSs), triangular norms on complete lattice $(\mathbf{L},\sqsubseteq)$ or $(\mathbf{L_u},\sqsubseteq)$ can be used to model the compositional rule of inference, where $\textbf{L}$ is the set of all…
This paper mainly investigates the distributive laws between extended nullnorms and uninorms on fuzzy truth values under the condition that the nullnorm is conditionally distributive over the uninorm. It presents the distributive laws…
Type-2 fuzzy set (T2 FS) were introduced by Zadeh in 1965, and the membership degrees of T2 FSs are type-1 fuzzy sets (T1 FSs). Owing to the fuzziness of membership degrees, T2 FSs can better model the uncertainty of real life, and thus,…
We present generalization of the Bloom variety theorem of ordered algebras in fuzzy setting. We introduce algebras with fuzzy orders which consist of sets of functions which are compatible with particular binary fuzzy relations called fuzzy…
Traditional scoring approaches on hesitant fuzzy sets often lack a formal base in order theory. This paper proposes a unified framework, where each score is explicitly defined with respect to a given order. This order-oriented perspective…
Rosenfeld defined a fuzzy subgroup of group $G$ as a fuzzy subset of $G$ with two special conditions attached\cite{Rosenfeld1971Fuzzysubgroups}. In this paper, we introduce the fuzzy $t$-norms and vague $t$-norms. The unit interval with a…
The concept of a fuzzy number is generalized to the case of a finite carrier set of partially ordered elements, more precisely, a lattice, when a membership function also takes values in a partially ordered set (a lattice). Zadeh's…
This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…
This paper proves that a binary operation ${\star}$ on ${[0, 1]}$, ensuring that the binary operation ${\curlywedge}$ is a ${t}$-norm or ${\curlyvee}$ is a ${t}$-conorm, is a ${t}$-norm, where ${\curlywedge}$ and ${\curlyvee}$ are special…
This paper constructs a $t_{r}$-norm and a $t_{r}$-conorm on the set of all normal and convex functions from ${[0, 1]}$ to ${[0, 1]}$, which are not obtained by using the following two formulas on binary operations ${\curlywedge}$ and…
To deal with uncertainty in reasoning, interval-valued logic has been developed. But uniform intervals cannot capture the difference in degrees of belief for different values in the interval. To salvage the problem triangular and…
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
In this paper we deal with the problem of extending Zadeh's operators on fuzzy sets (FSs) to interval-valued (IVFSs), set-valued (SVFSs) and type-2 (T2FSs) fuzzy sets. Namely, it is known that seeing FSs as SVFSs, or T2FSs, whose membership…
Let $\Gamma$ be a non-uniform lattice in $SL(2, \mathbb R)$. In this paper, we study various $L^2$-norms of automorphic representations of $SL(2, \mathbb R)$. We bound these norms with intrinsic norms defined on the representation.…
Mediative Fuzzy Logic was conceived as a practical scheme for reconciling hesitant or conflicting assessments in fuzzy control and decision-making. However, its logical and semantic foundations remain underdeveloped, especially beyond…
Soft set theory, introduced by Molodtsov [Molodtsov, D. (1999). Soft set theory-first results. Comput. Math. Appl., 37(4-5), 19-31], provides a flexible framework for managing uncertainty and vagueness, addressing limitations in traditional…
In this paper, we present the fuzzy monoids and vague monoids by using aggregation operators. The unit interval with a $t$-norm or a $t$-conorm is a special monoid, so we mainly talk about fuzzy subsets of monoids. Firstly, the…
The ordinal sum of t-norms on a bounded lattice has been used to construct other t-norms. However, an ordinal sum of binary operations (not necessarily t-norms) defined on the fixed subintervals of a bounded lattice may not be a t-norm.…