Journal of Fuzzy Extension and Applications
Volume:3 Issue: 2, Spring 2022

The present paper proposes a new application of the prediction of human behavior using TOPSIS as an appropriate tool for data optimization. Our hypothesis was that the analysis of the candidates with this method was influenced by the change of their behavior. We found that the behavior change could occur in more than one time span when the behavior of two candidates changed simultaneously. One of the advantages of this study is that the pattern of the behavior change with time is predicted with this method. Another advantage is that the modifications in the TOPSIS algorithm have made the predictions independent from the need of changing the fuzzy membership degrees of the candidates. This is the first time that these modifications in this technique with a new application including the numerical analysis of cognitive date are reported. Our results can be used in cognitive science, experimental psychology, cognitive informatics and artificial intelligence.

In fuzzy decision-making, incomplete information always leads to uncertain and partially reliable judgements. The emergence of fuzzy set theory helps decision-makers in handling uncertainty and vagueness when making judgements. Intuitionistic Fuzzy Numbers (IFN) measure the degree of uncertainty better than classical fuzzy numbers, while Z-numbers help to highlight the reliability of the judgements. Combining these two fuzzy numbers produces Intuitionistic Z-Numbers (IZN). Both restriction and reliability components are characterized by the membership and non-membership functions, exhibiting a degree of uncertainties that arise due to the lack of information when decision-makers are making preferences. Decision information in the form of IZN needs to be defuzzified during the decision-making process before the final preferences can be determined. This paper proposes an Intuitive Multiple Centroid (IMC) defuzzification of IZN. A novel Multi-Criteria Decision-Making (MCDM) model based on IZN is developed. The proposed MCDM model is implemented in a supplier selection problem for an automobile manufacturing company. An arithmetic averaging operator is used to aggregate the preferences of all decision-makers, and a ranking function based on centroid is used to rank the alternatives. The IZN play the role of representing the uncertainty of decision-makers, which finally determine the ranking of alternatives.

Fermatean Fuzzy Sets (FFSs) provide an effective way to handle uncertainty and vagueness by expanding the scope of membership and Non-Membership Degrees (NMDs) of Intuitionistic Fuzzy Set (IFS) and Pythagorean Fuzzy Set (PFS), respectively. FFS handles uncertain information more easily in the process of decision making. The concept of composite relation is an operational information measure for decision making. This study establishes Fermatean fuzzy composite relation based on max-average rule to enhance the viability of FFSs in machine learning via soft computing approach. Some numerical illustrations are provided to show the merit of the proposed max-average approach over existing the max-min-max computational process. To demonstrate the application of the approach, we discuss some pattern recognition problems of building materials and mineral fields with the aid of the Fermatean fuzzy modified composite relation and Fermatean fuzzy max-min-max approach to underscore comparative analyses. In recap, the objectives of the paper include: 1) discussion of FFS and its composite relations, 2) numerical demonstration of Fermatean fuzzy composite relations, 3) establishment of a decision application framework under FFS in pattern recognition cases, and 4) comparative analyses to showcase the merit of the new approach of Fermatean fuzzy composite relation. In future, this Fermatean fuzzy modified composite relation could be studied in different environments like picture fuzzy sets, spherical fuzzy sets, and so on.

Much of a person’s cognitive activity depends on the ability to reason analogically. Analogical reasoning (AR) compares the similarities between new and past knowledge and uses them to obtain an understanding of the new knowledge. The mechanisms, however, under which the human mind works are not fully investigated and as a result AR is characterized by a degree of fuzziness and uncertainty. Probability theory has been proved sufficient for dealing with the cases of uncertainty due to randomness. During the last 50-60 years, however, various mathematical theories have been introduced for tackling effectively the other forms of uncertainty, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, rough sets, etc. The combination of two or more of those theories gives frequently better results for the solution of the corresponding problems. A hybrid assessment method of AR skills under fuzzy conditions is developed in this work using Grey Numbers (GN) and soft sets as tools, which is illustrated by an application on evaluating student analogical problem solving skills.

In this study, a hybrid model for prediction issues based on IT2FLS and Particle Swarm Optimization (PSO) is proposed. The main contribution of this work is to discover the ideal strategy for creating an optimal value vector to optimize the membership function of the fuzzy controller. It should be emphasized that the optimized fuzzy controller is a type-2 interval fuzzy controller, which is better than a type-1 fuzzy controller in handling uncertainty. The limiting membership functions of the type-2 fuzzy set domain is type-1 fuzzy sets, which explains the trace of uncertainty in this situation. The proposed optimization strategy was tested using ECG signal data. The accuracy of the proposed IT2FLS_PSO estimation technique was evaluated using a number of performance metrics (MSE, RMSE, error mean, error STD). RMSE and MSE with IT2FI were calculated as 0.1183 and 0.0535, respectively. With IT2FISPSO, these values were calculated as 0.0140 and 0.0029, respectively. The proposed PSO-optimized IT2FIS controller significantly improved its performance under various operating conditions. The simulation results show that PSO is effective in designing optimal type 2 fuzzy controllers. The experimental results show that the proposed optimization strategy significantly improves the prediction accuracy.

This paper deals with a multi-objective linear fractional programming problem in fuzzy environment. The problem is considered by introducing all the parameters as piecewise quadratic fuzzy numbers. Through the use of the associated real number of the close interval approximation and the order relation of the piecewise quadratic fuzzy numbers, the problem is transformed into the corresponding crisp problem. A proposed method introduces to generate ideals and the set of all fuzzy efficient solutions. The advantage of it helps the decision maker to handle the real life problem. A numerical example is given illustrate the method.

Industry 4.0 implementations are competitive tools of recent production systems in which complex computerized systems are employed. Efficiency of these systems is generally measured by Data Envelopment Analysis (DEA) under certainty. However, the required data in modelling the system involve high degree of uncertainty, which necessitates the usage of fuzzy set theory. Fuzzy DEA models can successfully handle this problem and present efficient solutions for Industry 4.0 implementation. In this paper, efficiency of Industry 4.0 applications is measured by classical DEA and fuzzy DEA models, allowing the variables to have different units of measurement and to be independent from analytical production functions. Besides that, fuzzy algorithms for output-oriented DEA are proposed for BBC and CCR models. To the best of our knowledge, this article is the first quantitative academic study to measure the effects of Industry 4.0 applications on productivity. It also shows how fuzzy factors can affect decision-making by comparing fuzzy and classical DEA results.  A real application of the models is realized in a company of home appliances manufacturing sector having Industry 4.0 applications. The effect of Industry 4.0 implementation on machine productivity, and superiority of fuzzy DEA over classical DEA are shown through the application.