Starting with crisp set theory, fuzzy sets and concepts of fuzzy logic are introduced in Chapter 2. Some of the key operators are discussed and utilized in a number of examples. Membership functions, membership operators, their programming in Matlab, as well as logic operators using membership functions are explained. Along with conditional statements such as fuzzy rules and linguistic variables concepts such as antecedents, consequences and inference are discussed and shown how to implement this type of reasoning in Matlab.

This chapter discusses selected studies of orthography that focus on the spelling practices by mere users of the language (in crucial opposition to actors from the literate elite – norm makers), concentrating on what they reveal about processes of language change as exemplified by spelling variation. The chapter supports the idea that, within the field of historical sociolinguistics, orthographic variables are now considered a type of linguistic variables. The author shows, on the basis of specific historical sociolinguistic studies, that writers’ variable choices of orthography can inform us about broader mechanisms of language change, but always alongside other types of variation or linguistic information. This chapter examines almost exclusively material from the French language, with the studies under consideration addressing either regional French in France or different varieties of French in Canada. The author situates French orthographic variables within the broader language evolution context, explicating what information spelling variation discloses about the writer’s attitudes toward the (written or spoken) norm, toward the written form, and toward the writer’s linguistic community as a whole. The author also considers how spelling variation compares to other types of language variation in order to contribute to a greater understanding of language change.

The chapter ’#StatsWithCats’ shows some statistical methods to interpret and visualise the cat-related online data. The selected sociolinguistic variables are the social media platforms and the cat account types. The chapter takes frequencies and crosstabs to describe linguistic variation across four social media platforms and four cat account types. The selected linguistic variables refer to the choices of non-meowlogisms and meowlogisms on Facebook, Instagram, Twitter, and Youtube as well as in collective, for-profit celebrity, working-for-cause, and individual cat accounts. Additionally, the chapter uses social network analysis to illustrate the networks in cat-related digital spaces.

We define a linguistic distribution as the range of values for a quantitative linguistic variable across the texts in a corpus. An accurate parameter estimate means that the measures based on the corpus are close to the actual values of a parameter in the domain. Precision refers to whether or not the corpus is large enough to reliably capture the distribution of a particular linguistic feature. Distribution considerations relate to the question of how many texts are needed. The answer will vary depending on the nature of the linguistic variable of interest. Linguistic variables can be categorized broadly as linguistic tokens (rates of occurrence for a feature) and linguistic types (the number of different items that occur). The distribution considerations for linguistic tokens and linguistic types are fundamentally different. Corpora can be “undersampled” or “oversampled” – neither of which is desirable. Statistical measures can be used to evaluate corpus size relative to research goals – one set of measures enables researchers to determine the required sample size for a new corpus, while another provides a means to determine precision for an existing corpus. The adage “bigger is better” aptly captures our best recommendation for studies of words and other linguistic types.

The approach to language variation developed over the last half century has focused on systematic variation of variants for a single structural unit under the construct of the linguistic variable. While this approach may offer important detail for particular variables, it is essential to examine the overall configuration of a language variety as well. Composite linguistic measures facilitate the exploration of social factors and offer a profile of change for the entire linguistic system. We describe the methodological tools to provide a global description of language variation, “the composite index”, and to fully capture when and why individuals change their linguistic behavior over time. We emphasize the need to view language as a system by moving beyond individual variables to more fully characterize the ways in which individual linguistic features move in-tandem across the lifespan. The study demonstrates that a composite index score like the Dialect Density Measure (DDM) can be used as a means of tracking trajectories of language use across the lifespan on a unidimensional scale.