Abstract
The notions of (quasi, pseudo) star-shaped sets are introduced, and several related properties are investigated. Characterizations of (quasi) star-shaped sets are considered. The translation of (quasi, pseudo) star-shaped sets are discussed. Unions and intersections of quasi star-shaped sets are conceived. Conditions for a quasi (or, pseudo) star-shaped set to be a star-shaped set are provided.
Highlights
Convexity is a basic notion in geometry, and it is widely used in other areas of mathematics
It is used to denote the geometrical property of a bounded planar set that from some reference point within the set all halflines intersect the boundary exactly once, and the star-shapedness is applied to linear spaces and algebraic structures etc
Star-shaped fuzzy sets are useful for processing positive information, but there is a limit to dealing with negative information
Summary
Convexity is a basic notion in geometry, and it is widely used in other areas of mathematics (see [1]). As a generalization of convexity, the term star-shapedness is being used in several contexts. It is used to denote the geometrical property of a bounded planar set that from some reference point within the set all halflines intersect the boundary exactly once, and the star-shapedness is applied to linear spaces and algebraic structures etc., (see [2,3,5,6]). Star-shaped fuzzy sets are useful for processing positive information, but there is a limit to dealing with negative information. We introduce the notions of (quasi, pseudo) star-shaped sets, and investigate several related properties. We show that the property of being (quasi, pseudo) star-shapedness is translation invariant in Rn. We consider characterizations of (quasi) star-shaped sets. We discuss union and intersection of quasi star-shaped sets
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