scholarly journals The Dual Triple I Methods of FMT and IFMT

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Liu Yan ◽  
Zheng Mucong
Keyword(s):  
Fuzzy Sets ◽  
Decomposition Method ◽  
Difference Operator ◽  
Lattice Structure ◽  
Intuitionistic Fuzzy Sets ◽  
Approximate Reasoning ◽  
Modus Tollens ◽  
Intuitionistic Fuzzy ◽  
Triple I Method

The Triple I method for the model of intuitionistic fuzzy modus tollens (IFMT) satisfies the local reductivity instead of the reductivity. In order to improve the quality of the Triple I method for lack of reductivity, the paper is intended to present a new approximate reasoning method for IFMT problem. First, the concept of intuitionistic fuzzy difference operator is proposed and its properties on the lattice structure of intuitionistic fuzzy sets are studied. Then, the dual Triple I method for FMT based on residual fuzzy difference operator is presented and the dual Triple I method is generated for IFMT. Moreover, a decomposition method of IFMT is provided. Furthermore, the reductivity of methods is investigated. Finally,α-dual Triple I method of IFMT is proposed.

Novel Similarity Measures, Entropy of Intuitionistic Fuzzy Sets and their Application in Software Quality Evaluation

2021 ◽  
Author(s):  
Xuan Thao Nguyen ◽  
Shuo Yan Chou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Uncertain Information ◽  
Membership Functions ◽  
Software Projects ◽  
Intuitionistic Fuzzy ◽  
Software Quality Evaluation

Abstract Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping stone to calculate the weights of the criteria in the proposed multi-criteria decision making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

Rough Sets and Approximate Reasoning

2014 ◽  
pp. 180-228 ◽  
Author(s):  
B. K. Tripathy
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Approximate Reasoning ◽  
Human Reasoning ◽  
Intuitionistic Fuzzy ◽  
Application Point ◽  
Future Work

Several models have been introduced to capture impreciseness in data. Fuzzy sets introduced by Zadeh and Rough sets introduced by Pawlak are two of the most popular such models. In addition, the notion of intuitionistic fuzzy sets introduced by Atanassov and the hybrid models obtained thereof have been very fruitful from the application point of view. The introduction of fuzzy logic and the approximate reasoning obtained through it are more realistic as they are closer to human reasoning. Equality of sets in crisp mathematics is too restricted from the application point of view. Therefore, extending these concepts, three types of approximate equalities were introduced by Novotny and Pawlak using rough sets. These notions were found to be restrictive in the sense that they again boil down to equality of sets and also the lower approximate equality is artificial. Keeping these points in view, three other types of approximate equalities were introduced by Tripathy in several papers. These approximate equalities were further generalised to cover the approximate equalities of fuzzy sets and intuitionistic fuzzy sets by him. In addition, considering the generalisations of basic rough sets like the covering-based rough sets and multigranular rough sets, the study has been carried out further. In this chapter, the authors provide a comprehensive study of all these forms of approximate equalities and illustrate their applicability through several examples. In addition, they provide some problems for future work.

Reverse triple I method based on single valued neutrosophic fuzzy inference

2020 ◽  
Vol 39 (5) ◽  
pp. 7071-7083
Author(s):  
Ruirui Zhao ◽  
Minxia Luo ◽  
Shenggang Li
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Inference ◽  
Intuitionistic Fuzzy Sets ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Intuitionistic Fuzzy ◽  
Triple I Method

The theory of single valued neutrosophic sets, which is a generalization of intuitionistic fuzzy sets, is more capable of dealing with inconsistent information in practice. In this paper, we propose reverse triple I method under single valued neutrosophic environment. Firstly, we give the definitions of single valued neutrosophic t-representation t-norms and single valued neutrosophic residual implications. Secondly, we develop a formula for calculating single valued neutrosophic residual implications. Then we propose reverse triple I method based on left-continuous single valued neutrosophic t-representation t-norms and its solutions. Lastly, we discuss the robustness of reverse triple I method based on the proposed similarity measure.

One Hundredth of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 10 (3) ◽  
pp. 445-453
Author(s):  
R. Nagalingam ◽  
S. Rajaram
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy
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