A construction of sound semantic linguistic scales using 4-tuple representation of term semantics

• Introduced are concepts of linguistic scales and their quantitative semantic scales.
• Properties of context-dependent semantics are studied.
• 4-tuple linguistic representation and 4-tuple semantic linguistic scales are examined.
• A methodology to construct a sound 4-tuple semantic linguistic scale is proposed.

Data semantics plays a fundamental role in computer science, in general, and in computing with words, in particular. The semantics of words arises as a sophisticated problem, since words being actually vague linguistic terms are pieces of information characterized by impreciseness, incompleteness, uncertainty and/or vagueness. The qualitative semantics and the quantitative semantics are two aspects of vague linguistic information, which are closely related. However, the qualitative semantics of linguistic terms, and even the qualitative semantics of the symbolic approaches, seem to be not elaborated on directly in the literature. In this study, we propose an interpretation of the inherent order-based semantics of terms through their qualitative semantics modeled by hedge algebra structures. The quantitative semantics of terms are developed based on the quantification of hedge algebras. With this explicit approach, we propose two concepts of assessment scales to address decision problems: linguistic scales used for representing expert linguistic assessments and semantic linguistic scales based on 4-tuple linguistic representation model, which forms a formalized structure useful for computing with words. An example of a simple multi-criteria decision problem is examined by running a comparative study. We also analyze the main advantages of the proposed approach.