Fuzzy morphological operators in image processing

First of all, in this paper we propose a family of fuzzy implication operators, which the generalised Luckasiewicz's one, and to analyse the impacts of Smets and Magrez properties on these operators. The result of this approach will be a characterisation of a proposed family of inclusion grade operators (in Bandler and Kohout's manner) that satisfies the axioms of Divyendu and Dogherty. Second, we propose a method to define fuzzy morphological operators (erosions and dilations). A family of fuzzy implication operators and the inclusion grade are the basis for this method

Generation of fuzzy mathematical morphologies

Fuzzy Mathematical Morphology aims to extend the binary morphological operators to grey-level images. In order to define the basic morphological operations fuzzy erosion, dilation, opening and closing, we introduce a general method based upon fuzzy implication and inclusion grade operators, including as particular case, other ones existing in related literature In the definition of fuzzy erosion and dilation we use several fuzzy implications (Annexe A, Table of fuzzy implications), the paper includes a study on their practical effects on digital image processing. We also present some graphic examples of erosion and dilation with three different structuring elements $B(i, j)=1$, $B(i, j)=0.7$, $B(i, j)=0.4$, $i, j \in \{ 1,2, 3\}$ and various fuzzy implications

Interval-valued algebras and fuzzy logics

In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter

Strong fuzzy subsethood measures and strong equalities via implication functions

In this work we present the definition of strong fuzzy subsethood measure as a unifiying concept for the different notions of fuzzy subsethood that can be found in the literature. We analyze the relations of our new concept with the definitions by Kitainik ( [20]), Young ( [26]) and Sinha and Dougherty ( [23]) and we prove that the most relevant properties of the latter are preserved. We show also several construction methods. © 2014 Old City Publishing, Inc

Implementation of Fuzzy Inference System with Tsukamoto Method for Study Programme Selection

Deciding study programme is crucial because any fault in making the decision will affect students' learning motivation, length of study period which exceeds the standard, and the students' failure. With a methodical selection of study programme, each student is expected to focus on his interest and capability more. Fuzzy Inference System (FIS) with Tsukamoto method can be applied to support the settlement. In the method, output is obtained with four stages, namely the formation of fuzzy sets, the establishment of rules, the application of implicated functions, and defuzzification. The purpose of this study is to apply FIS with Tsukamoto method to the decision of study programme which fits prospective students' interest and capability. Moreover, the input variables involve Interview Scores, Scores of Informatics Engineering, Scores of Information Systems and Scores of Written Tests. Output variables are the students' interest either in the Department of Informatics Engeenering or the Department of Information Syste