Abstract Explainable Artificial Intelligence (XAI) is a crucial domain within research and industry, aiming to develop AI models that provide human-understandable explanations for their decisions. While the challenges in AI, deep learning, and big data have been extensively explored, the specific concerns of XAI developers have received limited attention. To address this gap, we analysed discussions on Stack Exchange websites to delve into these issues. Through a combination of automated and Manual analysis, we identified 6 overarching categories, 10 distinct topics, and 40 sub-topics commonly discussed by developers. Our examination revealed a steady rise in discussions on XAI since late 2015, initially focusing on conceptualisation and practical applications, with a notable surge in activity across all topic categories since 2019. Notably, Concepts and Applications, Tools Troubleshooting, and Neural Networks Interpretation emerged as the most popular topics. Troubleshooting challenges were commonly encountered with tools like SHAP, ELI5, and AIF360, while visualisation issues were prevalent with Yellowbrick and SHAP. Furthermore, our analysis suggests that addressing questions related to XAI poses greater difficulty compared to other machine-learning questions.

Abstract Software development effort estimation (SDEE) is a critical activity in developing software. Accurate effort estimation in the early phases of software design life cycle has important effects on the success of software projects. COCOMO (Constructive Cost Model) is a parametric data‐driven SDEE model whose parameters must be calibrated with an organization's local data for accurate estimation. Such data are scarce for most organizations. On the other hand, CoBRA (Cost estimation, Benchmarking, and Risk Assessment) is one of the powerful hybrid methods that need a small number of local historical data for effort estimation. However, data gathering in CoBRA is time‐consuming and costly. To ease the use of CoBRA, in this paper, we design a methodology that extracts CoBRA‐required data from COCOMO datasets. By the proposed method, data collected for COCOMO would be used in CoBRA. Using CoBRA, a more accurate estimation of the required effort would be achieved with fewer number of historical data than what is required to calibrate the COCOMO model. We apply the proposed method on six well‐known public COCOMO datasets and use them in CoBRA. Obtained results depict an increase in the accuracy of estimations in comparison with other existing methods.

Defuzzification plays an important role in the applications of interval type-2 fuzzy sets (IT2FSs). However, computational complexity of existing defuzzification methods has turned this procedure into an important bottleneck toward the use of IT2FSs. It has been proved that the Nie-Tan method is an accurate discretizing-based method for calculating the center of gravity (COG) of IT2FSs. In this article, we propose a fast and accurate method for calculating the COG-Nie-Tan defuzzification-of polygonal IT2FSs on discrete and continuous domains without the need of discretization. The proposed method calculates the accurate COG for trapezoidal and triangular IT2FSs as special cases of polygonal IT2FSs. Moreover, any IT2FS can be approximated by a polygonal IT2FS-the higher the order of polygonal IT2FS, the better the approximation. Hence, using the proposed method on an IT2FS that is approximated by an appropriate polygonal IT2FS results in a more accurate COG.

Processing type-2 fuzzy sets is more demanding than processing interval type-2 fuzzy sets or type-1 fuzzy sets. In this paper we propose a method for calculating union and intersection operations using min t-norm and max t-conorm on general type-2 fuzzy sets. The proposed method is based on Zadeh's separation theorem and though is straightforward. The important feature of the algorithm is its simplicity and applicability on the type-2 fuzzy sets with convex membership grades.

Granulation of information by using type-2 fuzzy sets is receiving more attention nowadays. This is due to the superior capability of type-2 fuzzy sets in handling the data uncertainty. From a theoretical perspective, a set containing type-2 fuzzy sets has no trivial geometric structure; therefore, a proper metric cannot be easily defined. As a consequence, common pattern recognition systems, which in one way or another rely on some (geo)metric structure of the input space, are not easily applicable to a space of type-2 fuzzy sets. In this paper, we study the problem of designing a classifier in the input space of type-2 fuzzy sets. Type-2 fuzzy sets are hence interpreted as (granular) patterns forming a given input dataset. By decomposing a type-2 fuzzy set into a sequence of simpler (lower type) fuzzy sets, we explore the possibility of defining and building dissimilarity and kernel-based classification systems on input spaces of type-2 fuzzy sets. Such an interpretation provided in terms of sequences allows us to conceive an effective sequence matching strategy, which can be suitably embedded into well-established pattern recognition systems. We support the methodological developments by performing experiments on synthetically generated classification problems for datasets composed of type-2 fuzzy sets, with adjustable and controlled level of difficulty. Results are promising and suggest to further investigate on the possibility of interpreting type-2 fuzzy sets as input patterns of a given data-driven inference system.

This paper presents a universal methodology for generating an interval type-2 fuzzy set membership function from a collection of type-1 fuzzy sets. The key idea of the proposed methodology is to designate a specific type-1 fuzzy set as the representative of all input type-1 fuzzy sets. To this end, we use a novel measure of similarity between type-1 fuzzy sets, which relies on both kernel functions and fuzzy information processing methods. Based on the selected representative type-1 fuzzy set, and with respect to the principle of justifiable granularity, an interval type-2 fuzzy set is then formed. The results of the conducted experiments demonstrate the effectiveness of the proposed methodology for generating sound interval type-2 fuzzy sets.

The existing methods of determining an α-cut of a fuzzy set to construct its underlying shadowed set do not fully comply with the concept of shadowed sets, namely, a retention of the total amount of fuzziness and its localized redistribution throughout a universe of discourse. Moreover, no closed formula to calculate the corresponding α-cut is available. This paper proposes analytical formulas to calculate threshold values required in the construction of shadowed sets. We introduce a new algorithm to design a shadowed set from a given fuzzy set. The proposed algorithm, which adheres to the main premise of shadowed sets of capturing the essence of fuzzy sets, helps localize fuzziness present in a given fuzzy set. We represent the fuzziness of a fuzzy set as a gradual number. Through defuzzification of the gradual number of fuzziness, we determine the required threshold (i.e., some α-cut) used in the formation of the shadowed set. We show that the shadowed set obtained in this way comes with a measure of fuzziness that is equal to the one characterizing the original fuzzy set.

Type-2 fuzzy sets, an elaboration over type-1 fuzzy sets, are an interesting method for handling uncertainty in rules and parameters in fuzzy systems. However, their adoption has not been as wide as one could have expected. In this paper we provide a simple introduction to type-2 fuzzy sets; then we propose a novel method for calculating operations on type-2 fuzzy sets with normal type-1 membership values, for which we redefine set ordering. Finally, based on the max ordering of fuzzy set and highest degree of separation, we propose an approximation for performing the operations, which ensures that the calculation is accurate for the most important parts of the membership values.