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In particular, the term well-defined is used with respect to (binary) operations on cosets. In this case, one can view the operation as a function of two variables, and the property of being well-defined is the same as that for a function. For example, addition on the integers modulo some n can be defined naturally in terms of integer addition.
Scholars distinguish between well-defined and ill-defined problems. Briggs and Reinig defined a well-defined solution in terms of space solution space. Pretz, Naples, and Sternberg defined a well-defined problem as one for which the parts of the solution are closely related or clearly based on the information given. Problem finding applies to ...
The term problem solving has a slightly different meaning depending on the discipline. For instance, it is a mental process in psychology and a computerized process in computer science. There are two different types of problems: ill-defined and well-defined; different approaches are used for each.
Calculations or statements which are ill-defined, such that they cannot be unambiguously encoded into a Turing machine: ("Paul loves me twice as much as Joe"). Problem statements which do appear to be well-defined, but for which it can be proved that no Turing machine exists to solve them (such as the halting problem).
Divide and conquer divides the problem into multiple subproblems and so the conquer stage is more complex than decrease and conquer algorithms. [citation needed] An example of a decrease and conquer algorithm is the binary search algorithm. Search and enumeration Many problems (such as playing chess) can be modelled as problems on graphs.
The following articles contain lists of problems: List of philosophical problems; List of undecidable problems; Lists of unsolved problems; List of NP-complete problems;
Hard systems approaches such as systems analysis (structured methods), operations research and so on, assume that the problems associated with such systems are well-defined and likely to have a single, optimum solution, so a problem-solving approach will work well as technical factors tend to predominate. [1] [2]
The issue-based information system (IBIS) is an argumentation-based approach to clarifying wicked problems—complex, ill-defined problems that involve multiple stakeholders. [1] Diagrammatic visualization using IBIS notation is often called issue mapping. [2]: ix IBIS was invented by Werner Kunz and Horst Rittel in the 1960s. According to Kunz ...