Graded logic and its applications

Graded logic is a seamless soft computing generalization of classical Boolean logic. The main aggregator in graded logic is called GCD (graded conjunction/disjunction). GCD systematically covers all regions of the unit hypercube, providing a parameterized continuous transition from drastic conjunction to drastic disjunction in a way that is consistent with observable properties of human evaluation reasoning. Andness and orness are continuously adjustable parameters of GCD. GCD supports the conjecture that human evaluation reasoning uses 10 observable (necessary and sufficient) types of basic logic operations: hyperconjunction, conjunction, hard and soft partial conjunction, neutrality, soft and hard partial disjunction, disjunction, hyperdisjunction, and negation. We use graded logic as the soft computing mathematical infrastructure for developing a decision engineering framework based on the LSP (logic scoring of preference) decision method and the corresponding software support. The LSP method has O(n) complexity and is suitable for solving industrial evaluation problems with large number of inputs (typically 50-600). The LSP-based decision engineering framework is applicable in all situations where we need justifiable and explainable complex logic criteria. Typical professional application areas include computer engineering, software engineering, medicine, ecology, geography, and agriculture.

JOZO DUJMOVIĆ, ScD, is a professor of computer science and former chair of the Computer Science Department at San Francisco State University, where he teaches and researches soft computing, software metrics, and computer performance evaluation. His first industrial experience was in Institute “M. Pupin,” Belgrade, followed by 25 years of professorship with the School of Electrical Engineering at the University of Belgrade. He was the professor of computer science with the University of Florida, Gainesville, FL, USA; the University of Texas, Dallas, TX, USA; and Worcester Polytechnic Institute, Worcester, MA, USA. He is the author of more than 170 refereed publications and the founder and principal of SEAS, a San Francisco company specializing in soft computing decision models and software support for the LSP method. His latest book entitled Soft Computing Evaluation Logic was published by John Wiley and IEEE Press in 2018.