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We give a geometrically motivated measure of skewness, define a mean value triangle number, and dispersion (in that order) of a fuzzy number without reference or seeking analogy to the namesake but parallel concepts in probability theory.…
Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is widely used in many real applications. With the desirable property of efficient handling with the uncertain information in decision making, the fuzzy DEMATEL is heavily…
This paper presents a method to measure the similarity between different fuzzy concepts in order to optimize Semantic networks. The problem approached is the minimization of the time of research and identification of user's Objects and…
We introduce the concept of indexed identity, where the usual notion of identity is a particular case. Our mathematical framework allows us a generalized method for `indexing' predicates, which corresponds to `fuzzification' of properties,…
In this paper we maximize a class of functionals under certain constraints. We find sufficient and necessary conditions for these maximizers to exist and be unique. Moreover, we characterize them and discuss the optimality of our results by…
In this paper we provide new several Jackson-type approximations results for continuous fuzzy-number-valued functions which improve several previous ones. We use alternative techniques adapted from Interval Analysis which rely on the…
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…
This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear…
This paper considers a new fuzzy fractional differential variational inequality with integral boundary conditions comprising a fuzzy fractional differential inclusion with integral boundary conditions and a variational inequality in…
This paper enriches preexisting satisfiability tests for unquantified languages, which in turn augment a fragment of Tarski's elementary algebra with unary real functions possessing a continuous first derivative. Two sorts of individual…
We provide a verification and characterization result of optimal maximal sub-solutions of BSDEs in terms of fully coupled forward backward stochastic differential equations. We illustrate the application thereof in utility optimization with…
Value distribution and uniqueness problems of difference operator of an entire function have been investigated in this article. This research shows that a finite ordered entire function $ f $ when sharing a set $ \mathcal{S}=\{\alpha(z),…
Important advances have been made in the fuzzy quantification field. Nevertheless, some problems remain when we face the decision of selecting the most convenient model for a specific application. In the literature, several desirable…
In this paper, systems of linear differential equations with crisp real coefficients and with initial condition described by a vector of fuzzy numbers are studied. A new method based on the geometric representations of linear…
The optimal value function is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the cost/revenue generated while minimizing/maximizing a given function under some…
This paper managed to induce probability theory (sigma system) and possibility theory (max system) respectively from the clearly-defined randomness and fuzziness, while focusing the question why the key axiom of "maxitivity" is adopted for…
Fuzzy relational identification builds a relational model describing systems behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on simplified max-min relational equation.…
Federated Learning (FL) has been becoming a popular interdisciplinary research area in both applied mathematics and information sciences. Mathematically, FL aims to collaboratively optimize aggregate objective functions over distributed…
A new approach for uncertainty management for fuzzy, rule based decision support systems is proposed: The domain expert's knowledge is expressed by a set of rules that frequently refer to vague and uncertain propositions. The certainty of…
A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is…