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2008•Journal of Sichuan Normal UniversityRequires access

Autocontinuity of Set-valued Fuzzy Measures

Guijun Wang

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Abstract

By introducing a new order structure in the class of subsets of an m dimensional positive Euclid space,the concept of convergence(in respect to the order) of set sequences is defined.Then autocontinuity,uniform autocontinuity,converse-autocontinuity and uniform converse-autocontinuity for the set-valued fuzzy measure are discussed.The definitions for the so-called converse-null-additivity,converse-autocontinuity,and uniform converse-autocontinuity are presented.The implication relationship among them is studied.The obtained results enrich the theory of set-valued fuzzy measures and set-valued fuzzy integrals.

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What this paper is about

By introducing a new order structure in the class of subsets of an m dimensional positive Euclid space,the concept of convergence(in respect to the order) of set sequences is defined.Then autocontinuity,uniform autocontinuity,converse-autocontinuity and uniform converse-autocontinuity for the set-valued fuzzy measure are discussed.The definitions for the so-called converse-null-additivity,converse-autocontinuity,and uniform converse-autocontinuity are presented.The implication relationship among them is studied.The obtained results enrich the theory of set-valued fuzzy measures and set-valued fuzzy integrals.

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

By introducing a new order structure in the class of subsets of an m dimensional positive Euclid space,the concept of convergence(in respect to the order) of set sequences is defined.Then autocontinuity,uniform autocontinuity,converse-autocontinuity and uniform converse-autocontinuity for the set-valued fuzzy measure are discussed.The definitions for the so-called converse-null-additivity,converse-autocontinuity,and uniform converse-autocontinuity are presented.The implication relationship among them is studied.The obtained results enrich the theory of set-valued fuzzy measures and set-valued fuzzy integrals.

Key concepts: Converse, Mathematics, Set (abstract data type), Fuzzy set, Class (philosophy), Measure (data warehouse), Fuzzy logic, Additive function

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