scholarly journals The new approach to the construction of parametric membership functions for fuzzy sets with unequal supports

2017 ◽  
Vol 112 ◽  
pp. 2057-2065 ◽  
Author(s):  
Elisabeth Rakus-Andersson
Keyword(s):  
Fuzzy Sets ◽  
Membership Functions ◽  
New Approach

New Negations on the Membership Functions of Type-2 Fuzzy Sets

2019 ◽  
Vol 27 (7) ◽  
pp. 1397-1406 ◽  
Author(s):  
Carmen Torres-Blanc ◽  
Susana Cubillo ◽  
Pablo Hernandez-Varela
Keyword(s):  
Fuzzy Sets ◽  
Membership Functions

A new approach to uncertainty description through accomplishment membership functions

2015 ◽  
Vol 42 (21) ◽  
pp. 7895-7904 ◽  
Author(s):  
Luis Ibarra ◽  
Pedro Ponce ◽  
Arturo Molina
Keyword(s):  
Membership Functions ◽  
New Approach

scholarly journals RESEARCH OF THE BANKRUPTCY PREDICTION RELIABILITY IN CASE TO INTRODUCE A NEW CATEGORY OF THE COMPANIES FINANCIAL POSITION

2020 ◽  
pp. 105-122
Author(s):  
Aleksandra Noskova ◽  
◽  
Aleksander Alekseev
Keyword(s):  
Fuzzy Sets ◽  
Balance Sheet ◽  
Point Of View ◽  
Linguistic Variables ◽  
Membership Functions ◽  
Financial Position ◽  
Fixed Assets ◽  
Theoretical Significance ◽  
Prediction Reliability ◽  
Accuracy Increase

The motivation for this research was the result obtained earlier by the authors in the field of developing industry models for predicting bankruptcy with high prognostic ability. The article examines the prediction reliability of the financial position of companies in the case of introducing an additional category of financial position that reflects the position between financial solvency and insolvency (bankruptcy). The authors hypothesize that the reliability of models decreases if the requirements for their accuracy increase due to the introduction of an additional category of financial position. Hypothesis testing is performed using a non-entropic approach. This approach should reduce the measure of uncertainty in terms of the uncharacteristic nature of some of the identified features of financial position relative to the initial categories. At the same time, features of financial position are defined as ranges of specific weight of balance sheet items that have positive or negative information importance. Information importance is determined based on the methods of system-cognitive analysis, implemented automatically in the EIDOS X++ system, as well as by reproducing information models using MS Excel tools. Normalization of the informational importance values of features and their interpolation allowed us to obtain functions similar to the membership functions in the theory of fuzzy sets. When constructing membership functions relative to ranges of significant balance sheet items ("Fixed assets", "Inventory", "Accounts Receivable", "Short-Term financial investments", "Retained earnings (uncovered loss)", "Accounts payable"), ranges with zero or insignificant values of characteristic functions corresponding to the initial categories of financial position are identified. This actually meant a high level of uncertainty in the prediction. The authors propose to introduce additional linguistic variables and their corresponding fuzzy sets, whose carriers are the relative scales of the above balance items, this will reduce uncertainty. A total of 5 such fuzzy sets were identified, where the researchers used the concept of "gray zone" as a linguistic variable, which was actually used as a new category of financial position. All calculations are shown on the example of fixed assets. The prognostic ability of models based on an optimized sample, where the category of the position of companies that have at least 3 out of 5 features of the "gray zone" has been replaced, is reduced, as expected, but only slightly. And in the case of reproducing algorithms of system-cognitive analysis using MS Excel tools, there is even an increase in the prognostic ability of one of the models. In fact, the hypothesis that the reliability of models decreases if the requirements for their accuracy increase was not confirmed. From an economic point of view, the theoretical significance of the obtained result is that with the help of a non-entropic approach it was possible to show the need to introduce a new category of financial position. From a mathematical point of view, the theoretical significance lies in the fact that membership functions for linguistic variables are obtained based on real data on the financial position of almost two hundred Russian companies, these reduction functions can be used by specialists in the field of fuzzy set theory in the future. The results obtained are applicable at least for the construction industry, but can also be replicated relative to other sectors of the economy when forming the corresponding samples.

A new approach for computing with fuzzy sets using interval analysis

2007 ◽  
Author(s):  
Arunas Mazeika ◽  
Luc Jaulin ◽  
Christophe Osswald
Keyword(s):  
Fuzzy Sets ◽  
Interval Analysis ◽  
New Approach

Novel Similarity Measures, Entropy of Intuitionistic Fuzzy Sets and their Application in Software Quality Evaluation

2021 ◽  
Author(s):  
Xuan Thao Nguyen ◽  
Shuo Yan Chou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Membership Functions ◽  
Software Projects ◽  
Intuitionistic Fuzzy ◽  
Software Quality Evaluation

Abstract Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping stone to calculate the weights of the criteria in the proposed multi-criteria decision making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

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