scholarly journals Neutrosophic Variational Inequalities with Applications in Decision-Making

2021 ◽  
Author(s):  
Muhammad Zeeshan ◽  
Madad Khan ◽  
Suhail Iqbal
Keyword(s):  
Decision Making ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Function ◽  
Convex Set ◽  
Optimization Theory ◽  
Neutrosophic Set ◽  
New Concepts ◽  
General Variational Inequality ◽  
General Convex

Abstract In this paper, we introduced some new concepts of a neutrosophic set such as neutrosophic convex set, strongly neutrosophic convex set, neutrosophic convex function, strongly neutrosophic convex function, the minimum and maximum of a function f with respect to neutrosophic set, min and max neutrosophic variational inequality, neutrosophic general convex set, neutrosophic general convex function and min, max neutrosophic general variational inequality. We introduced some basic results on these new concepts. Moreover, we discussed the application of neutrosophic set in optimization theory. We developed an algorithm using neutrosophic min and max variational inequality and identified the maximum and minimum profit of the company.

scholarly journals Solution existence of general variational inequalities and coincidence points

2014 ◽  
Vol 30 (1) ◽  
pp. 15-22
Author(s):  
ALIREZA AMINI-HARANDI ◽  
◽  
SZILARD LASZLO ◽  
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Simple Technique ◽  
Coincidence Point ◽  
Existence Results ◽  
Solution Existence ◽  
Coincidence Points ◽  
General Variational Inequality ◽  
General Variational Inequalities

In this paper, by using a simple technique, we obtain several existence results of the solutions for general variational inequalities of Stampacchia type. We also show, that the existence of a coincidence point of two mappings is equivalent to the existence of the solution of a particular general variational inequality of Stampacchia type. As applications several coincidence and fixed point results are obtained.

scholarly journals Iterative Algorithms Approach to Variational Inequalities and Fixed Point Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yeong-Cheng Liou ◽  
Yonghong Yao ◽  
Chun-Wei Tseng ◽  
Hui-To Lin ◽  
Pei-Xia Yang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Nonexpansive Mapping ◽  
Nonlinear Operator ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Solution Set ◽  
Point Problem ◽  
General Variational Inequality

We consider a general variational inequality and fixed point problem, which is to find a pointx*with the property that (GVF):x*∈GVI(C,A)andg(x*)∈Fix(S)whereGVI(C,A)is the solution set of some variational inequalityFix(S)is the fixed points set of nonexpansive mappingS, andgis a nonlinear operator. Assume the solution setΩof (GVF) is nonempty. For solving (GVF), we suggest the following methodg(xn+1)=βg(xn)+(1-β)SPC[αnF(xn)+(1-αn)(g(xn)-λAxn)],n≥0. It is shown that the sequence{xn}converges strongly tox*∈Ωwhich is the unique solution of the variational inequality〈F(x*)-g(x*),g(x)-g(x*)〉≤0, for allx∈Ω.

scholarly journals Existence conditions in general quasimonotone variational inequalities

2005 ◽  
Vol 71 (2) ◽  
pp. 285-303 ◽  
Author(s):  
D. Aussel ◽  
D. T. Luc
Keyword(s):  
Variational Inequality ◽  
Contact Problem ◽  
Variational Inequalities ◽  
Vector Space ◽  
Topological Vector Space ◽  
Equilibrium Problems ◽  
Existence Of Solutions ◽  
Quasimonotone Operators ◽  
General Variational Inequality ◽  
Existence Conditions

In this paper we study a general variational inequality model with set-valued quasimonotone operators, a model which includes several variational inequalities and equilibrium problems. We establish unifying conditions for existence of solutions in a topological vector space setting. Applications to parametric equilibrium models and to a contact problem are given.

scholarly journals On well-posedness associated with a class of controlled variational inequalities

2021 ◽  
Author(s):  
Savin Treanta ◽  
Shalini Jha
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Integral Functional ◽  
Solution Set ◽  
Variational Inequality Problems ◽  
Well Posedness ◽  
New Concepts ◽  
Curvilinear Integral ◽  
Theoretical Developments

In this paper, by using the new concepts of monotonicity, pseudomonotonicity and hemicontinuity associated with the considered curvilinear integral functional, we investigate the well-posedness and well-posedness in generalized sense for a class of controlled variational inequality problems. More precisely, by introducing the approximating solution set of the considered class of controlled variational inequality problems, we formulate and prove some characterization results on well-posedness and well-posedness in generalized sense. Also, the theoretical developments presented in the paper are accompanied by illustrative examples.

scholarly journals On a Class of Differential Variational Inequalities in Infinite-Dimensional Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 266 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Optimal Control Theory ◽  
Infinite Dimensional ◽  
Nash Games ◽  
New Class ◽  
Set Valued Mappings ◽  
Differential Variational Inequalities ◽  
Theoretical Developments

A new class of differential variational inequalities (DVIs), governed by a variational inequality and an evolution equation formulated in infinite-dimensional spaces, is investigated in this paper. More precisely, based on Browder’s result, optimal control theory, measurability of set-valued mappings and the theory of semigroups, we establish that the solution set of DVI is nonempty and compact. In addition, the theoretical developments are accompanied by an application to differential Nash games.

