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A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.
The paper starts from the observation on the complexity of the manipulation of fuzzy processes that increases very rapidly with the extents of the processes representation. Therefore, a productive approach is to divide the problem into…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Using the concept of fuzzy field, we have considered the fuzzy field of real and complex numbers and thereafter we have established a few standard results of real and complex numbers with respect to a membership function.
Most fuzzy systems including fuzzy decision support and fuzzy control systems provide out-puts in the form of fuzzy sets that represent the inferred conclusions. Linguistic interpretation of such outputs often involves the use of linguistic…
We present a procedure to approximate a plane contour by piecewise polynomial functions, depending on various parameters, such as degree, number of local patches, selection of knots. This procedure aims to be adopted to study how…
In this paper, I obtain an $S$-type fuzzy point when two fuzzy numbers for two independent variables and a corresponding fuzzy number for the dependent variable are given. A comprehensive study on a conceptualization of a fuzzy plane as a…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
This contribution introduces the concept of granular F-transform and investigates its basic properties by using the theory of fuzzy numbers and horizontal membership functions. Further, we present a numerical method based on granular…
The conventional clustering algorithms have difficulties in handling the challenges posed by the collection of natural data which is often vague and uncertain. Fuzzy clustering methods have the potential to manage such situations…
This paper presents some concepts of the theory of interactive fuzzy numbers, and mainly, a class of interactive fuzzy numbers, called $f$-correlated fuzzy numbers. We start from the foundations of general fuzzy mathematics and go through…
This article develops an approximate proximal approach for the generalized method of lines. The present results are extensions and applications of previous ones which have been published since 2011, in books and articles such as [3,4,5,6].…
In the paper we define the convergence of compact fuzzy sets as a convergence of alpha-cuts in the topology of compact subsets of a metric space. Furthermore we define typical convergences of fuzzy variables and show relations with…
In this article, we develop a new method to approximate numerically the fractional Laplacian of functions defined on $\mathbb R$, as well as some more general singular integrals. After mapping $\mathbb R$ into a finite interval, we…
This research will present a hybrid approach to accelerate convergence in a second order optimization. An online finite difference approximation of the diagonal Hessian matrix will be introduced, along with fuzzy inferencing of several…
At the first, we revise the Kosinski definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy…
As the deep neural networks are being applied to complex tasks, the size of the networks and architecture increases and their topology becomes more complicated too. At the same time, training becomes slow and at some instances inefficient.…
In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak's model is becoming a…
In this paper, notion of p - norm generalized trapezoidal intuitionistic fuzzy numbers is introduced. A new ranking method is introduced for p - norm generalized trapezoidal intuitionistic fuzzy numbers. Also we consider linear programming…