## 1 Introduction  
### Contributions  
The design of temporal knowledge bases in complex domains, such as medicine, territories, management, and psychology, must incorporate many attributes of different kinds from a large number and variety of objects, which are often themselves components of larger, complex objects. Temporal case-based reasoning (TCBR) is an extension of case-based reasoning (CBR) that requires a comparison of the evolution of the complex structure over time. This requires a temporal comparison of the complex structure's component objects and their states (the value of their attributes), where component objects must be considered at different levels of granularity, according to their composition in the complex structure. This paper uses a fuzzy vector space object-oriented model and method (FVSOOMM), proposed by [PERSON] [1]. In the ESM'2019 conference paper [2], FVSOOMM was presented and utilized to model the personality, cognitive dissonance, and emotions in a marketing case example. [PERSON]'s paper presented the main advantages and drawbacks of fuzzy rules. It also described the advantages of FVSOOMM in assessing the evolution of a knowledge object's structure and attributes, compared to rule-based systems that rely on fuzzification/defuzzification operations and induction on a set of selected attributes. FVSOOMM extends the object-oriented model mainly based on the object-composition relationship [3]. FVSOOMM is not a fuzzy logic approach, but rather a fuzzy extension of object models that offer a more general model of knowledge than fuzzy logic [4]. [PERSON] himself mentioned that object-oriented approaches offer a more general model of knowledge representation than fuzzy logic [5]. This paper presents the following contributions:  
1. Extension of the TFVS model This paper extends the temporal fuzzy vector space (TFVS) model with the different steps of the method within FVSOOMM. This provides a new mechanism to model knowledge bases in many different and complex domains, and to capture the semantics of the relationships between the objects and actors described in the ontology of their knowledge domain. In common with other authors [6; 7; 8; 9], the present authors trust that object-oriented approaches offer a more general model of knowledge representation than just from fuzzy logic alone.
2. Design and implementation of a platform The novelty of the tool is a platform that supports the method and provides three interfaces: an expert interface that allows the expert to describe the class diagram of the domain knowledge, and an attribute language that is used to define the attribute descriptors that are made available in a repository to the practitioners. A practitioners' interface allows stakeholders in the field to choose object types and to instantiate the necessary knowledge objects and their attribute descriptors that define and control the characteristics and range of attribute values of knowledge objects. The third interface is for end users, who simply enter the attribute values during their professional practice as they are solving real cases, where they are then stored in an experience case database. The case database is an experience repository that is particularly useful to practitioners, as it elaborates new research in their field. The method of FVSOMM describes the whole process of a knowledge base design and how to develop the corresponding decision support system (DSS).
3. A method for temporal case-based reasoning This advances other works as case-based reasoning (CBR) based on an object-oriented model to develop DSS. The method defines the distances required to implement temporal case-based reasoning (TCBR) by comparing the time fuzzy vector functions that describe the evolution of the case objects and their attributes over time. The TCBR system sorts similar cases within an interval of time.