Matrix Game with Payoffs Represented by Triangular Dual Hesitant Fuzzy Numbers

Matrix Game with Payoffs RepresentedDue to the complexity of information or the inaccuracy of decision-makers’ cognition, it is difficult for experts to quantify the information accurately in the decision-making process. However, the integration of the fuzzy set and game theory provides a way to help decision makers solve the problem. This research aims to develop a methodology for solving matrix game with payoffs represented by triangular dual hesitant fuzzy numbers (TDHFNs). First, the definition of TDHFNs with their cut sets are presented. The inequality relations between two TDHFNs are also introduced. Second, the matrix game with payoffs represented by TDHFNs is investigated. Moreover, two TDHFNs programming models are transformed into two linear programming models to obtain the numerical solution of the proposed fuzzy matrix game. Furthermore, a case study is given to to illustrate the efficiency and applicability of the proposed methodology. Our results also demonstrate the advantage of the proposed concept of TDHFNs

(R1976) A Novel Approach to Solve Fuzzy Rough Matrix Game with Two Players

This paper proposes a new method for solving a two-person zero-sum fuzzy matrix game with goals, payoffs, and decision variables represented as triangular fuzzy rough numbers. We created a pair of fully fuzzy rough linear programming problems for players. Triangular fuzzy rough numbers can be used to formulate two fuzzy linear programming problems for the first player in the form of upper approximation intervals and lower approximation intervals. Two problems for the second player can be created in the same way. These problems have been split into five sub-crisp problems for the player first and five sub-crisp problems for the player second. The solution to the game can be obtained by solving these ten fuzzy linear programming problems. To demonstrate the method, a numerical example is provided. Using Wolfram Cloud, optimal strategies and game values are calculated for various parameters. Sensitivity analysis is carried out by altering the values of parameters

Advancing the state of the art in the modelling and simulation of information systems evaluation

It is widely accepted that Information Systems Evaluation (ISE) is a powerful and useful technique that can be used to assess IT/IS investments in an a-priori or a-posteriori sense. Traditional approaches to ISE have tended to centre upon financial and management accounting frameworks, seeking to reconcile tangible and intangible costs, benefits, risks and value factors. Such techniques, however, do not provide the IS researcher or practitioner with further insight or appreciation of any inherent and implicit inter-relationships, in the investment justification process. Thus, this paper outlines and discusses via a taxonomy and resulting classification, alternative and complementary approaches that can be applied to ISE from the fields of Artificial Intelligence (AI), Operational Research (OR) and Management Science (MS). The paper subsequently concludes that such approaches can be potentially used by researchers and practitioners in the field, as a basis for carrying out further research in the field of applied ISE

Fuzzy decision making system and the dynamics of business games

Effective and efficient strategic decision making is the backbone for the success of a business organisation among its competitors in a particular industry. The results of these decision making processes determine whether the business will continue to survive or not. In this thesis, fuzzy logic (FL) concepts and game theory are being used to model strategic decision making processes in business organisations. We generally modelled competition by business organisations in industries as games where each business organization is a player. A player formulates his own decisions by making strategic moves based on uncertain information he has gained about the opponents. This information relates to prevailing market demand, cost of production, marketing, consolidation efforts and other business variables. This uncertain information is being modelled using the concept of fuzzy logic. In this thesis, simulation experiments were run and results obtained in six different settings. The first experiment addresses the payoff of the fuzzy player in a typical duopoly system. The second analyses payoff in an n-player game which was used to model a perfect market competition with many players. It is an extension of the two-player game of a duopoly market which we considered in the first experiment. The third experiment used and analysed real data of companies in a case study. Here, we chose the competition between Coca-cola and PepsiCo companies who are major players in the beverage industry. Data were extracted from their published financial statements to validate our experiment. In the fourth experiment, we modelled competition in business networks with uncertain information and varying level of connectivity. We varied the level of interconnections (connectivity) among business units in the business networks and investigated how missing links affect the payoffs of players on the networks. We used the fifth experiment to model business competition as games on boards with possible constraints or restrictions and varying level of connectivity on the boards. We also investigated this for games with uncertain information. We varied the level of interconnections (connectivity) among the nodes on the boards and investigated how these a ect the payoffs of players that played on the boards. We principally used these experiments to investigate how the level of availability of vital infrastructures (such as road networks) in a particular location or region affects profitability of businesses in that particular region. The sixth experiment contains simulations in which we introduced the fuzzy game approach to wage negotiation in managing employers and employees (unions) relationships. The scheme proposes how employers and employees (unions) can successfully manage the deadlocks that usually accompany wage negotiations. In all cases, fuzzy rules are constructed that symbolise various rules and strategic variables that firms take into consideration before taken decisions. The models also include learning procedures that enable the agents to optimize these fuzzy rules and their decision processes. This is the main contribution of the thesis: a set of fuzzy models that include learning, and can be used to improve decision making in business

