A method for the detection of the most suitable fuzzy implication for data applications
- PDF / 1,481,084 Bytes
- 11 Pages / 595.276 x 790.866 pts Page_size
- 112 Downloads / 191 Views
ORIGINAL PAPER
A method for the detection of the most suitable fuzzy implication for data applications Panagiotis Pagouropoulos1 · Christos D. Tzimopoulos2 · Basil K. Papadopoulos1 Received: 31 December 2017 / Accepted: 13 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract Fuzzy implications are widely used in applications where propositional logic is applicable. In cases where a variety of fuzzy implications can be used for a specific application, it is important that the optimal candidate to be chosen in order valuable inference to be drawn for a given set of data. This study introduces a method for detecting the most suitable fuzzy implica‑ tion among others under consideration by evaluating the metric distance between each implication and the ideal implication for a given data application. The ideal implication I is defined and used as a reference in order to measure the suitability of fuzzy implications. The method incorporates an algorithm which results in two extreme cases of fuzzy implications regarding their suitability for inference making; the most suitable and the least suitable implications. An example involving five fuzzy implications is included to illustrate the procedure of the method. The results obtained verify that the resulting implication is the optimal operator for inference making for the data. Keywords Fuzzy sets · Fuzzy implications · Fuzzy conditional propositions · Fuzzy set distance · Linguistic variables
1 Introduction Logic is the study of reasoning. A fundamental area of logic, called propositional logic, deals with propositions, which involve logic variables and logic functions that assign a truth value to other logic variables or propositions. Logic variables are propositions of the form ‘s is P’, where s is a subject and P designates a predicate that characterizes a property and takes a truth value. For example, the proposi‑ tion ‘7 is a prime number’ is true. Number ‘7’ stands for a subject and ‘a prime number’ is a predicate that character‑ izes the property of being a natural number greater than one whose only positive integer factors are the number itself and number one. The most common logic functions used in propositional logic, as discussed in Tzimopoulos and Papa‑ dopoulos (2013), are the negation (NOT), disjunction (OR) and conjunction (AND). Combinations of these operations * Basil K. Papadopoulos [email protected] 1
Department of Civil Engineering, Democritus University of Thrace, Building A’‑ Campus, Kimmeria, 67100 Xanthi, Greece
Aristotle University of Thessaloniki, 54124 Thessaloníki, Greece
2
form other logic functions. Such functions are the implica‑ tions which are used in conditional propositions. Implica‑ tions assign a truth value to two logic variables using the negation and disjunction operators. One of the two logic variables or propositions is the antecedent, while the other is the consequent. Once the truth values of an antecedent and a consequent are evaluated, the degree of truth of an impli‑ cation indic
Data Loading...
