The additivity property of the ``measure'', one of the most important concepts in mathematics, is often inflexible or too rigid to represent the many facets of human reasoning. In order to be able to express human subjectivity, recent researches proposed to replace this property by a weaker one, the ``monotonicity'' and called these non-additive monotonic measures ``fuzzy measures''. “Fuzzy int...

in this paper, we propose a numerical method for the approximate solution of fuzzy Fredholm functional integral equations of the second kind by using an iterative interpolation. For this purpose, we convert the linear fuzzy Fredholm integral equations to a crisp linear system of integral equations. The proposed method is illustrated by some fuzzy integral equations in numerical examples. Keywor...

Fuzzy measures and integrals have been used in multiple applications in the area of information fusion. They can be used to aggregate information when information sources are not independent. Fuzzy measures are used to represent our background knowledge on the information sources. In particular, they can be used to model the dependencies between the variables. One of the applications of Choquet...

Some simple yet pragmatic methods of consistency test are developed to check whether an interval fuzzy preference relation is consistent. Based on the definition of additive consistent fuzzy preference relations proposed by Tanino [Fuzzy Sets and Systems 12 (1984) 117131], a study is carried out to examine the correspondence between the element and weight vector of a fuzzy preference relation. ...

In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

We introduce three reasonable versions of fuzzy approximately additive functions in fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately additive function can be approximated by an additive mapping in a fuzzy sense. © 2007 Elsevier B.V. All rights reserved. MSC: primary 46S40secondary 39B52 39B82 26E50 46S50

In 1974, Sugeno introduced the notion of fuzzy measure and integral to evaluate nonadditive or non-linear quality in systems engineering. In the same year, Dobrakov independently introduced the notion of submeasure from mathematical point of view to show that most of the theory of countably additive measures remain valid for such measures. Fuzzy measures and submeasures are both special kinds o...

the purpose of this paper is to study the fuzzy fractional differentialequations. we prove that fuzzy fractional differential equation isequivalent to the fuzzy integral equation and then using this equivalenceexistence and uniqueness result is establish. fuzzy derivative is considerin the goetschel-voxman sense and fractional derivative is consider in theriemann liouville sense. at the end, we...

In this paper, we are discuss about the issue of synchronization for singular complex dynamical networks with Markovian jumping parameters and additive time-varying delays through pinning control by Takagi-Sugeno (T-S) fuzzy theory.The complex dynamical systems consist of m nodes and the systems switch from one mode to another, a Markovian chain with glorious transition probabili...