Renewable energy selection based on a new entropy and dissimilarity measure on an interval-valued neutrosophic set

2021 ◽  
pp. 1-18
Author(s):  
ShuoYan Chou ◽  
Truong ThiThuy Duong ◽  
Nguyen Xuan Thao
Keyword(s):  
Decision Making ◽  
Renewable Energy ◽  
Membership Function ◽  
Fossil Fuels ◽  
Multiple Criteria Decision Making ◽  
Clean Energy ◽  
Dissimilarity Measure ◽  
Neutrosophic Set ◽  
Trade Offs ◽  
And Performance

Energy plays a central part in economic development, yet alongside fossil fuels bring vast environmental impact. In recent years, renewable energy has gradually become a viable source for clean energy to alleviate and decouple with a negative connotation. Different types of renewable energy are not without trade-offs beyond costs and performance. Multiple-criteria decision-making (MCDM) has become one of the most prominent tools in making decisions with multiple conflicting criteria existing in many complex real-world problems. Information obtained for decision making may be ambiguous or uncertain. Neutrosophic is an extension of fuzzy set types with three membership functions: truth membership function, falsity membership function and indeterminacy membership function. It is a useful tool when dealing with uncertainty issues. Entropy measures the uncertainty of information under neutrosophic circumstances which can be used to identify the weights of criteria in MCDM model. Meanwhile, the dissimilarity measure is useful in dealing with the ranking of alternatives in term of distance. This article proposes to build a new entropy and dissimilarity measure as well as to construct a novel MCDM model based on them to improve the inclusiveness of the perspectives for decision making. In this paper, we also give out a case study of using this model through the process of a renewable energy selection scenario in Taiwan performed and assessed.

A framework of decision making based on bipolar fuzzy competition hypergraphs

2021 ◽  
pp. 1-21
Author(s):  
Sundas Shahzadi ◽  
Areen Rasool ◽  
Musavarah Sarwar ◽  
Muhammad Akram
Keyword(s):  
Biological Sciences ◽  
Decision Making ◽  
Comparative Analysis ◽  
Social Networking ◽  
Real World ◽  
Fuzzy Models ◽  
New Concepts ◽  
Proposed Model ◽  
Business Market ◽  
Strength Of Competition

Bipolarity plays a key role in different domains such as technology, social networking and biological sciences for illustrating real-world phenomenon using bipolar fuzzy models. In this article, novel concepts of bipolar fuzzy competition hypergraphs are introduced and discuss the application of the proposed model. The main contribution is to illustrate different methods for the construction of bipolar fuzzy competition hypergraphs and their variants. Authors study various new concepts including bipolar fuzzy row hypergraphs, bipolar fuzzy column hypergraphs, bipolar fuzzy k-competition hypergraphs, bipolar fuzzy neighborhood hypergraphs and strong hyperedges. Besides, we develop some relations between bipolar fuzzy k-competition hypergraphs and bipolar fuzzy neighborhood hypergraphs. Moreover, authors design an algorithm to compute the strength of competition among companies in business market. A comparative analysis of the proposed model is discuss with the existing models such bipolar fuzzy competition graphs and fuzzy competition hypergraphs.

scholarly journals Multistep Hybrid Extragradient Method for Triple Hierarchical Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Zhao-Rong Kong ◽  
Lu-Chuan Ceng ◽  
Qamrul Hasan Ansari ◽  
Chin-Tzong Pang
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Variational Inequality Problem ◽  
Extragradient Method ◽  
Fixed Point Set ◽  
Inequality Problem ◽  
Hybrid Extragradient Method ◽  
Point Set ◽  
Hierarchical Variational Inequalities

We consider a triple hierarchical variational inequality problem (THVIP), that is, a variational inequality problem defined over the set of solutions of another variational inequality problem which is defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Moreover, we propose a multistep hybrid extragradient method to compute the approximate solutions of the THVIP and present the convergence analysis of the sequence generated by the proposed method. We also derive a solution method for solving a system of hierarchical variational inequalities (SHVI), that is, a system of variational inequalities defined over the intersection of the fixed point set of a strict pseudocontractive mapping and the solution set of the classical variational inequality problem. Under very mild conditions, it is proven that the sequence generated by the proposed method converges strongly to a unique solution of the SHVI.

scholarly journals An Extended VIKOR Method for Multiple Criteria Group Decision Making with Triangular Fuzzy Neutrosophic Numbers

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 497 ◽  
Author(s):  
Jie Wang ◽  
Guiwu Wei ◽  
Mao Lu
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Multiple Criteria ◽  
New Method ◽  
Neutrosophic Set ◽  
Technology Commercialization ◽  
Vikor Method ◽  
Calculating Method ◽  
Potential Evaluation

In this article, we combine the original VIKOR model with a triangular fuzzy neutrosophic set to propose the triangular fuzzy neutrosophic VIKOR method. In the extended method, we use the triangular fuzzy neutrosophic numbers (TFNNs) to present the criteria values in multiple criteria group decision making (MCGDM) problems. Firstly, we summarily introduce the fundamental concepts, operation formulas and distance calculating method of TFNNs. Then we review some aggregation operators of TFNNs. Thereafter, we extend the original VIKOR model to the triangular fuzzy neutrosophic environment and introduce the calculating steps of the TFNNs VIKOR method, our proposed method which is more reasonable and scientific for considering the conflicting criteria. Furthermore, a numerical example for potential evaluation of emerging technology commercialization is presented to illustrate the new method, and some comparisons are also conducted to further illustrate advantages of the new method.

scholarly journals An Interior Projected-Like Subgradient Method for Mixed Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Guo-ji Tang ◽  
Xing Wang
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Subgradient Method ◽  
Mixed Variational Inequality ◽  
Convergence Estimate ◽  
Finite Dimensional ◽  
Mixed Variational Inequalities

An interior projected-like subgradient method for mixed variational inequalities is proposed in finite dimensional spaces, which is based on using non-Euclidean projection-like operator. Under suitable assumptions, we prove that the sequence generated by the proposed method converges to a solution of the mixed variational inequality. Moreover, we give the convergence estimate of the method. The results presented in this paper generalize some recent results given in the literatures.

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