Multiple Definite Integrals of Intuitionistic Fuzzy Calculus and Isomorphic Mappings

2018 ◽  
Vol 26 (2) ◽  
pp. 670-680 ◽  
Author(s):  
Zhenghai Ai ◽  
Zeshui Xu
Keyword(s):  
Definite Integrals ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Calculus

An Approach Based on Definite Integrals to Multi-Criteria Decision Making with Correlative Intuitionistic Fuzzy Information

2016 ◽  
Vol 24 (06) ◽  
pp. 807-829 ◽  
Author(s):  
Shan Yu ◽  
Zeshui Xu
Keyword(s):  
Decision Making ◽  
Fuzzy Measure ◽  
Multi Criteria Decision Making ◽  
Fuzzy Information ◽  
Definite Integrals ◽  
Intuitionistic Fuzzy ◽  
Technology Improvement ◽  
Fusion Methods

Integration plays a very important role in the fusion methods. In this paper, we put forward the subtraction and division definite integrals based on the fuzzy measure and the admissible order for aggregating not only discrete but also continuous correlative intuitionistic fuzzy information. These definite integrals are implemented by constructing the integrands and the integral limits respectively, and based on which an approach to multi-criteria decision making with correlative intuitionistic fuzzy information is developed. Finally, an illustrative example involving technology improvement of Midwest American Manufacturing Corp is employed to verify the practicality and effectiveness of our approach.

scholarly journals Foundation of Interval-Valued Intuitionistic Fuzzy Limit and Differential Theory and an Application to Continuous Data

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Zhenghai Ai ◽  
Xiaoqin Shu ◽  
Zeshui Xu
Keyword(s):  
Fuzzy Numbers ◽  
Primary Task ◽  
Continuous Data ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Operational Laws ◽  
Fuzzy Calculus ◽  
Interval Valued

The intuitionistic fuzzy calculus (IFC), based on the basic operational laws of intuitionistic fuzzy numbers (IFNs), has been put forward. However, the interval-valued IFC (IVIFC), based on the basic operational laws of interval-valued IFNs (IVIFNs), is only in the original stage. To further develop the theory of the IVIFC and make it be rigorous, the primary task is to systematically investigate the characteristics of the limits and differentials, which is a foundation of the IVIFC. Moreover, there is quite a lot of literature on IVIFNs; however, the scholars did not reveal the relationships between IFNs and the IVIFNs. To do that, we first investigate the limit of interval-valued intuitionistic fuzzy sequences, and then, we focus on investigating the limit, the continuity, and the differential of IVIFFs in detail and reveal their relationships. After that, due to the fact that the IFC and the IVIFC are based on the basic operational laws of IFNs and IVIFNs, respectively, we reveal the relationships between the IFNs and the IVIFNs via some homomorphic mappings. Finally, a case study about continuous data of IVIFNs is provided to illustrate the advantages of continuous data.

Definite Integrals of Atanassov's Intuitionistic Fuzzy Information

2015 ◽  
Vol 23 (5) ◽  
pp. 1519-1533 ◽  
Author(s):  
Qian Lei ◽  
Zeshui Xu ◽  
Humberto Bustince ◽  
Ana Burusco
Keyword(s):  
Fuzzy Information ◽  
Definite Integrals ◽  
Intuitionistic Fuzzy
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