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symbol mA(x) is the membership function. Its value on the unit interval [0,1] measures the degree to which element x belongs to the **fuzzy** set A, xi is the input to node i and Ai is the linguistic label for each input variable associated with this node. Each node in this layer is an adaptive node, that is, the output of each node depends on the parameters pertaining to these nodes. Thus the membership function for A can be any appropriate parameterized membership function. The most commonly used membership functions are triangular, trapezoidal, Gaussian, and bell shaped. Any of these choices may be used. The triangular and trapezoidal membership functions have been used extensively, especially in real-time implementations, due to their simple formulas and computational efficiency. In our original **fuzzy** model [8,5], we have used triangular membership functions. However, since these membership functions are composed of straight-line segments, they are not smooth at the corner points specified by the parameters. Though the parameters of these membership functions can be optimized using direct search methods but they are less efficient and more time consuming [32,33]. Also, the derivatives of these functions are not continuous so the powerful and more efficient gradient methods cannot be used for optimizing their parameters. Gaussian and bell shaped membership functions are becoming increasingly popular for specifying **fuzzy** sets as they are nonlinear and smooth and their derivatives are continuous. Gradient methods can be used easily for optimizing their design parameters. Thus in this model, we have replaced the triangular **fuzzy** memberships with bell shaped functions. The bell or generalized bell (or gbell) shaped membership function is specified by a set of three fitting parameters {a, b, c} as

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The model is useful for all classes of machines in online condition monitoring system. The vibration data used above was approximate of a class three machine. It predicts problems and protects machine from permanent breakdown. It also identifies and displays the problematic location in the machine without any **human** intervention. Excessive vibration can damage the machine components therefore this system will increase the machine lifetime.

In this paper, we will use **fuzzy** operations [5] to represent the knowledge about each factor. This will enable us to detect the emotion of a person using **fuzzy** inputs of the various factors. For example, we can use a **fuzzy** rule such as “IF (Temperature is High) AND (Heart Rate is High) THEN (Person is Excited).” Al- though **fuzzy** sets and operations are useful for representing the knowledge base, they fail to model the individual behavior of each and every person. Obviously, a model that is able to adapt to various categories of **human** responses would be pre- ferred. Consequently, an adaptive learning mechanism is required to adjust the model if we were to cater for the differences in emotions between various humans. This requirement calls for the use of an adaptive learning system such as artificial neural networks (ANN) (Abraham 2005) [6]. However, the ANN model does not allow the use of **fuzzy** sets or rules, which is the more natural way of representing the relation between **human** emotions and **human** physical and physiological param- eters. ANN uses exact and crisp values for representing the model ’ s input.

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Pattern recognition (PR) find its applications in most of the engineering and medical field like automatic image recognition, document processing, medical diagnosis, biomedicine, remote sensing, etc. The recent increase in processing capacity of computer, made an exhaustive research in the PR field to simulate **human** reading and recognition. The PR system classifies assigns the input pattern to the exact class. It includes data collection, pre-processing, feature extraction and classifier subsystems. Different models of subsystems are proposed by the researchers to increase accuracy and recognition speed for PR system. The design of PR system classifiers usually based on the set of features extracted and the availability of training samples. Different feature extraction, selection, and classification approaches are listed in the review article [1].

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In this chapter, we will be concerned with truth-functional operators. An operator is called truth-functional if the truth value of the resulting proposition is determined solely by the truth values of its operands. That is, the truth value of (say) A AND B is determined only by the truth values of A and B, and no other information is required. Negation, written NOT P, is the simplest example of a truth-functional oper- ator; the truth value of NOT P depends only on the truth value of P, and not on any- thing else. (For classical **logic**, this seems obvious; for **fuzzy** **logic**, it is not so obvious, as we shall see later in Chapter 4, Section 4.2.2.) We will use throughout this book tv(NOT P) ¼ 1 2 tv(P). The two other most common truth-functional operators, also called connectives, are AND and OR. (As we shall see later, these operators are not necessarily truth-functional, although this is seldom admitted!) A set of truth-functional operators that can generate all the others is called a primitive set of operators. It is well known in propositional calculus that all the other truth-functional operators can be constructed from either the NOT and AND or the NOT and OR oper- ators. Computer scientists, electrical engineers, and logicians use different sets of primitive connectives. The NAND operator is defined as A NAND B ¼ NOT (A AND B), and from the NAND operator alone all other logical operators may be constructed; electronic engineers, often take NAND as a primitive, since it is easily implemented in circuitry. Logicians sometimes take the implication operator (A IMPLIES B, defined below), as a member of the primitive set; all other logical oper- ators can be defined from the NOT and IMPLIES operators. Most computer languages furnish AND, OR, and NOT as basic operators. Since our interest is in expert systems implemented in a computer language, we will take AND, OR, and NOT as basic.

