An Optimal Algorithm for a Fuzzy Transportation Problem

This paper deals with the optimal approximate solution to a special type of optimization problem called a fuzzy transportation problem using pentagonal fuzzy numbers. The values of the cost, supply, and demand for fuzzy transportation problems are taken as pentagonal fuzzy numbers. The pentagonal fuzzy numbers are converted into crisp values using a novel suggested ranking function. By comparing this with the conventional ranking methods, we can achieve better results with the aid of the proposed new ranking method. Vogel’s Approximation Method is then applied to obtain the solution. Several experiments have been conducted in order to investigate the suggested technique.

Determining Fuzzy Distance between Sets by Application of Fixed Point Technique Using Weak Contractions and Fuzzy Geometric Notions

In the present paper, we solve the problem of determining the fuzzy distance between two subsets of a fuzzy metric space. We address the problem by reducing it to the problem of finding an optimal approximate solution of a fixed point equation. This approach is well studied for the corresponding problem in metric spaces and is known as proximity point problem. We employ fuzzy weak contractions for that purpose. Fuzzy weak contraction is a recently introduced concept intermediate to a fuzzy contraction and a fuzzy non-expansive mapping. Fuzzy versions of some geometric properties essentially belonging to Hilbert spaces are considered in the main theorem. We include an illustrative example and two corollaries, one of which comes from a well-known fixed point theorem. The illustrative example shows that the main theorem properly includes its corollaries. The work is in the domain of fuzzy global optimization by use of fixed point methods.

Optimal Approximate Solution of Coincidence Point Equations in Fuzzy Metric Spaces

The purpose of this paper is to introduce α f -proximal H -contraction of the first and second kind in the setup of complete fuzzy metric space and to obtain optimal coincidence point results. The obtained results unify, extend and generalize various comparable results in the literature. We also present some examples to support the results obtained herein.

Global Optimization for Quasi-Noncyclic Relatively Nonexpansive Mappings with Application to Analytic Complex Functions

The purpose of this article is to resolve a global optimization problem for quasi-noncyclic relatively nonexpansive mappings by giving an algorithm that determines an optimal approximate solution of the following minimization problem, min x ∈ A d ( x , T x ) , min y ∈ B d ( y , T y ) and min ( x , y ) ∈ A × B d ( x , y ) ; also, we provide some illustrative examples to support our results. As an application, the existence of a solution of the analytic complex function is discussed.

An inverse eigenproblem for generalized reflexive matrices with normal $k+1$-potencies

Let $P,~Q\in\mathbb{C}^{n\times n}$ be two normal $\{k+1\}$-potent matrices, i.e., $PP^{*}=P^{*}P,~P^{k+1}=P$, $QQ^{*}=Q^{*}Q,~Q^{k+1}=Q$, $k\in\mathbb{N}$. A matrix $A\in\mathbb{C}^{n\times n}$ is referred to as generalized reflexive with two normal $\{k+1\}$-potent matrices $P$ and $Q$ if and only if $A=PAQ$. The set of all $n\times n$ generalized reflexive matrices which rely on the matrices $P$ and $Q$ is denoted by $\mathcal{GR}^{n\times n}(P,Q)$. The left and right inverse eigenproblem of such matrices ask from us to find a matrix $A\in\mathcal{GR}^{n\times n}(P,Q)$ containing a given part of left and right eigenvalues and corresponding left and right eigenvectors. In this paper, first necessary and sufficient conditions such that the problem is solvable are obtained. A general representation of the solution is presented. Then an expression of the solution for the optimal Frobenius norm approximation problem is exploited. A stability analysis of the optimal approximate solution, which has scarcely been considered in existing literature, is also developed.

Optimization of Tour Line Structure Flow Assignment Model: Based on Resort Environment Pressure

To set up a resort’s equilibrium tourist flow assignment model, the tour line features of the tourists are considered. This model firstly initiates a tourist equilibrium distribution model for the resort and then gets an optimal approximate solution when a tourist group reaches a certain scale. Next, the resort’s tourist equilibrium shunting model is built and an optimal approximate solution is provided from the present resort tourist distribution. By analyzing the results, it is found that this model is able to realize the resort’s dynamic shunting steadily, to effectively lower the resort’s congestion and to reduce the ecological environment pressure.