Decision-Making Based on Partition Order Product Space

Introduction

Zadeh proposed and discussed the concept of fuzzy information granularity, which was the first time the concept of “granularity” was proposed (Zadeh, 1979). Hobbs published a paper directly titled “Granularity” (Hobbs, 1985), discussing the decomposition and merging of granules, and proposing methods and models for generating granules of different granularities. Lin T.Y. proposed “Granular Computing” during a visit in the University of California, Berkeley (Lin, 1998). Granular computing focuses on structured thinking and problem solving, which are viewed as human-inspired paradigms of computing and information processing (Bargiela & Pedrycz, 2008; Pedrycz, Skowron, & Kreinovich, 2008; Yao, 2009; Yao, 2016). It solves complex problem based on granular structure. In granular structure, a set of attributes (features) is often selected as a view to describe objects from a particular angle. In each view, objects can be further described from different levels of granularities (abstraction), and each granularity determines a level. Multiview and multilevel are two basic principles of granular computing (Yao, 2009; Yao, 2016). In real applications, to achieve a more comprehensive and reasonable solution in problem solving, people usually simultaneously solve a problem from both multiple views and multiple levels rather than just solving a problem from either multiple views or multiple levels (Bargiela & Pedrycz, 2008; Yao, 2009; Yao, 2016). We select medical diagnosis as an example to illustrate the importance of combining multiple views and multiple levels. In medical diagnosis, assume that a doctor needs to diagnose whether a patient has influenza or pneumonia. To obtain accurate diagnostic conclusions, patients usually have to undergo several kinds of examinations, such as routine examinations, including assessments of a patient’s temperature, cough and sore throat; biochemical examinations, including routine blood tests, C-reactive protein tests and mycoplasma pneumonia tests; and imaging examinations, including X-ray, CT and MRI. Different kinds of examinations provide information about patients from different horizontal perspectives, and each kind of examination can be described as a view. In each view, with an increase in the number of examination items, information about patients becomes increasingly detailed, which constructs multiple levels of information and provides information about patients from different vertical perspectives. First, if a doctor gives the diagnosis conclusion only from a single view, such as routine examinations, there is a great possibility of misdiagnosis. Therefore, to make an accurate diagnosis, the doctor usually makes a decision from multiple views. Second, in a view such as imaging examinations, a patient does not complete all examination items at one time, after which the doctor makes a conclusion. Instead, the patient may first implement an X-ray, and then the doctor tries to make a diagnosis. If a diagnosis cannot be reached, the patient may further implement CT. Namely, in each view, doctors usually make decisions from multiple levels step by step. Last, with multiple views and multiple levels of each view, according to the real needs of the patient, he or she can flexibly implement examinations of different views and different levels. For example, the patient may first undergo examinations to assess temperature, cough and routine blood tests. If the diagnosis conclusion cannot be reached from these examination results, then the patient may undergo an X-ray examination and a C-reactive protein test. The doctor usually simultaneously combines the examination results of multiview and multilevel and flexibly chooses different views and different levels in a view to obtain more reasonable decision results.