Graded logic for decision support systems
Jozo J. Dujmovic · International Journal of Intelligent Systems · 2019
We present the soft computing graded logic (GL) as a mathematical infrastructure for a soft computing propositional calculus, and GL aggregation. The GL aggregation of degrees of truth (or fuzzy membership) is a crucial component of complex criterion functions used in decision support systems. In the context of GL we propose aggregation functions that integrate means and t-norms/conorms, combining logic and probabilistic reasoning. We also propose a set of necessary and sufficient basic logic functions (models of simultaneity, substitutability, and complementing of degrees of truth) and their analytic forms. GL is developed as a seamless soft computing generalization of classical Boolean logic. The proposed generalizations include: (1) the continuous parameterized transition from drastic conjunction to drastic disjunction, integrating the regions of hyperconjunction, hard and soft partial conjunction, logic neutrality, soft and hard partial disjunction, and hyperdisjunction and (2) semantic generalization where we assign a degree of importance to each degree of truth, in a way that is consistent with observable properties of human intuitive reasoning. These generalizations reflect the fact that degrees of truth are not anonymous real numbers, but values that have semantic identity derived from goals and requirements of decision-maker. The basic goal of GL is to provide humancentric mathematical models of logic aggregators that can be used in the decision process of comparison and selection of alternatives based on the evaluation of each alternative. This paper is structured to present the characteristic properties of entire GL in a way that is both concise and complete.