Quotient Space Based Problem Solving. A Theoretical by Ling Zhang, Bo Zhang

By Ling Zhang, Bo Zhang

Quotient house dependent challenge Solving presents an in-depth remedy of hierarchical challenge fixing, computational complexity, and the foundations and purposes of multi-granular computing, together with inference, details fusing, making plans, and heuristic search.

      • Explains the idea of hierarchical challenge fixing, its computational complexity, and discusses the primary and functions of multi-granular computing
      • Describes a human-like, theoretical framework utilizing quotient house concept, that might be of curiosity to researchers in synthetic intelligence.
      • Provides many purposes and examples within the engineering and laptop technological know-how area.
      • Includes entire assurance of making plans, heuristic seek and insurance of strictly mathematical models.

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      29 ðX; TÞ is a semi-order space. For A3X, if CX ðAÞ ¼ A, A is called semi-order closed on ðX; TÞ, or semi-order closed for short. The properties of CX ðAÞ are as follows. 2 ðX; TÞ is a semi-order space. For A3X, CX ðAÞ is semi-order closed. , x3 ; x4 ; x5 ; x6 ˛ A; x3 < x1 < x4 ; x5 < x2 < x6 . We have x3 < x1 < y; y < x2 < x6 ; x3 < y < x6 ; y ˛ CX ðAÞ. Thus, CX ðAÞ is semi-order closed. 3 ðX; TÞ is a semi-order space. Assuming A3X, then vCðAÞ A is semi-order closed. Proof: Assuming x1 < y < x2 ; x1 ; x2 ˛ vCðAÞ A, have y ˛ CðAÞ.

      This is the key to multi-granular computing. 8. 6 Selection and Adjustment of Grain-Sizes The ability to select a proper grain-size world for a given problem is fundamental to human intelligence and flexibility. The ability enables us to map the complex world around us into a simple one that is computationally tractable. At the same time, the attributes in question of the world are still preserved. As mentioned before, it is not necessarily true that any classification can achieve the goal. Problem Representations 33 How to select a proper grain-size is a domain-dependent problem mainly.

      2001) can be used to get the structures behind data that are not involved in the book. 2 The Estimation of Computational Complexity The aim of this section is to estimate the computational complexity, based on the mathematical model presented in Chapter 1, when the multi-granular computing is used (Zhang and Zhang, 1990d, 1992). 1 The Assumptions A problem space is assumed to be a finite set. Symbol jXj denotes the number of elements in X. Sometimes, we simply use X instead of jXj if no confusion is made.

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