Optimisation of complex product innovation processes based on trend models with three-valued logic

TL;DR

This work addresses the challenge of modelling complex product innovation under data scarcity by introducing trend-based modelling with three-valued logic. It constructs trend models from objective correlation information and subjective knowledge, solving for a comprehensive set of scenarios and transitions via a transition graph. A case study on a multinational knowledge-transfer network yields seven scenarios and two terminal compromises, illustrating trade-offs among four objectives. The approach provides an interpretable, non-numeric framework that preserves dynamic behaviour and generates a complete futures set for decision support in PI contexts.

Abstract

This paper investigates complex product-innovation processes using models grounded in a set of heuristics. Each heuristic is expressed through simple trends -- increasing, decreasing, or constant -- which serve as minimally information-intensive quantifiers, avoiding reliance on numerical values or rough sets. A solution to a trend model is defined as a set of scenarios with possible transitions between them, represented by a transition graph. Any possible future or past behaviour of the system under study can thus be depicted by a path within this graph.

Figures (6)

• Figure 1: Illustration of the example of a subjective knowledge item: variable $U$ decreases with increasing $I$, while the rate of decrease gradually slows down (a convex decreasing trend)
• Figure 2: Illustration of accelerating growth, linear growth, and decelerating growth
• Figure 3: Illustration of accelerating decrease, linear decrease, and decelerating decrease
• Figure 4: Illustration of one-dimensional oscillation of the variable $X$
• Figure 5: Transitional graph corresponding to the one-dimensional oscillation of the variable $X$