Pettis integrability of fuzzy mappings with values in arbitrary Banach spaces

In this paper we study the Pettis integral of fuzzy mappings in arbitrary Banach spaces. We present some properties of the Pettis integral of fuzzy mappings and we give conditions under which a scalarly integrable fuzzy mapping is Pettis integrable

Algorithm of arithmetical operations with fuzzy numerical data

In this article the theoretical generalization for representation of arithmetic operations with fuzzy numbers is considered. Fuzzy numbers are generalized by means of fuzzy measures. On the basis of this generalization the new algorithm of fuzzy arithmetic which uses a principle of entropy maximum is created. As example, the summation of two fuzzy numbers is considered. The algorithm is realized in the software "Fuzzy for Microsoft Excel".fuzzy measure (Sugeno), fuzzy integral (Sugeno), fuzzy numbers; arithmetical operations; principle of entropy maximum

Possibility expectation and its decision making algorithm

The fuzzy integral has been shown to be an effective tool for the aggregation of evidence in decision making. Of primary importance in the development of a fuzzy integral pattern recognition algorithm is the choice (construction) of the measure which embodies the importance of subsets of sources of evidence. Sugeno fuzzy measures have received the most attention due to the recursive nature of the fabrication of the measure on nested sequences of subsets. Possibility measures exhibit an even simpler generation capability, but usually require that one of the sources of information possess complete credibility. In real applications, such normalization may not be possible, or even desirable. In this report, both the theory and a decision making algorithm for a variation of the fuzzy integral are presented. This integral is based on a possibility measure where it is not required that the measure of the universe be unity. A training algorithm for the possibility densities in a pattern recognition application is also presented with the results demonstrated on the shuttle-earth-space training and testing images

Hybrid fuzzy- proportionl integral derivative controller (F-PID-C) for control of speed brushless direct curren motor (BLDCM)

Hybrid Fuzzy proportional-integral-derivative (PID) controllers (F-PID-C) is designed and analyzed for controlling speed of brushless DC (BLDC) motor. A simulation investigation of the controller for controlling the speed of BLDC motors is performed to beat the presence of nonlinearities and uncertainties in the system. The fuzzy logic controller (FLC) is designed according to fuzzy rules so that the systems are fundamentally robust. There are 49 fuzzy rules for each parameter of FUZZY-PID controller. Fuzzy Logic is used to tune each parameter of the proportional, integral and derivative ( kp,ki,kd) gains, respectively of the PID controller. The FLC has two inputs i.e., i) the motor speed error between the reference and actual speed and ii) the change in speed of error (rate of change error). The three outputs of the FLC are the proportional gain, kp, integral gain ki and derivative gain kd, gains to be used as the parameters of PID controller in order to control the speed of the BLDC motor. Various types of membership functions have been used in this project i.e., gaussian, trapezoidal and triangular are assessed in the fuzzy control and these membership functions are used in FUZZY PID for comparative analysis. The membership functions and the rules have been defined using fuzzy system editor given in MATLAB. Two distinct situations are simulated, which are start response, step response with load and without load. The FUZZY-PID controller has been tuned by trial and error and performance parameters are rise time, settling time and overshoot. The findings show that the trapezoidal membership function give good results of short rise time, fast settling time and minimum overshoot compared to others for speed control of the BLDC motor

A new integral for capacities

A new integral for capacities, different from the Choquet integral, is introduced and characterized. The main feature of the new integral is concavity, which might be interpreted as uncertainty aversion. The integral is then extended to fuzzy capacities, which assign subjective expected values to random variables (e.g., portfolios) and may assign subjective probability only to a partial set of events. An equivalence between minimum over sets of additive capacities (not necessarily probability distributions) and the integral w.r.t. fuzzy capacities is demonstrated. The extension to fuzzy capacities enables one to calculate the integral also when there is information only about a few events and not about all of them.new integral, capacity, choquet integral, fuzzy capacity, concavity

On the Minkowski-H\"{o}lder type inequalities for generalized Sugeno integrals with an application

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.Comment: 19 page