A Type 2 Fuzzy Set Approach for Building Linear Linguistic Regression Analysis under Multi Uncertainty

Abstract

In this paper, we propose a novel heuristic algorithm for constructing a Type-2 Fuzzy Set of the Linear Linguistic Regression (T2F-LLR) model, designed to address uncertainty and vagueness in real-world decision-making. We consider a practical scenario involving a cosmetic company's promotional planning across four product categories: Basic Face Care, Face Cleaning, Cosmetics, and Body Care, aimed at both male and female consumers. Data are collected using fuzzy linguistic questionnaires from customers and expert managers, with responses expressed using qualitative terms such as 'always', 'frequently', 'Often', 'Sometimes', and 'frequently'. These linguistic evaluations are modeled as Type-2 Fuzzy Set of Linear Linguistic regression (T2F-LLR) variables to capture both randomness and higher-order fuzziness. We rigorously develop a solution framework based on a one-sigma confidence interval using the credibility measure to calculate the expected values and variances of the model output. To improve computational efficiency and usability of decisions, we introduce a heuristic algorithm tailored for non-meta datasets, significantly reducing the complexity of the model solving process. The experimental results demonstrate the effectiveness of our approach, which yields a mean absolute percentage error (MAPE) of weight equals 7.97\% with all variables statistically significant. We also provide the significant results for each product using the one-way analysis of variance test (one-way ANOVA test) ($p$-value = 0.15) and the paired $t$ test ($p$-value = 0.16). The results show that there is no significant difference between observed and predicted weights overall. This paper provides a robust and interpretable methodology for decision makers dealing with imprecise data and time-sensitive planning.