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TugaTAC achieved positive profit. The cumulative balance chart in Fig. 7 corroborates that the strategy seeks somehow for wholesale independence, by showing a more squared shape in TugaTAC’s balances meaning equilibrated participation on the markets. Finally, Fig. 8 shows the trading prices on this simulation. It is easy to see that the **fuzzy** model guaranteed a good adjustment on competitiveness. TugaTAC was able to negotiate less energy with a better relation of customers prices when compared to the prices paid on wholesale. In fact, TugaTAC has demonstrated to be good competing with other agents. The experiments have shown that the profit margin is very similar to the values achieved on the real competition [ 18 ].

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We conclude that the complexity of **human** concepts is a direct result of the combinations of a few relatively simple concepts. In fact, some suitable simple concepts play the same role as used in linear vector spaces and we can regard them as a “basis”.

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As the science of robotics advances, robots are interacting with people more frequently. Robots are appearing in our houses and places of work acting as assistants in many capacities. One aspect of this interaction is determining spatial relationships between objects. People and robots simply can not communicate effectively without references to the physical world and how those objects relate to each other. In this research **fuzzy** **logic** is used to help determine the spatial relationships between objects as **fuzzy** **logic** lends itself to the inherent imprecision of spatial relationships. Objects are rarely absolutely in front of or to the right of another, especially when dealing with multiple objects. This research compares three methods of **fuzzy** **logic**, the angle aggregation method, the centroid method and the histogram of angles – composition method. First we use a robot to gather real world data on the geometries between objects, and then we adapt the **fuzzy** **logic** techniques for the geometry between objects from the robot's perspective which is then used on the generated robot data. Last we perform an in depth analysis comparing the three techniques with the **human** survey data to determine which may predict spatial relationships most accurately under these conditions as a **human** would. Previous

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Woods titles Chapter 6 “Economizing.” He points out that cognitive procedures that lead to error need not be an overall bad thing. They give us occasion “to learn from experience. They are fruitful contexts for trial and error” (p. 185) Woods’s next point is that due to the convergence of the normative and the normal, errors made in drawing a conclusion are far less fre- quent than errors in accepting the premises one draws a conclu- sion from. **Human** beings are limited in terms of cognitive re- sources available to them, in particular the amount of infor- mation which is available to them, the time to process, i.e., draw inferences from that information, and their capacity to remember it all. Having made this observation, Woods asserts what I take to be an empirical claim that individual cognitive agents propor- tion their cognitive targets to their cognitive resources (194). These resources ordinarily will not allow the cognitive agents to satisfy the standards of a deductive argument nor of a confirma- tion argument. But as Woods puts it, the default requirements for such targets to be acceptable neither call for deductive va- lidity nor inductive strength. Invalidating inductive weaknesses are not reasons for rejecting that the **reasoning** is good (193). Rather, “something is an error of **reasoning** only if it violates a rule of right **reasoning** that is contextually in force” (193, italics in original).

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Factual divinatory questions can be distinguished with respect to their usage: some questions are concerned with the present or past, they are used for diagnosis, and some questions are concerned with the future, and they are used for prediction. The distinction between diagnostic and predictive divinatory questions has been made by Zeitlyn [21, p.526]. Diagnostic ques- tions are asked to find out what caused a particular situation (in the present or in the past). Predictive questions are asked to find out what will happen if the client does nothing to avoid this (usually bad) outcome. In other words, prediction is hypothetical. As Zeitlyn notices, diagnosis and prediction shade into one another. On the one hand, in order to predict the future one has to diagnose the past. On the other hand, a diagnosis may have predictive implications [21, p.526]. However, he also points out that despite this over- lap, the distinction between diagnostic and predictive use of divination is heuristically useful, since these two uses have different relations to evidence. Diagnostic and predictive statements are evaluated in different ways. **Human** agency may change the truth value of the divinatory predictions. As Zeitlyn formulates it, “we act to change the world, making some predictions literally false but, by divinatory **logic**, true for all that” [21, p.528]. Since the truth value of divinatory predictions is changeable, my surmise is that a more tol- erant attitude can be expected regarding contradictory answers to predictive questions than regarding contradictory answers to diagnostic questions. This may explain why divination session D continues, without abandoning the spi- der, even though the answers “sua will solve the problem” and “sua will not solve the problem” contradict each other. I will elaborate on this suggestion

