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1. Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets.

Author

Zheng, Mucong, Shi, Zhongke, and Liu, Yan

Subjects
*APPROXIMATION theory, *INTUITIONISTIC mathematics, *FUZZY sets, *LATTICE theory, *MATHEMATICAL models, *PROBLEM solving
Abstract

Abstract: Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning. [Copyright &y& Elsevier]

Published
2014
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2. On the entropy for Atanassov's intuitionistic fuzzy sets: An interpretation from the perspective of amount of knowledge.

Author

Guo, Kaihong and Song, Qi

Subjects
ENTROPY (Information theory), FUZZY sets, INTUITIONISTIC mathematics, KNOWLEDGE management, MATHEMATICAL models
Abstract

Given the fact that totally unknown information cannot be expressed by Zadeh's fuzzy sets but can well be represented by Atanassov's intuitionistic fuzzy sets (A-IFSs), we provide in this paper a new idea, from the perspective of amount of knowledge, that the entropy for such information should be unique so that it may differ significantly from the entropy of a particular fuzzy element of which the membership and non-membership values are both equal to 0.5. Motivated by this idea, we present a more strict axiomatic definition of entropy on A-IFSs, and then develop a new entropy measure of A-IFSs that satisfies the refined axioms, with the aim of overcoming some drawbacks and ambiguities the existing entropy brings about and building a new entropy measurement model in the A-IFSs context to show some unique features of A-IFSs from the viewpoint of a specific purpose, notably those related to decision making. This allows us to capture the intrinsic amount of knowledge and the additional features that may be relevant when making decisions, and ultimately may be able to help us distinguish such particular cases in which the membership values are equal to the corresponding non-membership values in the A-IFSs context. Finally, a real-life example is provided for an in-depth discussion on the application of the developed models in decision making under uncertainty. [ABSTRACT FROM AUTHOR]

Published
2014
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3. The theory of intuitionistic fuzzy sets based on the intuitionistic fuzzy special sets.

Author

Yuan, Xue-hai, Li, Hong-xing, and Zhang, Cheng

Subjects
*INTUITIONISTIC mathematics, *FUZZY sets, *MATHEMATICS theorems, *MATHEMATICAL decomposition, *GROUP theory, *MATHEMATICAL models
Abstract

Abstract: In this paper, we build up a connection between intuitionistic fuzzy special set (IFSS) and intuitionistic fuzzy set (IFS). Firstly, by using the concept of IFSS, we present the concept of intuitionistic nested set (INS) and show that an IFS can be determined by an INS. Secondly, we introduce the concept of -cut sets of IFS and show that -cut sets of IFS have the same properties as the cut sets of Zadeh fuzzy set. Thirdly, by using the concepts of -cut set of IFS and INS, we build up the decomposition theorem, representation theorem and extension principle of IFS. Finally, we apply our theory to intuitionistic fuzzy algebra and obtain the concept of intuitionistic fuzzy subgroup. [Copyright &y& Elsevier]

Published
2014
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