Generalized Modus Tollens with Linguistic Modifiers for Inverse Approximate Reasoning

Abstract

Based on our previous researchs about generalized modus ponens (GMP) with linguistic modifiers for If … Then rules, this paper proposes new generalized modus tollens (GMT) inference rules with linguistic modifiers in linguistic many-valued logic framework with using hedge moving rules for inverse approximate reasoning.

An approach for linguistic multi-attribute decision making based on linguistic many-valued logic

“…In [26], the authors show that, hedges of Mono-HA are "context-free", i.e., a hedge adjusts the meaning of a linguistic value independently of prior hedges in the string of hedge.…”

“…In practice, humans only use linguistic values with a finite length of modifier for the vague concepts, i.e., humans only use a finite string of hedges for truth values [26]. This leads to the necessity to limit the hedge string's length in the truth value domain to make it not surpass L-any positive number [26]. Based on Mono-HA, we set finite monotonous hedge algebra to make linguistic truth value domain.…”

“…The rules of generalized Modus ponens with linguistic modifiers (GMPLM) have been introduced in [21], [26]. Given 𝛼, 𝛽, 𝛿, 𝜎, 𝜃, 𝜕, 𝛼′, 𝛽′, 𝛿′, 𝜃′, and 𝜕′ are the hedge strings; get 𝛼 = ℎ 1 ℎ 2 .…”

Linguistic Negation and 2-Tuple Fuzzy Linguistic Representation Model: A New Proposal

“…For example the issue of polarity (affirmative vs. negative terms) is not easy to tackle because linguistic negation is much more complicated than logical negation [8][9][10]. Negation, as a unique feature of human communication [11], has also been addressed from a linguistic, logical and psycholinguistic point of view [12][13][14]. From Aristotle's original square of opposition (where A and E are contraries, I and O are sub-contraries and A and O as well as E and I are contradictories, see Table 1) to Greimas' semiotic square [15], there still remains several ways to consider the linguistic negation.…”