In this paper, I provide the basis for a measureand integral-theoretic formulation of possibility theory. It is shown that, using a general definition of possibility measures, and a generalization of Sugeno’s fuzzy integral – the seminormed fuzzy integral, or possibility integral –, a unified and consistent account can be given of many of the possibilistic results extant in the literature. The ...

Failure mode and effects analysis (FMEA) is a popular and useful approach applied to examine potential failures in different products, designs, processes, and services. As a vital index, the risk priority number (RPN) can determine the risk priorities of failure modes by some risk factors such as occurrence (O), severity (S), and detection (D). However, in FMEA, the traditional risk priority nu...

In this note, we study an approximation property of regular fuzzy neural network(RFNN). It is shown that any fuzzy-valued measurable function can be approximated by the four-layer RFNN in the sense of fuzzy integral norm for the finite sub-additive fuzzy measure on R.

Non-monotonic fuzzy measures induced by an intuitinistic fuzzy set are introduced. Then, using the Choquet integral with respect to the non-monotonic fuzzy measure, the weighted distance between two intuitionistic fuzzy sets is defined. As it will be shown here, under some conditions, the weighted distance coincides with the Hamming distance.

This paper will present a novel concept of expected values of fuzzy variables, which is essentially a type of Choquet integral and coincides with that of random variables. In order to calculate the expected value of general fuzzy variable, a fuzzy simulation technique is also designed. Finally, we construct a spectrum of fuzzy expected value models, and integrate fuzzy simulation, neural networ...

In this paper the fixed point theorem of Schauder is used to prove the existence of a continuous solution of the nonlinear fuzzy Volterra integral equations. Then using some conditions the uniqueness of the solution is investigated.

In this paper, we review two of the most well-known citation indexes and establish their connections with the Choquet and Sugeno integrals. In particular, we show that the recently established -index is a particular case of the Sugeno integral, and that the number of citations corresponds to the Choquet integral. In both cases, they use the same fuzzy measure. The results presented here permit ...

In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernstein polynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve t...

prompt detection and diagnosis of faults in industrial systems areessential to minimize the production losses, increase the safety of the operatorand the equipment. several techniques are available in the literature to achievethese objectives. this paper presents fuzzy based control and fault detection for a6/4 switched reluctance motor. the fuzzy logic control performs like a classicalproporti...