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Complex fuzzy set-valued complex fuzzy measures and their properties.
1College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, China ; School of Information and Technology, Hainan Normal University, Haikou 571158, China.
Thescientificworldjournal
|August 6, 2014
Summary
This study extends classical and measure-theoretical concepts to complex fuzzy sets, introducing fuzzy complex number-valued distances and measures. Properties of these new fuzzy measures are then explored in detail.
Area of Science:
- Mathematics
- Fuzzy Set Theory
- Measure Theory
Background:
- Classical measure theory and distance concepts are foundational in mathematics.
- Fuzzy set theory extends classical sets to handle uncertainty and vagueness.
- Extending these concepts to complex fuzzy sets requires novel theoretical frameworks.
Purpose of the Study:
- To extend classical and measure-theoretical notions to the domain of complex fuzzy sets.
- To define and investigate fuzzy complex number-valued distances and measures.
- To analyze properties such as additivity, subtraction, and continuity for these new fuzzy measures.
Main Methods:
- Generalization of existing distance and measure definitions.
- Introduction of new concepts like fuzzy complex number-valued measures.
- Detailed examination of properties including null-additivity, pseudo-null-additivity, and various forms of autocontinuity.
Main Results:
- Successful extension of distance and measure concepts to fuzzy complex numbers.
- Introduction and characterization of novel fuzzy complex number-valued measures.
- Comprehensive study of the properties of these newly defined fuzzy measures.
Conclusions:
- The paper successfully bridges classical measure theory with complex fuzzy sets.
- The defined fuzzy complex number-valued measures and their properties offer a new mathematical framework.
- This work lays the groundwork for further research in complex fuzzy measure theory.
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