Well-formed formula

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Published in Phillip A. Laplante, Dictionary of Computer Science, Engineering, and Technology, 2017

well-formed formula (WFF) in first order predicate logic, a formula built from atomic formulas using the connectives “⋀” (and), “⋁” (or), “¬” (not), and the quantifiers “∀” (for all) and “∃” (there exists). All atomic formulas are WFF’s, and if ϕ and ψ are well-formed formulas, then so are the conjunction (ϕ ∧ ψ), the disjunction (ϕ ∨ ψ), the negation ¬ϕ, and the quantified formulas ∀Xϕ, ∃Xϕ, where “X” is a variable symbol.

Some fuzzy measure modeled multi-criteria formulations

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Published in International Journal of General Systems, 2020

Ronald R. Yager

Again assume C = {C1, … .., Cn} are our criteria of interest. We first consider the situation were we express our desired aggregation requirement with respect to these multiple criteria in the form of a well-formed formula, WFF, in the language of propositional logic (Kleene 1967; Mendelson 1964). Here we express the WFF using the set of criteria C and the propositional connectives ∧ (and), ∨ (or), (not) and → (if … then) (Mendelson 1964). We note that statements in natural language can often formally be expressed as a well-formed formula, WFF, in the language of propositional logic. Examples of this are the statements:

Well-formed formula

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Some fuzzy measure modeled multi-criteria formulations