A comparative study on decision-making methodology

Decision making (DM), the process of determining and selecting alternative decisions based on information and the preferences of decision makers (DMs), plays a significant role in our daily personal and professional lives. Many DM methods have been developed to assist DMs in their unique type of decision process. In this thesis, DM methods associated with two types of DM processes are studied: Decision-making under uncertainty (DMUU) and Multi-criteria decision making (MCDM). DMUU is making a decision when there are many unknowns or uncertainties about the kinds of states of nature (a complete description of the external factors) that could occur in the future to alter the outcome of a decision. DMUU has two subcategories: decision-making under strict uncertainty (DMUSU) and decision-making under risk (DMUR). Five classic DMUSU methods are Laplace’s insufficient reason principle, Wald’s Maximin, Savage’s Minimax regret, Hurwicz’s pessimism-optimism index criterion and Starr’s domain criterion. Furthermore, based on a review of the relation between a two-player game in game theory and DMUSU, Nash equilibrium is considered a method for approaching DMUSU as well. The well-known DMUR DM methods are expected monetary value, expected opportunity loss, most probable states of nature and expected utility. MCDM is a sub-discipline of operations research, where DMs evaluate multiple conflicting criteria in order to find a compromise solution subject to all the criteria. Numerous MCDM methods exist nowadays. The Analytic Hierarchy Process (AHP), the ELimination et Choix Traduisant la REalité (ELECTRE), the Preference Ranking Organization METHod for Enrichment Evaluations (PROMETHEE) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) are the most employed of all the various MCDM methods. This PhD work focuses on presenting a comparative study of DM methods theoretically and evaluating the performance of different methods on a single decision problem. This contribution can guide DMs in gathering the relative objective and subjective information, structuring the decision problem and selecting the right DM method to make the decision that suits not only their subjective preferences, but also the objective facts. The case study used here is the selection of a sewer network construction plan. It is a representative and complex practical decision problem that requires the quality, life-cycle maintenance and performance of the selected sewer system to meet long-term planning for future climate changes and urban development. La prise de décision (DM), un processus de détermination et de sélection de décisions alternatives en fonction des informations et des préférences des décideurs (DM), apparaît largement dans notre vie personnelle et professionnelle quotidienne. Un grand nombre de méthodes DM ont été développées pour aider les DM dans leur type unique de processus de décision. Dans cette thèse, les méthodes DM associées à deux types de processus DM sont étudiées : la prise de décision sous incertitude (DMUU) et la prise de décision multicritère (MCDM). La DMUU doit prendre la décision lorsqu'il existe de nombreuses inconnues ou incertitudes sur le type d'états de la nature (une description complète des facteurs externes) qui pourraient se produire à l'avenir pour modifier le résultat d'une décision. La DMUU comprend deux sous-catégories : la prise de décision sous incertitude stricte (DMUSU) et la prise de décision sous risque (DMUR). Cinq méthodes classiques de DM pour DMUSU sont le principe de raison insuffisante de Laplace, le Waldimin Maximin, le regret Savage Minimax, le critère d'index pessimisme-optimisme de Hurwitz et le critère de domaine de Starr. En outre, l'examen de la relation entre un jeu à deux joueurs dans la théorie des jeux et l'équilibre DMUSU et Nash Equilibrium est également considéré comme l'une des méthodes pour résoudre le DMUSU. Les méthodes DM bien connues de DMUR sont la valeur monétaire attendue, la perte d'opportunité attendue, les états de nature les plus probables et l'utilité attendue. Le MCDM est une sous-discipline de la recherche opérationnelle, où les DM évaluent plusieurs critères conflictuels afin de trouver la solution compromise soumise à tous les critères. Un certain nombre de méthodes DM pour MCDM sont présentes de nos jours. Le processus de hiérarchie analytique (AHP), l'élimination et le choix traduisant la réalité (ELECTRE), les méthodes d'organisation du classement des préférences pour les évaluations d'enrichissement (PROMETHEE) et la technique de préférence par ordre de similitude et de solution idéale (TOPSIS) sont les plus choisies et utilisées des méthodes parmi toutes les différentes méthodes MCDM. Ce travail de thèse se concentre sur la présentation théorique d'une étude comparative des méthodes DM et l'évaluation des performances de différentes méthodes avec un problème de décision particulier. Cette contribution peut guider les DM à rassembler les informations relatives objectives et subjectives, à structurer le problème de décision et à sélectionner la bonne méthode de DM pour prendre la décision qui convient non seulement à leurs préférences subjectives, mais aussi aux faits objectifs. L'étude de cas utilisée ici est la sélection du plan de construction du réseau d'égouts. Il s'agit d'un problème de décision pratique représentatif et complexe qui nécessite la qualité, l'entretien du cycle de vie et les performances du réseau d'égouts sélectionné pour répondre à la planification à long terme des futurs changements climatiques et du développement urbain