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Trapezoidal approximation operators preserving the most indicators of fuzzy numbers-relationships and applications

SOFT COMPUTING 2022年第15期26卷 7081-7105页

作者： Chehlabi, M. Islamic Azad Univ Dept Math Savadkooh Branch Savadkooh Iran

The aim of this paper is the study of trapezoidal approximation operators, preserving more indicators of fuzzy numbers, relationships between them and their applications. Initial results lead to achieve three main trapezoidal approximation operators that one of them preserves the core, value and the ambiguity, and another one preserves the core and the expected interval, and third operator preserves the value, ambiguity and expected interval. The related concepts and the important properties of these operators and also, comparisons between them are brought, in details. Finally, a ranking method, an approximation operator preserving the most indicators of fuzzy numbers, and a trapezoidal approximation algorithm with its advantages and comparative examples are given as practical applications of the obtained results.

关键词： Fuzzy numbers Trapezoidal approximation approximation operators

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Using single axioms to characterize (S,T)-intuitionistic fuzzy rough approximation operators

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INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2019年第1期10卷 27-42页

作者： Wu, Wei-Zhi Shao, Ming-Wen Wang, Xia Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Zhejiang Peoples R China Zhejiang Ocean Univ Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Zhejiang Peoples R China Chinese Univ Petr Coll Comp & Commun Engn Qingdao 266580 Shandong Peoples R China

In this paper axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy triangular norm T and its dual intuitionistic fuzzy triangular conorm S on [0,1]x[0,1] are proposed. The constructive definitions and properties of S-lower and T-upper intuitionistic fuzzy rough approximation operators are first introduced. Operator-oriented characterizations of (S,T)-intuitionistic fuzzy rough approximation operators are then explored. Different sets of independent axioms for characterizing the essential properties of (S,T)-intuitionistic fuzzy rough approximation operators generated by various intuitionistic fuzzy relations are presented. Finally, it is examined that these sets of axioms can all be replaced by single axioms.

关键词： approximation operators Intuitionistic fuzzy rough sets Intuitionistic fuzzy sets Rough sets Triangular norms

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On characterization of (I,N)-single valued neutrosophic rough approximation operators

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SOFT COMPUTING 2019年第15期23卷 6065-6084页

作者： Bao, Yan-Ling Yang, Hai-Long Li, Sheng-Gang Shaanxi Normal Univ Coll Math & Informat Sci Xian 710062 Shaanxi Peoples R China

This paper presents a general framework for the study of (I,N)-single valued neutrosophic rough sets from constructive and axiomatic perspectives. In the constructive approach, a pair of single valued neutrosophic rough approximation operators based on single valued neutrosophic implicator I and single valued neutrosophic norm N is first proposed. Moreover, some basic properties of (I,N)-single valued neutrosophic rough approximation operators are explored. In addition, connections between single valued neutrosophic relations and (I,N)-single valued neutrosophic rough approximation operators are systematically discussed. In the axiomatic approach, axiomatic characterization of (I,N)-single valued neutrosophic approximation operators is studied. Specifically, different axiom sets characterizing the intrinsic properties of (I,N)-single valued neutrosophic rough approximation operators associated with diverse single valued neutrosophic relations are investigated in detail.

关键词： Single valued neutrosophic sets Rough sets Single valued neutrosophic rough sets approximation operators SVN-norms SVN-implicators

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Using one axiom to characterize L-fuzzy rough approximation operators based on residuated lattices

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FUZZY SETS AND SYSTEMS 2018年第Apr.1期336卷 87-115页

作者： Bao, Yan-Ling Yang, Hai-Long She, Yan-Hong Shaanxi Normal Univ Coll Math & Informat Sci Xian 710119 Shaanxi Peoples R China Xian Shiyou Univ Coll Sci Xian 710065 Shaanxi Peoples R China

Axiomatic characterization of approximation operators plays an important role in the study of rough set theory. Different axiom sets of abstract operators can illustrate different classes of rough set systems. In this paper, we are devoted to searching for a single axiom to characterize L-fuzzy rough approximation operators based on residuated lattices. Axioms of L-fuzzy set theoretic operators make sure of the existence of certain types of L-fuzzy relations which produce the same operators. We demonstrate that the lower (upper) L-fuzzy rough approximation operators generated by a generalized L-fuzzy relation can be characterized by only one axiom. Furthermore, we also use one axiom to characterize L-fuzzy rough approximation operators produced by the L-fuzzy serial, reflexive, symmetric and T-transitive relations as well as any of their compositions. (c) 2017 Elsevier B.V. All rights reserved.

关键词： Rough sets Residuated lattices L-fuzzy rough sets approximation operators Axioms

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approximation operators in Covering Based Rough Sets from Submodular Functions

Approximation Operators in Covering Based Rough Sets from Su...

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International Joint Conference on Rough Sets (IJCRS)

作者： Restrepo, Mauricio Univ Militar Nueva Granada Dept Math Bogota Colombia

ISBN: (纸本)9783319608372;9783319608365

We present a new collection of upper approximation operators for covering based rough sets, obtained from sub modular functions and closure operators. Each non decreasing submodular function defines a closure operator that can be considered as an approximation operator. The construction allows us to define several upper approximation operators. Some properties of these operators are studied.

