Introduction. Required Background in Set Theory. Fuzzy Measures. Extensions. Structural Characteristics for Set Functions. Measurable Functions on Fuzzy Measure Spaces. Fuzzy Integrals. PanIntegrals. Applications. Index.

In this paper, we present the definition of λ-fuzzy signed measure, its generalized transform function, and the distribution properties of λ-fuzzy measures. Then investors' heterogeneity is revealed with a family of λ-fuzzy measures. The approach to asset pricing based on λ-fuzzy measures breaks through the traditional ”identical rationality” assumption, and provides an useful analytical tool for recent researches of behavioral economics and finance.

Fuzzy Measure Theory

The generalization of λ-fuzzy measures with application to the fuzzy option

There is presented probabilistic von Neumann-Morgenstern type approach to engineering design. Further generalization of the utility theory, using pseudo-analysis, first based on possibility theory, and second, as a common generalization through hybridization of the both preceding approaches are given. In modeling uncertainty in engineering design it is very useful the fuzzy system approach, which involves further real operations as aggregation functions.

Pseudo-analysis in Engineering Decision Making

A general Minkowski type inequalities for the semiconormed fuzzy integrals on abstract spaces are studied. Some related inequalities to this type one and Chebyshev type one for the semiconormed fuzzy integral are also discussed. Also a related inequalities for the Minkoski type inequality are obtained

General Minkowski type and Related Inequalities for Semi-conormed Fuzzy Integrals

http://diposit.ub.edu/dspace/bitstream/2445/120168/1/676954.pdf

Continuous m-dimensional distorted probabilities

Critical systems are today exposed to new kinds of security threats. Cyber security is determine with cyberspace safe from threats, it is called cyber-threats. Cyber-threats is applied the malicious use of information and communication technologies or the behaviour of attackers. Because of the importance of cyber threats, operating system (OS) selection is a critical decision that can significantly affect future competitiveness and performance of an organization. It is increasingly valuable in today’s current administration and businesses because of its ability to integrate the information. An operating system, especially with the weakness in security can lead to serious financial losses. The aim of this study is to develop a decision model based on Analitic Network Process (ANP)-choquet integral integration that select the appropriate operating system for critical computer systems by taking subjective judgments of decision makers into consideration. Proposed approach is based on ANP-choquet integral method. ANP method is used in determining the weights of the criteria by decision makers and then choquet integral is applied in rankings of the operating systems. Numerical study has also been demonstrated.

http://www.ijiss.org/ijiss/index.php/ijiss/article/download/12/pdf

Fuzzy Measure Theory

Citations

The generalization of λ-fuzzy measures with application to the fuzzy option

Pseudo-analysis in Engineering Decision Making

General Minkowski type and Related Inequalities for Semi-conormed Fuzzy Integrals

Continuous m-dimensional distorted probabilities

A Study on OS Selection Using ANP Based Choquet Integral in Terms of Cyber Threats

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