# Hesitant Fuzzy Linguistic Term and TOPSIS to Assess Lean Performance
## 1 Introduction  
Lean manufacturing (LM) combines a wide rage of management practices, such as just in time (JIT), quality systems, work teams, cellular manufacturing, and supply chain management (SCM) in a whole system [1]. The LM method aims at saving costs by reducing waste in the manufacturing system, thereby dealing with economic aspects [2]. Nowadays, LM covers the multiple stages of a product's life cycle, from its development and manufacturing to its delivery [3]; however, LM is also a challenge amid mass production practices, especially as quality products, and customer satisfaction are prioritized, inventory, time to market and manufacturing space, and everything that adds no value to a product is systematically categorized as waste [4]. LM is often discussed with respect to key performance indicators (KPIs) [5; 6]. In addition, [PERSON] et al. [7] affirm the KPI parameters have an association with LM performance. In fact, research evidence has found that LM practices have a positive impact on operational performance [8; 9], yet it is often challenging to assess company performance with respect to LM implementation [10; 11] and, according to [12; 13], it is an attractive and hot topic for exploration through multi-criteria decision-making (MCDM) methodologies.  
MCDM has recently gained relevance, especially in engineering [14; 15]; however, when an MCDM problem involves objective and subjective information, experts discuss the classical hybrid MCDM methodwith the fuzzy sets theory [16; 17]. In this sense, motivated by the hesitant fuzzy set, [PERSON] et al. [18] introduced the hesitant fuzzy linguistic term sets (HFLTS), which allows decision makers to elicit several linguistic terms for the same linguistic variable [17; 19]. Nowadays, the HFLTS is a popular effective tool for representing hesitant qualitative judgments from decision makers; consequently, multiple HFLTS-based decision-making methods have been developed [20]. For instance, in their work, [PERSON] and [PERSON] [21] introduced the Technique of Order of Preference by Similarity to Ideal Solution (TOPSIS) method. TOPSIS method is denoted like a significant research issue, which has received a prodigious deal of attention from academics [22; 23; 24; 25]. Additionally, there is HFLTS of TOPSIS proposed by [26; 27].  
The two main contributions of this work can be stated as follows: first, we propose an HFLTS-based data handling procedure to deal with lean manufacturing performance assessments. The procedure can handle KPI matrices of arbitrary preferences in decision-making situations. Second, we propose a systematic solution to measure the LM performance with respect to a series of criteria. The remainder of this paper is organized in five sections. Section 2 introduces a series of basic definitions of HFLTS and TOPSIS, whereas in Section 3 we present materials and methods which describes details about our application. Next, whereas Section 4 presents a numerical example to illustrate our approach to multi-attribute decision making, in Section 5, we describe the result analysis and discussions related to our method. Finally, research conclusions are proposed in Section 6.