When dealing with complex issues,developing comprehensive strategies,or making critical decisions,it is necessary to think and analyze from multiple perspectives,levels,or dimensions.Three-way decision is triadic thinking,triadic method,and triadic computing.Following the principles of three-way decision,the concept of double triadic thinking and the associated 3×3 methods and structures are introduced.Double triadic thinking is based on a combination of two triadic structures,which allows us to think,analyze and solve problems from nine different perspectives or dimensions.Two particular 3×3 methods are proposed by combining trilevel hierarchical thinking and triangular thinking.One is the application of triangular methods at each of the three levels of a hierarchy,which is called a(3-level)×(3-angle)method.The other is the application of trilevel methods at each of the three vertices of a triangle,which is called a(3-angle)×(3-level)method.As a case study,3×3 methods are applied to explainable artificial intelligence.By means of the concept of Symbols-Meaning-Value(SMV)space,we consider specific semantics of the nine elements of a 3×3 method.The SMV space based 3×3 method can analyze and interpret the data,assumptions,principles,and outcomes of an intelligent system at multiple levels.It provides a construction process and structure of explanation for intelligent systems,making an explanation easier to communicate,understand,and accept.
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