Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of L-fuzzy mathematical morphology

Mathematical morphology (MM) offers a wide range of tools for image processing and computer vision. MM was originally conceived for the processing of binary images and later extended to gray-scale morphology. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory that give rise to fuzzy mathematical morphology (FMM). From a mathematical point of view, FMM relies on the fact that the class of all fuzzy sets over a certain universe forms a complete lattice. Recall that complete lattices provide for the most general framework in which MM can be conducted. The concept of L-fuzzy set generalizes not only the concept of fuzzy set but also the concepts of interval-valued fuzzy set and Atanassov’s intuitionistic fuzzy set. In addition, the class of L-fuzzy sets forms a complete lattice whenever the underlying set L constitutes a complete lattice. Based on these observations, we develop a general approach towards L-fuzzy mathematical morphology in this paper. Our focus is in particular on the construction of connectives for interval-valued and intuitionistic fuzzy mathematical morphologies that arise as special, isomorphic cases of L-fuzzy MM. As an application of these ideas, we generate a combination of some well-known medical image reconstruction techniques in terms of interval-valued fuzzy image processing

Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach

A fuzzy approach of online reliability modeling and estimation.

International audienceIn maintenance field, traditional concepts like preventive and corrective strategies are progressively completed by new ones like predictive and proactive maintenance. For that purpose, a fundamental task is the estimation of the provisional reliability of equipment as well as its remaining useful life. However, traditional approach of reliability based on statistical analysis can be not suitable as very few knowledge can be available. Within this frame, the general purpose of the work is to explore the way of developing a fuzzy approach of on-line reliability modeling and estimation in order to take into account the uncertainty as welle as possible. A federative point of view of the reliability modeling process and of the prognostic of degradation activity is proposed. From that, two ways of considering uncertainty in reliability modeling are discussed (probabilistic, fuzzy/possibility approaches), and the inherent limits of both methods are pointed out

Using MathML to Represent Units of Measurement for Improved Ontology Alignment

Ontologies provide a formal description of concepts and their relationships in a knowledge domain. The goal of ontology alignment is to identify semantically matching concepts and relationships across independently developed ontologies that purport to describe the same knowledge. In order to handle the widest possible class of ontologies, many alignment algorithms rely on terminological and structural meth- ods, but the often fuzzy nature of concepts complicates the matching process. However, one area that should provide clear matching solutions due to its mathematical nature, is units of measurement. Several on- tologies for units of measurement are available, but there has been no attempt to align them, notwithstanding the obvious importance for tech- nical interoperability. We propose a general strategy to map these (and similar) ontologies by introducing MathML to accurately capture the semantic description of concepts specified therein. We provide mapping results for three ontologies, and show that our approach improves on lexical comparisons.Comment: Conferences on Intelligent Computer Mathematics (CICM 2013), Bath, Englan

Integrating Fuzzy Decisioning Models With Relational Database Constructs

Human learning and classification is a nebulous area in computer science. Classic decisioning problems can be solved given enough time and computational power, but discrete algorithms cannot easily solve fuzzy problems. Fuzzy decisioning can resolve more real-world fuzzy problems, but existing algorithms are often slow, cumbersome and unable to give responses within a reasonable timeframe to anything other than predetermined, small dataset problems. We have developed a database-integrated highly scalable solution to training and using fuzzy decision models on large datasets. The Fuzzy Decision Tree algorithm is the integration of the Quinlan ID3 decision-tree algorithm together with fuzzy set theory and fuzzy logic. In existing research, when applied to the microRNA prediction problem, Fuzzy Decision Tree outperformed other machine learning algorithms including Random Forest, C4.5, SVM and Knn. In this research, we propose that the effectiveness with which large dataset fuzzy decisions can be resolved via the Fuzzy Decision Tree algorithm is significantly improved when using a relational database as the storage unit for the fuzzy ID3 objects, versus traditional storage objects. Furthermore, it is demonstrated that pre-processing certain pieces of the decisioning within the database layer can lead to much swifter membership determinations, especially on Big Data datasets. The proposed algorithm uses the concepts inherent to databases: separated schemas, indexing, partitioning, pipe-and-filter transformations, preprocessing data, materialized and regular views, etc., to present a model with a potential to learn from itself. Further, this work presents a general application model to re-architect Big Data applications in order to efficiently present decisioned results: lowering the volume of data being handled by the application itself, and significantly decreasing response wait times while allowing the flexibility and permanence of a standard relational SQL database, supplying optimal user satisfaction in today\u27s Data Analytics world. We experimentally demonstrate the effectiveness of our approach

On the similarity relation within fuzzy ontology components

Ontology reuse is an important research issue. Ontology merging, integration, mapping, alignment and versioning are some of its subprocesses. A considerable research work has been conducted on them. One common issue to these subprocesses is the problem of defining similarity relations among ontologies components. Crisp ontologies become less suitable in all domains in which the concepts to be represented have vague, uncertain and imprecise definitions. Fuzzy ontologies are developed to cope with these aspects. They are equally concerned with the problem of ontology reuse. Defining similarity relations within fuzzy context may be realized basing on the linguistic similarity among ontologies components or may be deduced from their intentional definitions. The latter approach needs to be dealt with differently in crisp and fuzzy ontologies. This is the scope of this paper.ou

On Modeling the Quality of Nutrition for Healthy Ageing Using Fuzzy Cognitive Maps

Modelling dietary intake of older adults can prevent nutritional deficiencies and diet-related diseases, improving their quality of life. Towards such direction, a Fuzzy Cognitive Map (FCM)-based modelling approach that models the interdependencies between the factors that affect the Quality of Nutrition (QoN) is presented here. The proposed FCM-QoN model uses a FCM with seven input-one output concepts, i.e., five food groups of the UK Eatwell Plate, Water (H2O), and older adult’s Emotional State (EmoS), outputting the QoN. The weights incorporated in the FCM structure were drawn from an experts’ panel, via a Fuzzy Logic-based knowledge representation process. Using various levels of analysis (causalities, static/feedback cycles), the role of EmoS and H2O in the QoN was identified, along with the one of Fruits/Vegetables and Protein affecting the sustainability of effective food combinations. In general, the FCM-QoN approach has the potential to explore different dietary scenarios, helping health professionals to promote healthy ageing and providing prognostic simulations for diseases effect (such as Parkinson’s) on dietary habits, as used in the H2020 i-Prognosis project (www.i-prognosis.eu)