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

Enhancement of dronogram aid to visual interpretation of target objects via intuitionistic fuzzy hesitant sets

In this paper, we address the hesitant information in enhancement task often caused by differences in image contrast. Enhancement approaches generally use certain filters which generate artifacts or are unable to recover all the objects details in images. Typically, the contrast of an image quantifies a unique ratio between the amounts of black and white through a single pixel. However, contrast is better represented by a group of pix- els. We have proposed a novel image enhancement scheme based on intuitionistic hesi- tant fuzzy sets (IHFSs) for drone images (dronogram) to facilitate better interpretations of target objects. First, a given dronogram is divided into foreground and background areas based on an estimated threshold from which the proposed model measures the amount of black/white intensity levels. Next, we fuzzify both of them and determine the hesitant score indicated by the distance between the two areas for each point in the fuzzy plane. Finally, a hyperbolic operator is adopted for each membership grade to improve the pho- tographic quality leading to enhanced results via defuzzification. The proposed method is tested on a large drone image database. Results demonstrate better contrast enhancement, improved visual quality, and better recognition compared to the state-of-the-art methods.Web of Science500866

Interval type-2 intuitionistic fuzzy logic system for time series and identification problems - a comparative study

This paper proposes a sliding mode control-based learning of interval type-2 intuitionistic fuzzy logic system for time series and identification problems. Until now, derivative-based algorithms such as gradient descent back propagation, extended Kalman filter, decoupled extended Kalman filter and hybrid method of decoupled extended Kalman filter and gradient descent methods have been utilized for the optimization of the parameters of interval type-2 intuitionistic fuzzy logic systems. The proposed model is based on a Takagi-Sugeno-Kang inference system. The evaluations of the model are conducted using both real world and artificially generated datasets. Analysis of results reveals that the proposed interval type-2 intuitionistic fuzzy logic system trained with sliding mode control learning algorithm (derivative-free) do outperforms some existing models in terms of the test root mean squared error while competing favourable with other models in the literature. Moreover, the proposed model may stand as a good choice for real time applications where running time is paramount compared to the derivative-based models

Investigation on soft computing techniques for airport environment evaluation systems

Spatial and temporal information exist widely in engineering fields, especially in airport environmental management systems. Airport environment is influenced by many different factors and uncertainty is a significant part of the system. Decision support considering this kind of spatial and temporal information and uncertainty is crucial for airport environment related engineering planning and operation. Geographical information systems and computer aided design are two powerful tools in supporting spatial and temporal information systems. However, the present geographical information systems and computer aided design software are still too general in considering the special features in airport environment, especially for uncertainty. In this thesis, a series of parameters and methods for neural network-based knowledge discovery and training improvement are put forward, such as the relative strength of effect, dynamic state space search strategy and compound architecture. [Continues.

A new extension of fuzzy sets using rough sets: R-fuzzy sets

This paper presents a new extension of fuzzy sets: R-fuzzy sets. The membership of an element of a R-fuzzy set is represented as a rough set. This new extension facilitates the representation of an uncertain fuzzy membership with a rough approximation. Based on our definition of R-fuzzy sets and their operations, the relationships between R-fuzzy sets and other fuzzy sets are discussed and some examples are provided

Interval type-2 intuitionistic fuzzy logic system for non-linear system prediction

This paper presents an approach to prediction based on a new interval type-2 intuitionistic fuzzy logic system (IT2IFLS) of Takagi-Sugeno-Kang (TSK) fuzzy inference. The gradient descent algorithm (GDA) is used to adapt the parame- ters of the IT2IFLS. The empirical comparison is made on the designed system using two synthetic datasets. Analysis of our results reveal that the presence of additional degrees of freedom in terms of non-membership functions and hesitation indexes in IT2IFLS tend to reduce the root mean square error (RMSE) of the system compared to a type-1 fuzzy logic approach and some interval type-2 fuzzy systems

Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of B.W.M. and interval valued intuitionistic fuzzy T.O.D.I.M.

open access articleDeveloping and accepting industry 4.0 influences the industry structure and customer willingness. To a successful transition to industry 4.0, implementation strategies should be selected with a systematic and comprehensive view to responding to the changes flexibly. This research aims to identify and prioritise the strategies for implementing industry 4.0. For this purpose, at first, evaluation attributes of strategies and also strategies to put industry 4.0 in practice are recognised. Then, the attributes are weighted to the experts’ opinion by using the Best Worst Method (BWM). Subsequently, the strategies for implementing industry 4.0 in Fara-Sanat Company, as a case study, have been ranked based on the Interval Valued Intuitionistic Fuzzy (IVIF) of the TODIM method. The results indicated that the attributes of ‘Technology’, ‘Quality’, and ‘Operation’ have respectively the highest importance. Furthermore, the strategies for “new business models development’, ‘Improving information systems’ and ‘Human resource management’ received a higher rank. Eventually, some research and executive recommendations are provided. Having strategies for implementing industry 4.0 is a very important solution. Accordingly, multi-criteria decision-making (MCDM) methods are a useful tool for adopting and selecting appropriate strategies. In this research, a novel and hybrid combination of BWM-TODIM is presented under IVIF information

Uncertainty and Congestion Elimination in 4G Network Call Admission Control using Interval Type-2 Intuitionistic Fuzzy Logic

The management and control of the global growth and complex nature of wireless Fourth Generation (4G) Networks elicits the need for Call Admission Control (CAC). However, CAC faces the challenge of network congestion, thereby deteriorating the network Quality of Service (QoS) due to inherent imprecision and uncertainties in the QoS data which leads to difficulties in measuring some objective and constraints of QoS using crisp values. Previous researches have shown the strength of Interval Type-2 Fuzzy Logic System (IT2FLS) in coping adequately with linguistic uncertainties. Intuitionistic fuzzy sets (IFSs) have indicated their ability to further reduce uncertainty by handling conflicting evaluation involving membership (M), nonmembership (NM) and hesitation. This paper applies the Interval Type-2 Intuitionistic Fuzzy Logic System (IT2IFLS) in solving CAC problem in order to achieve a better QoS in 4G Networks