关键词： Covering rough sets approximation operators Submodular functions

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Notes on covering-based rough sets from topological point of view: Relationships with general framework of dual approximation operators

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2017年第Sep.期88卷 295-305页

作者： D'eer, Lynn Cornelis, Chris Univ Ghent Dept Appl Math Comp Sci & Stat Ghent Belgium

In the recent article "On some types of covering rough sets from topological points of view" [14], the author develops a topological approach to covering-based rough sets. In this context, a number of corresponding approximation operators are introduced, their inclusion relationships are verified, and various conditions under which the operators coincide are proven. On the other hand, a lot of effort has recently been dedicated by several authors to study covering-based approximation operators within a general framework of dual approximation operators [2,3,7-10,12]. In this note, we study correspondences between the framework of Zhao and the framework established in [2]. In particular, we evaluate how the newly introduced topological approximation operators relate to existing ones in terms of equalities and partial order relations. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Rough sets Coverings approximation operators Topology

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On Simplified Axiomatic Characterizations of (θ, σ)-Fuzzy Rough approximation operators

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INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2017年第3期25卷 457-476页

作者： Zhang, Hongying Song, Haijuan Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Provinc Peoples R China

The axiomatic approach is more appropriate than constructive approach for studying the algebraic structure of rough sets. In this paper, the more simple axiomatic characterizations of (theta, sigma)-fuzzy rough approximation operators are explored where u is a residuated implicator and sigma is its dual implicator. Firstly, we review the existing independent axiomatic sets to characterize various types of 19-lower and a-upper fuzzy rough approximation operators. Secondly, we present one-axiom characterizations of (theta, sigma)-fuzzy rough approximation operators constructed by a serial fuzzy relation on two universes. Furthermore, we show that (theta, sigma)-fuzzy rough approximation operators, corresponding to reflexive, symmetric and T-transitive fuzzy relations, can be presented by only two axioms respectively. We conclude the paper by introducing some potential applications and future works.

关键词： Fuzzy rough sets approximation operators residuated implicators axiomatic characterizations

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Axiomatic characterizations of (S, T)-fuzzy rough approximation operators

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INFORMATION SCIENCES 2016年 334卷 17-43页

作者： Wu, Wei-Zhi Xu, You-Hong Shao, Ming-Wen Wang, Guoyin Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Zhejiang Peoples R China Zhejiang Ocean Univ Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Zhejiang Peoples R China Chinese Univ Petr Coll Comp & Commun Engn Qingdao 266580 Shandong Peoples R China Chongqing Univ Posts & Telecommun Chongqing Key Lab Computat Intelligence Chongqing 400065 Peoples R China

Axiomatic characterizations of approximation operators are of importance in the study of rough set theory. In this paper axiomatic characterizations of relation-based (S, T)-fuzzy rough approximation operators are investigated. By employing a triangular conorm S and a triangular norm T on [0, 1], we first introduced the constructive definitions of S-lower and T-upper fuzzy rough approximation operators with their essential properties. We then propose an operator-oriented characterization of (S, T)-fuzzy rough sets, that is, fuzzy set-theoretic operators defined by axioms guarantee the existence of different types of fuzzy relations which produce the same operators. We show that the S-lower (and, respectively, T-upper) fuzzy rough approximation operators generated by a generalized fuzzy relation can be described by only one axiom. We further show that (S, T)-fuzzy rough approximation operators corresponding to special types of fuzzy relations, such as serial, reflexive, symmetric, and T-transitive ones as well as any of their compositions, can also be characterized by single axioms. (C) 2015 Elsevier Inc. All rights reserved.

关键词： approximation operators Fuzzy relations Fuzzy rough sets Rough sets Triangular norms

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Using One Axiom to Characterize Fuzzy Rough approximation operators Determined by a Fuzzy Implication Operator

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FUNDAMENTA INFORMATICAE 2015年第1-4期142卷 87-104页

作者： Wu, Wei-Zhi Li, Tong-Jun Gu, Shen-Ming Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Zhejiang Peoples R China Zhejiang Ocean Univ Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Zhejiang Peoples R China

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based fuzzy rough approximation operators determined by a fuzzy implication operator I are investigated. We first review the constructive definitions and properties of lower and upper I-fuzzy rough approximation operators. We then propose an operator-oriented characterization of I-fuzzy rough sets. We show that the lower and upper I-fuzzy rough approximation operators generated by an arbitrary fuzzy relation can be described by single axioms. We further examine that I-fuzzy rough approximation operators corresponding to some special types of fuzzy relations, such as serial, reflexive, and T -transitive ones, can also be characterized by single axioms.

关键词： approximation operators fuzzy implication operators fuzzy rough sets rough sets triangular norms

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Axiomatic Characterizations of Reflexive and T-Transitive I-Intuitionistic Fuzzy Rough approximation operators 15th

Axiomatic Characterizations of Reflexive and T-Transitive I-...

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15th International Conference on Rough Sets, Fuzzy Sets, Data Mining and Granular Computing (RSFDGrC)

作者： Wu, Wei-Zhi Xu, You-Hong Li, Tong-Jun Wang, Xia Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Zhejiang Peoples R China Zhejiang Ocean Univ Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Zhejiang Peoples R China

ISBN: (纸本)9783319257839;9783319257822

Axiomatic characterizations of approximation operators are important in the study of rough set theory. In this paper, axiomatic characterizations of relation-based intuitionistic fuzzy rough approximation operators determined by an intuitionistic fuzzy implication operator I are investigated. We present a set of axioms of lower/upper I-intuitionistic fuzzy set-theoretic operator which is necessary and sufficient for the existence of an intuitionistic fuzzy relation producing the same operator. We show that the lower and upper I-intuitionistic fuzzy rough approximation operators generated by an arbitrary intuitionistic fuzzy relation can be described by single axioms. Moreover, the I-intuitionistic fuzzy rough approximation operators generated by reflexive and T-transitive intuitionistic fuzzy relations can also be characterized by single axioms.

关键词： approximation operators Intuitionistic fuzzy implicators Intuitionistic fuzzy rough sets Intuitionistic fuzzy sets Rough sets

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