Computing Truth Values of Modus Ponens and Modus Tollens Rule for Linguistic Truth-Valued Propositions and Its Application in Taking Decisions in Health Care

• Published in: Advanced Soft Computing Techniques in Data Science, IoT and Cloud Computing Vol. 89; pp. 301 - 329
• Main Authors: Basu, Sumita, Chattaraj, Bithi
• Format: Book Chapter
• Language: English
• Published: Switzerland Springer International Publishing AG 2021; Springer International Publishing
• Series: Studies in Big Data
• Subjects: Lattice implication algebra; Modus Ponens; Modus Tollens; Quasi-lattice implication algebra
• ISBN: 9783030756567; 3030756564
• ISSN: 2197-6503; 2197-6511
• DOI: 10.1007/978-3-030-75657-4_14

Soft computing is used to find solutions of real life problems where exact computation is not possible. Soft computation models are usually approximate in nature. In this chapter we will discuss an approximate reasoning model. The basic reasoning tools in logic are Modus Ponens and Modus Tollens where a statement is either true or false. However our practical experience tells us that often we refer to a statement as quite true or somewhat false etc. Reasoning with such statements could not be done with basic tools of logic. We have tried to find the degree of truth or falsity of these reasoning tools for statements having such linguistic truth values. We have assumed that the propositions have linguistic truth values which are not completely ordered but may be represented by a lattice (Fig. 1 or Fig. 2). It was found that Modus Ponens and Modus Tollens rules with such propositions were not tautologies as in classical logic but have linguistic truth values. These truth values have been computed for all cases in this chapter. The results may be applied to physical, biological, economic or social phenomena. We have showed an application of decision making with linguistic truth-valued propositions in healthcare.