Related papers: n-ary Fuzzy Logic and Neutrosophic Logic Operators
In this study we follow a new framework for the theory that offers us, other than traditional, a new angle to observe and investigate some relations between finite sets, F-lattice L and their elements. The theory is based on the Fuzzy…
Fuzzy sets are the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling. Numerous works now combine fuzzy concepts with other scientific disciplines…
Fuzzy implication functions constitute fundamental operators in fuzzy logic systems, extending classical conditionals to manage uncertainty in logical inference. Among the extensive families of these operators, generalizations of the…
Standard dense retrievers lack a native calculus for multi-atom logical constraints. We introduce Neuro-Symbolic Fuzzy Logic (NSFL), a framework that adapts formal t-norms and t-conorms to neural embedding spaces without requiring…
We formulate and prove logical characterizations of crisp simulations and crisp directed simulations between fuzzy labeled transition systems with respect to fuzzy modal logics that use a general t-norm-based semantics. The considered…
We introduce the concept of a fuzzy aura topological space $(X, \tilde{\tau}, \tilde{a})$, obtained by equipping a Chang-type fuzzy topological space $(X, \tilde{\tau})$ with a fuzzy scope function $\tilde{a} : X \to \tilde{\tau}$…
Within the possibilistic approach to uncertainty modeling, the paper presents a modal logical system to reason about qualitative (comparative) statements of the possibility (and necessity) of fuzzy propositions. We relate this qualitative…
This article presents a theory of differential and integral calculus for mapping between Banach spaces formed by subsets of fuzzy numbers called A-linearly correlated fuzzy numbers, where both the domain and codomain are spaces composed of…
This book, in order to generalize the two models of fuzzy cognitive maps and neutrosophic cognitive maps, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe…
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…
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…
A new concept of a multi-valued associative memory is introduced, generalizing a similar one in fuzzy neural networks. We expand the results on fuzzy associative memory with thresholds, to the case of a multi-valued one: we introduce the…
Fractional differential (and difference) operators play a role in a number of diverse settings: integrable systems, mirror symmetry, Hurwitz numbers, the Bethe ansatz equations. We prove extensions of the three major results on algebras of…
Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy…
In this paper, we reduce the electromagnetic theory to future null infinity and obtain a vector theory at the boundary. We compute the Poincar\'e flux operators which could be generalized. We quantize the vector theory, and impose normal…
The introduction of Fuzzy Relational Equations (FREs) has made problems that were unsolvable using algebraic linear equations into solvable ones. FREs have been applied to problemsin medicine, industry, transportation and all types of…
In this book, for the first time we introduce the notion of neutrosophic algebraic structures for groups, loops, semigroups and groupoids; and also their neutrosophic N-algebraic structures. One is fully aware of the fact that many…
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
In various contexts in mathematical physics one needs to compute the logarithm of a positive unbounded operator. Examples include the von Neumann entropy of a density matrix and the flow of operators with the modular Hamiltonian in the…