József Mezei

A fuzzy pay-off method for real option valuation

Real Options analysis offers interesting insights on the value of assets and on the profitability of investments, which has made real options a growing field of academic research and practical application. Real option valuation is, however, often found to be difficult to understand and to implement due to the quite complex mathematics involved. Recent advances in modeling and analysis methods have made real option valuation easier to understand and to implement. This paper presents a new method (fuzzy pay-off method) for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date. The paper also presents the use of number of different types of fuzzy numbers with the method and an application of the new method in an industry setting.

How different are ranking methods for fuzzy numbers? A numerical study

Ranking fuzzy numbers is often a necessary step in many mathematical models, and a large number of ranking methods have been proposed to perform this task. However, few comparative studies exist and nowadays it is still unknown how similar ranking methods are in practice, i.e., how likely they are to induce the same ranking. In this study, by means of numerical simulations, we try to answer this question. We shall discover that there are some very similar methods as well as some outliers. We end the paper interpreting the results and giving some recommendations on the use of ranking methods.

A new consensus model for group decision making using fuzzy ontology

Involving many people in decision making does not guarantee success. In practice, there are always individuals who try to exert pressure in order to persuade others who could easily be influenced. In these situations, classical group decision making models fail. Thus, there is still the necessity of developing tools to help users reach collective decisions as if they participated in a real face to face meeting. In such a way, a proper negotiation process can lead to successful solutions. Therefore, we propose a new consensus model to deal with the psychology of negotiation by using the power of a fuzzy ontology as weapon of influence in order to improve group decision scenarios making them more precise and realistic. In addition, the use of a fuzzy ontology gives us the possibility to take into account large sets of alternatives.

Improving Supervised Learning Classification Methods Using Multigranular Linguistic Modeling and Fuzzy Entropy

Obtaining good classification results using supervised learning methods is critical if we want to obtain a high level of precision in the classification processes. The training data used for the learning process play a very important role in achieving this objective. Therefore, it is important to represent the data in a way that best expresses its meaning. For this purpose, we propose to apply linguistic modeling methods in order to obtain a linguistic representation. With the help of multigranular linguistic modeling, data can be transformed and expressed using different (unbalanced) linguistic label sets. Expressing the data using linguistic expressions instead of numbers increases the readability and reduces the complexity of the problem, and data recovering methods allow us to manually control the level of precision. In this paper, several datasets are transformed and utilized for classification tasks using several supervised learning algorithms. For each combination of datasets and algorithms, the data have been expressed using several linguistic label sets that have different granularity values. After carrying out the testing processes, we can conclude that, in some cases, reducing data complexity leads to better classification results. Therefore, it is found that linguistic representation of the training data with just the necessary and sufficient precision can improve the reliability of the classification process.

An improved index of interactivity for fuzzy numbers

In this paper we will introduce a new index of interactivity between marginal possibility distributions A and B of a joint possibility distribution C. The starting point of our approach is to equip each @c-level set of C with a uniform probability distribution, then the probabilistic correlation coefficient between its marginal probability distributions is interpreted as an index of interactivity between the @c-level sets of A and B. Then we define the index of interactivity between A and B as the weighted average of these indexes over the set of all membership grades. This new index of interactivity is meaningful for the whole family of joint possibility distributions.

Fuzzy Ontology Used for Knowledge Mobilization

Knowledge mobilization is a transition from the prevailing knowledge management to a new methodology through some innovative methods for knowledge representation, formation, and development and for knowledge retrieval and distribution. The context is industrial processes and finding solutions to complex problems that arise and for which at least partial solutions have been documented. The fact that a problem has been solved before normally makes it easier to solve it again and the existence of documents that describe how it was solved supports the problem‐solving process. But documents that describe the problem solving have to be retrieved from a large database of documents and the information that describes the content of a document is not precise. We show that fuzzy ontology will be useful for finding a sufficiently small set of documents that are relevant for the problem solving even if they are imprecisely classified with keywords.

A Fuzzy Pay-Off Method for Real Option Valuation

This paper presents a new method (fuzzy pay-off method) for real option valuation using fuzzy numbers that is based on findings from earlier real option valuation methods and from fuzzy real option valuation. The method is intuitive to understand and far less complicated than any previous real option valuation model to date. The paper also presents the use of triangular and trapezoidal fuzzy numbers with the method.

A fuzzy milp-model for the optimization of vehicle routing problem

In this article, a novel model for the solution of a fuzzy vehicle routing problem is presented. The model originates from a crisp MILP Mixed Integer Linear Programming model previously presented on a conference. This work is motivated by a business context of timber transportation. Within this context, uncertainties arise from the fact that the distances and times between pickup points are inherently fuzzy. The decisions to be made are routing decisions, truck assignment and the determination of the pickup order for a set of loads and available trucks. The paper also presents briefly how the model is implemented in the Microsoft Excel environment, utilizing the LP-solve freeware as the optimization engine. The model is also illustrated with a numerical example. To the authors knowledge, there are no previously reported vehicle routing MILP models, where the times and distances are allowed to be fuzzy numbers.

A Soft Computing Approach to Mastering Paper Machines

Paper machines are extremely complex systems which require a deep knowledge of the relations between levels of usage of factors and characteristics of the process/final product. In this paper we propose to capture the tacit knowledge of experts in the form of a fuzzy ontology. Based on the fuzzy ontology, we introduce a knowledge based system which can ultimately recommend what factors should be increased, or decreased, in order to obtain a different and better output. The system is based on an integer linear goal-programming optimization problem whose parameters come from the fuzzy ontology. We also propose extensions of our model to account for additional constraints and knowledge expressed in the form of fuzzy numbers.

Fuzzy entropy used for predictive analytics

Process interruptions in (very) large production systems are difficult to deal with. Modern processes are highly automated; data is collected with sensor technology that forms a big data context and offers challenges to identify coming failures from the very large sets of data. Feature selection is intended to reduce the complexity of identifying cases with high possibility of failure by excluding numerous factors in the process systems. We use fuzzy entropy as the basis of a feature selection method and we show how the outcome of feature selection can be utilized to further failure prediction steps.