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In this study, we offer a general view at the area of fuzzy modeling and fuzzymodels, identify the visible development phases and elaborate on a new and promisingdirections of system modeling by introducing a concept of granular models. Granularmodels, especially granular fuzzy models constitute an important generalization of existingfuzzy models and, in contrast to the existing models, generate results in the form ofinformation granules (such as intervals, fuzzy sets, rough sets and others). We present arationale and deliver some key motivating arguments behind the emergence of granularmodels and discuss their underlying design process. Central to the development of granularmodels are granular spaces, namely a granular space of parameters of the models and agranular input space. The development of the granular model is completed through anoptimal allocation of information granularity, which optimizes criteria of coverage andspecificity of granular information. The emergence of granular models of type-2 and type-n,in general, is discussed along with an elaboration on their formation. It is shown thatachieving a sound coverage-specificity tradeoff (compromise) is of paramount relevance inthe realization of the granular models.

In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely draws upon the notion of the clone relation of a (crisp) relation,introduced recently by Bouremel et al., and the partition of this clone relationin terms of three different types of pairs of clones. More specifically, reflexive related clones and irreflexive unrelated clones turn out to play a key role in thecharacterization of the fuzzy tolerance and fuzzy equivalence relations that agiven (crisp) relation is compatible with.

Emerging technologies increase the needs on self efficient mobile robotic applications that bring a new concern of sustainable and continuous power supply for the robotic platforms. This paper covers the various techniques and technologies used to design a solar powered robot, exploring the currently available products, software and limitations to this application. The main aim is to integrate a fuzzy logic based charging system which allows the batteries to be charged from solar panels, wall outlet, and a deploy-able solar charging station. The goal of this paper is to summarize the tested methods and results to expedite future researchers in the correct direction. This paper will cover only up to the design of the DC-DC converter and simulation, as further work is still pending implementation on actual hardware.Simulations results are provided to evaluate the feasibility of the paper for future implementations.

In this paper we turn the attention to a well developed theory of fuzzy/lin-guis-tic models that are interpretable and, moreover, can be learned from the data.We present four different situations demonstrating both interpretability as well as learning abilities of these models.

This research aims at proposing a new method for discovering frequent temporal itemsets in continuous subsets of a dataset with quantitative transactions. It is important to note that although these temporal itemsets may have relatively high textit{support} or occurrence within particular time intervals, they do not necessarily get similar textit{support} across the whole dataset, which makes it almost impossible to extract them using the existing traditional algorithms. This paper directly addresses this problem and introduces a new algorithm called Fuzzy Solid Linguistic Itemset Mining (FSLIM) to discover Solid Linguistic Itemsets (SLIs) within a quantitative dataset. SLI is a new concept introduced here as an essential part of the solution presented in this paper. The proposed method consists of two phases. In the first phase, fuzzy set theory is used to transform each quantitative value to a linguistic item; and in the second phase, all SLIs are extracted. Finally, the efficiency of FSLIM is compared in terms of execution time, scalability and the number of frequent patterns with those of two classic approaches on synthetic datasets. The proposed approach is also applied to an actual Mashhad Urban Traffic dataset in order to illustrate FSLIM's ability in discovering the hidden knowledge that could not be extracted by traditional methods.

Fuzzy relation inequalities based on max-F composition are discussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system $ A circ^{F}textbf{x}leqtextbf{b}$, we characterize all matrices $ A^{'} $ For which the solution set of the system $ A^{' } circ^{F}textbf{x}leqtextbf{b}$ is the same as the original solution set. Similarly, for a fixed matrix $ A $, the possible perturbations $ b^{'} $ of the right-hand side vector $ b $ not modifying the original solution set are determined. Several illustrative examples are included to clarify the results of the paper.

In this paper, an observer based fuzzy adaptive controller (FAC) is designed fora class of large scale systems with non-canonical non-affine nonlinear subsystems. It isassumed that functions of the subsystems and the interactions among subsystems areunknown. By constructing a new class of state observer for each follower, the proposedconsensus control method solves the problem of unmeasured states of nonlinear noncanonicalnon-affine subsystems. The main characteristics of the proposed observer-basedintelligent controller are: 1) on-line adaptation of the controller and the observer parameters,2) ultimate boundedness of both the output and the observer errors, 3) boundedness of allsignals involved, 4) employing experts’ knowledge in the controller design procedure and 5)chattering avoidance. The simulation results are further carried out to demonstrate better theeffectiveness of the proposed fuzzy based consensus controller method.

In this note, by considering the notions of the intuitionistic general L-fuzzy automaton and $(alpha, beta)$-language, we show that for any $(alpha, beta)$-language $mathcal{L}$, there exists a minimal intuitionistic general L-fuzzy automaton recognizing $mathcal{L}$.We prove that the minimal intuitionistic general L-fuzzy automaton is isomorphic with threshold $(alpha,beta)$ to any $(alpha, beta)$-reduced max-min intuitionistic general L-fuzzy automaton.%Also, we prove that the minimal intuitionistic general L-fuzzy automaton is an $(alpha, beta)$-reduced.Also, we show that for any strong deterministic max-min intuitionistic general L-fuzzy automaton there exists a statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.In particular, a connection between the minimal and statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton is presented.%We show if $tilde{F}^*$ is an $(alpha, beta)$-complete $(alpha, beta)$-accessible deterministic max-min intuitionistic general L-fuzzy automaton and it is recognizing $(alpha, beta)$-language $mathcal{L}$, then the minimal $tilde{F}^*_{mathcal{L}}$ is homomorphism with threshold $(alpha, beta)$ to statewise $(alpha, beta)$-minimal $tilde{F}_{m}^*$, where $tilde{F}_{m}^*$ is statewise $(alpha, beta)$-equivalent to $tilde{F}^*$.Also, for a given intuitionistic general L-fuzzy automaton, we present two algorithms, which determinesstates of the minimal intuitionistic general L-fuzzy automaton and the statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.Finally, by giving some examples, we comparison minimal intuitionistic general L-fuzzy automaton and statewise $(alpha, beta)$-minimal intuitionistic general L-fuzzy automaton.

In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

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