Markov chain based on neutrosophic numbers in decision making

Markov chain is a stochastic model for estimating the equilibrium of any system. It is a unique mathematical model in which the future behavior of the system depends only on the present. Often biased possibilities can be used over biased probabilities, for handling uncertain information to define Markov chain using fuzzy environment. Indeterminacy is different from randomness due to its construction type where the items involved in the space are true and false in the same time. In this context as an extension of conventional and fuzzy probabilities neutrosophic probability (NP) was introduced. These neutrosophic probabilities can be captured as neutrosophic numbers. In this paper, Markov chain based on neutrosophic numbers is introduced and a new approach to the ergoticity for the traffic states in the neutrosophic Markov chain based on neutrosophic numbers is verified. The proposed approach is applied to decision-making in the prediction of traffic volume.

Portfolio Optimization Efficiency Test Considering Data Snooping Bias

Background: In the portfolio optimization area, most of the research is focused on insample portfolio optimization. One may ask a rational question of what the efficiency of the portfolio optimization strategy is and how to measure it.Objectives: The objective of the paper is to propose the approach to measuring the efficiency of the portfolio strategy based on the hypothesis inference methodology and considering a possible data snooping bias. The proposed approach is demonstrated on the Markowitz minimum variance model and the fuzzy probabilities minimum variance model.Methods/Approach: The proposed approach is based on a statistical test. The null hypothesis is that the analysed portfolio optimization strategy creates a portfolio randomly, while the alternative hypothesis is that an optimized portfolio is created in such a way that the risk of the portfolio is lowered.Results: It is found out that the analysed strategies indeed lower the risk of the portfolio during the market’s decline in the global financial crisis and in 94% of the time in the 2009-2019 period.Conclusions: The analysed strategies lower the risk of the portfolio in the out-of-sample period.

Distribution Network Risk Assessment Using Multicriteria Fuzzy Influence Diagram

Risk assessment of distribution assets is one of the most important factors in the process of network development or maintenance planning decision-making. The process of decision-making is faced with uncertainties, involving technical, financial, safety, environmental, and other operational issues that make standard risk assessment techniques insufficient. Probabilistic uncertainties require appropriate mathematical modeling and quantification when predicting future state of the nature or the value of certain parameters. The paper is proposing a new methodology for the multicriteria risk assessment of the distribution network assets, based on influence diagrams and fuzzy probabilities. Influence diagram has been used to determine all relevant factors concerning risks and their interdependencies are depicted. Fuzzy probabilities are represented by triangular fuzzy numbers with constraints on feasibility of elicited probabilities. This methodology enables the decision process in uncertain environment, with the impact evaluation of each particular distribution asset, or the asset component. The methodology is illustrated on the example of a distribution substation circuit breaker maintenance strategy selection.

Product Selection in E-Commerce Under Fuzzy Environment: A MADM Game Theoretic Model

This paper introduces a methodology based on fuzzy game theory to determine the buyer's priority of the attributes and select a product in the e-business system. The game theory model developed in our paper considers the prioritization of attributes as strategies for the player (player 1) in one side and selection of the products for the opponent player (player 2). The fuzzy probabilities of the strategies in the game theory are obtained by using the concepts of similarities between the fuzzy numbers. The e-business system devises strategies for the player 1 by attaching appropriate priority levels to product attributes for maximum gain. On the other hand the opponent player 2 select the products as the strategies accordingly. The payoffs obtained in the game theory model as fuzzy numbers are subsequently converted to their equivalent probabilistic mean intervals. This process leads to transform the game theory model into a linear programming problem (LPP) with interval coefficients. The solution to LPP gives us the optimal strategies. These probability of strategies are considered as attributes' weights to determine ranking of the products in e-business system. The methodology is illustrated with the help of a numerical example.