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Indeed, the origi- nal motivation for using fuzzy logic in building heuristic controllers was that fuzzy logic is designed to capture human state- ments involving vague quantifiers s[r]

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In this paper, a framework for non-conscious ways of reasoning has been presented based on fuzzy 305. multivalued logic, fuzzy semantics and frame oriented knowledge representation[r]

The varying intensities of surprise result in different behaviors. In this case, the relationship between the surprise degrees and behaviors can be described by If- else rules: If agent is very surprise, then actions are cry and run away; If agent is surprise, then action is cry; If agent is little surprise, then there’s only facial expression. The interface for scene 1 includes upper and lower parts. In the upper part, there is a button. Click the button to randomly generate a picture of one object among the eight objects in Table II. In the lower part there is another button. To click on this button will call matlab **reasoning** process that generates the picture of the degree of surprise among three degrees. The **reasoning** process adopts Mamdani inference system. Fig. 16 shows one screenshot of the application for scene 1.

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When formal specifications are to be verified against real-world situations, one has to overcome the qualification problem that denotes the impossibility of listing all conditions required to decide compliance with the specification. To overcome this problem, McCarthy proposed the introduction of “common-sense” into formal **logic** [McC80]. Among the formalisms developed since then, Rei- ter’s default **logic** is one of the best known and most successful formalisms for modeling common-sense **reasoning**. Default **logic** extends the usual logical (first-order or propositional) derivations by patterns for default assumptions. These are of the form “in the absence of contrary information, assume . . .”. Reiter argued that his **logic** is an adequate formalization of **human** **reasoning** under the closed world assumption. In fact, default **logic** is used in various areas of artificial intelligence and computational **logic**, and is known to embed other nonmonotonic formalisms such as extended **logic** programs [GL91].

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elements of a cause of action or the definition of some term of art. Consider the examples below. Example: “Murder is the intentional killing of a **human** being. State v. Jones, 12 N.C. 345, 34 S.E.2d 56 (1929). Here, the defendant is an escaped convict who was already serving a life sentence for the murder of a police officer and was apprehended just two miles from where the victim’s body was found. Therefore, the defendant is guilty of murder.”

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A hybrid **fuzzy** **logic** is proposed for PI, PD and PID controllers. . **Fuzzy** **logic** is much closer in spirit to **human** thinking and natural language than the traditional logical systems. Hybrid controller seeks to achieve multiple performance objectives in locally adaptive sense by switching between members of a specified family of feedback functions. In this the hybrid **fuzzy** **logic** controller can be used to avoid the variation in the output voltage .

Since the initial release in mid 2006 the grow- ing user base has voiced a number of suggestions and requests for improving KNIME’s usability and functionality. From the beginning KNIME has sup- ported open standards for exchanging data and mod- els. Early on, support for the Predictive Model Markup Language (PMML) 15 was added and most of the KNIME mining modules natively support PMML, including association analysis, clustering, regressions, neural network, and tree models. With the latest KNIME release, PMML support was en- hanced to cover PMML 4.1. See 18 for more details. Before dicussing how **fuzzy** types and learning methods can be integrated into KNIME, let us first discuss the KNIME architecture in more detail.

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k-nearest neighbors (k-NN) is typically used to calculate similarity in the retrieval step (cases indexing). We compared our **Fuzzy** Inference Mechanism with decision tree and k-nearest neighbours. We noticed that case indexing for the selection of a diabetes surveillance plan is considerably better with our **Fuzzy** Inference Mechanism (FDT4CR). Compared to retrieval by k-nn which is costly in computing time, retrieval by FDT provides one major advantage, it optimizes the response time. Furthermore, **fuzzy** **reasoning** combined with data mining for retrieval presents several advantages. First, it reduces the complexity of similarity calculation between individuals. Second, it presents an improved retrieval in the CBR process of JColibri. However, FDT4CR has some disadvantages related to the complexity of the domain of Diabetes Diagnosis. Building the cases-base from diabetic patient databases, the encoding of case base knowledge with standard medical files and the adaptation of vague data are examples of these challenges. The case structure used in FDT4CR is quite simple. The part problem of cases has been described by Body mass index (BMI), 2-hour serum insulin (INS), Plasma glucose concentration in 2-hours OGTT (Glucose), Age (Age) and Diabetes pedigree function (DPF). The solution part is defined by a monitoring plan corresponding to a crisp output, with the classification option.

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