When Zadeh first introduced the notion of a fuzzy set, it was laughed away by the ruling caste of 'serious' mathematicians and logicians. Driven by ignorance, the main reason for it was probably strategic: as fuzzy set theory touches upon the very building block of mathematics, it might be better to deny it than to risk being taken out of business. Even the ample practical realizations had no e...

The author would like to thank Ioannis K. Vlachos, George D. Sergiadis [1] for providing some comments on the paper “Image thresholding using type II fuzzy sets” [2]. The main subject of the comments deals with the relationship between interval-values fuzzy sets (IVFSs) and the intuitionistic fuzzy sets (IFSs) on one side and the entropy measures introduced on the other side. Apparently, this i...

In our case study we look at one of the early papers that interrelates the concept of fuzzy set inclusion, power set and many-valued implication operators, namely the paper of Bandler and Kohout [3]. This is followed by discussion of the subsequent related work by the fuzzy community.

System modeling with fuzzy rule-based systems (FRBSs), i.e. fuzzy modeling (FM), usually comes with two contradictory requirements in the obtained model: the interpretability, capability to express the behavior of the real system in an understandable way, and the accuracy, capability to faithfully represent the real system. While linguistic FM (mainly developed by linguistic FRBSs) is focused o...

The international donor community has grave concerns about the prospects for poverty reduction in what it terms fragile states. A state is classified as fragile if its country policy and institutional assessment (CPIA) score falls below a particular threshold. Recognizing that all states are fragile to varying degrees, this paper questions the method used by the international community to deem ...

The international donor community has grave concerns about the prospects for poverty reduction in what it terms fragile states. A state is classified as fragile if its country policy and institutional assessment (CPIA) score falls below a particular threshold. Recognizing that all states are fragile to varying degrees, this paper questions the method used by the international community to deem ...

The segmentation of brain tumor in MR images is very essential in computer aided diagnosing, which has become a focus in medical research. In this paper, a new segmentation approach of brain tumor which combines the fuzzy affinity technology with the community structure detection technique based on the node similarity is proposed. The presented method consists of the standardization step, the r...

Edge-fuzzy graphs constitute an essential modeling paradigm across a broad spectrum of domains ranging from artificial intelligence to computational neuroscience and social network analysis. Under this model, fundamental graph properties such as edge length and graph diameter become stochastic and as such they are consequently expressed in probabilistic terms. Thus, algorithms for fuzzy graph a...

Recently the engineering community began to seek the possibly application of chaos. The fact that the cryptographic community had used discrete pseudo-chaotic systems for a long time to generate cipher keys that leads to the initiation of applying chaos to secure communications. This paper presents a schematic design methodology for a fuzzy observer based secure communication of hyper chaotic s...