Probabilistic fuzzy systems combine a linguistic description of the system behaviour with statistical properties of data. It was originally derived based on Zadeh’s concept of probability of a fuzzy event. Two possible and equivalent additive reasoning schemes were proposed, that lead to the estimation of the output’s conditional probability density. In this work we take a complementary approac...

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of ’bounded integral contractor’, introduced by Altman [1], is weaker than Lipschitz condition.

The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...

This paper establishes an evaluation system based on the low-carbon intensive land use in Jinan city from 2010 to 2017 and uses a multi-attribute approach named grey fuzzy integral build model. In this model, Mobius transformation coefficient of subjective objective weights index factors interaction degree between factors, 2-additive measures can be obtained; therefore, is processed by combinin...

In this paper, the Henstock integral for fuzzy-number-valued functions in R is defined and some properties of this integral are discussed. Finally, by using the embedding theorem the fuzzy number space E can be embedded into a concrete space, some characterized theorems for this integral are given. AMS Subject Classification: 94D05, 46S40, 47S40, 54A40

In this paper, a new fuzzy density function, called N-density, is proposed. A real data set about Students Valuing Science with 5-fold cross-validation RMSE is conducted, for comparing the performances of the Choquet integral regression model with respect to six measures, Pmeasure, λ-measure, L-measure, extensional L-measure, completed L-measure and extensional completed L-measure based on this...

Choquet-integral-based evaluation models are proposed. The evaluation parameters – fuzzy measures – are assigned from a fuzzy rule table. There are three variations in this model: TF-, BP-, and AV-type models. The TF-type model is a natural extension of ordinal Choquet integrals. The BP-type model involves an evaluation using a reference point. The AV-type model involves a neutral evaluation me...

In international trade offset practices (in Taiwan known as industrial cooperation program, ICP) have received increased attention over the past 20 years. In the coming 10 years, the Taiwanese government may expend roughly US$16 billion for purchasing Patriot-III missiles, P-3 long-range anti-submarine planes, and diesel-engine submarines from the United States through foreign military sale, an...

Fuzzy measure and fuzzy integral theory is an outgrowth of classical measure theory and has found applications in image processing and information fusion. This paper presents the review of a study on the development of a machinery fault diagnosis application of fuzzy measures and fuzzy integrals. Fuzzy measures and fuzzy integrals take into account the index of importance of criteria and intera...