A Novel Intuitionistic Fuzzy Time Series Method Based on Bootstrapped Combined Pi-Sigma Artificial Neural Network

Background: Intuitionistic fuzzy time series forecasting methods have been started to solve the forecasting problems in the literature. Intuitionistic fuzzy time series methods use both membership and non-membership values as auxiliary variables in their models. Because intuitionistic fuzzy sets take into consideration the hesitation margin and so the intuitionistic fuzzy time series models use more information than fuzzy time series models. The background of this study is about intuitionistic fuzzy time series forecasting methods. Objective: The study aims to propose a novel intuitionistic fuzzy time series method. It is expected that the proposed method will produce better forecasts than some selected benchmarks. Method: The proposed method uses bootstrapped combined Pi-Sigma artificial neural network and intuitionistic fuzzy c-means. The combined Pi-Sigma artificial neural network is proposed to model the intuitionistic fuzzy relations. Results and Conclusion: The proposed method is applied to different sets of SP&500 stock exchange time series. The proposed method can provide more accurate forecasts than established benchmarks for the SP&500 stock exchange time series. The most important contribution of the proposed method is that it creates statistical inference: probabilistic forecasting, confidence intervals and the empirical distribution of the forecasts. Moreover, the proposed method is better than the selected benchmarks for the SP&500 data set.

Industry 4.0 road mapping: A fuzzy linguistic approach

Background: The industry 4.0 transition is becoming crucial for organizations. The literature reviewed showed that whilst there are many studies on industry 4.0 assessment that help organizations evaluate their current state, limited studies exist for road-mapping activities. Objective: The main aim of this study is to construct a model that leads organizations to their fourth industrial revolution transition. Companies, especially small and medium-sized ones (SMEs), need clear, agile, and efficient road maps because of their limited resources. Lack of a procedure that guides organizations in the right way is the motivation of this study. Method: A linguistic fuzzy inference system is used in this study. Concepts are determined, and relations between concepts with if-then rules have been constructed according to the expert opinion. MATLAB R2015a is used for the inference system. Results: An exemplary case is considered, and the results show that the inference system can provide company-specific roadmaps. To which extend an industry 4.0 concept should be taken into account for a company can be seen with the proposed method. Conclusion: The proposed method showed that specific and agile roadmaps could be obtained. Because of the dependency of expert opinion for the fuzzy rule base, different methods for obtaining rules and relations may be a future research direction.

Fabrics Recommendation for Fashion Design by Using Fuzzy Logic and Rough Sets

Background: Fabric is one of the key and vital design factors in fashion design. However, selection of relevant fabrics is rather complex for designers and managers due to the complexity of criteria at different levels. Introduction: In this paper, we propose a new fabric recommendation model in order to quickly realize fabric selection from non-technical fashion features only and predict fashion features from any fabric technical parameters. This approach is extremely significant for fashion designers who do not completely master fabric technical details. It is also very useful for fabric developers who have no knowledge on fashion markets and fashion consumers. Method: The proposed fabric recommendation model has been built by exploiting designers’ professional knowledge and consumers’ preferences. Concretely, we first use fuzzy sets for formalizing and interpreting measured technical parameters and linguistic sensory properties of fabrics and then model the relation between the technical parameters and sensory properties by using rough sets. Next, we model the relation between fashion themes and sensory properties using fuzzy relations. By combining these two models, we establish a hybrid model characterizing the relation between fashion themes and technical parameters. Result: The proposed model has been validated through a real fabric recommendation case for designer’s specific requirements. We can find that the proposed model is efficient since the averaged value of prediction errors is 8.57%, which does not exceed 10% (generally considered as allowable range of human perception error). Conclusion: The proposed model will constitute one important component for establishing an intelligent recommender system for garment design, enabling to support innovations in textile/apparel industry in terms of mass customization and e-shopping.

Partial fuzzy quantifiers and their computation

Background: In computer science, one often meets the requirement to deal with partial functions. They naturally raise, for example, when a mistake such as the square root of a negative number or division by zero occurs, or when we want to express the semantics of the expression “Czech president in 18th century” because there was no such president before 1918. Method: In this paper, we will extend the theory of intermediate quantifiers (i.e., expressions such as “most, almost all, many, a few”, etc.) to deal with partially defined fuzzy sets. First, we extend algebraic operations that are used in fuzzy logic by additional value “undefined”. Then we will introduce intermediate quantifiers using the former. The theory of intermediate quantifiers has been usually developed as a special theory of higher-order fuzzy logic. Results: In this paper, we introduce the quantifiers semantically and show how they can be computed. The latter is also demonstrated in three illustrative examples. Conclusion: The paper contributes to the development of fuzzy quantifier theory by its extension by undefined values and suggests methods for computation of their truth values.

Fuzzy form of Euler Method to Solve Fuzzy Differential Equations

: This paper proposes fuzzy form of Euler method to solve fuzzy initial value problems. By this method, fuzzy differential equations can be solved directly using fuzzy arithmetic. The solution by this method is readily available in a form of fuzzy-valued function. The method does not require to re-write fuzzy differential equation into system of two crisp ordinary differential equations. Algorithm of the method and local error expression are discussed. An illustration and solution of fuzzy Riccati equation are provided for the applicability of the method.

A New Cutset-type Kernelled Possibilistic C-Means Clustering Segmentation Algorithm Based on SLIC Super-pixels

: The kernelled possibilistic C-means clustering algorithm (KPCM) can effectively cluster hyper-sphere data with noise and outliers by introducing the kernelled method to the possibilistic C-means clustering (PCM) algorithm. However, the KPCM still suffers from the same coincident clustering problem as the PCM algorithm due to the lack of between-class relationships. Therefore, this paper introduces the cut-set theory into the KPCM and modifies the possibilistic memberships in the iterative process. Then a cutset-type kernelled possibilistic C-means clustering (CKPCM) algorithm is proposed to overcome the coincident clustering problem of the KPCM. Simultaneously a adaptive method of estimating the cut-set threshold is also given by averaging inter-class distances. Additionally, a cutset-type kernelled possibilistic C-means clustering segmentation algorithm based on the SLIC super-pixels (SS-C-KPCM) is also proposed to improve the segmentation quality and efficiency of the color images. Several experimental results on artificial data sets and image segmentation simulation results prove the excellent performance of the proposed algorithms in this paper.

A Robust Fuzzy Decision Making on Global Warming

Background: In this article we develop a global warming indicator model under fuzzy system. It is the light of sun that environmental pollution is responsible for the cause and immediate effect of global warming. Limited amount of oxygen in the air, continuous decrease of fresh water volume, more especially the amount of drinking water and the rise of temperature in the globe are the major symptoms (variants) of global warming. Thus, to capture the facts we need to develop a mathematical model which has not yet been developed by the earlier researchers. Introduction: An efficient literature survey has been done over the three major parameters of the environment namely oxygen, fresh water and surface temperature exclusively. In fact we have accumulated 150 years-data structure for these major components and have analyzed them under fuzzy system so as to develop an efficient global warming indicator model. Method: First of all, we gave few definitions on fuzzy set. Utilizing the data set we have constructed appropriate membership functions of the three major components of the environment. Then applying goal programming problem, we have constructed a fuzzy global warming indicator (GWI) model subject to some goal constraints with respective priority vectors (Scenario 1 and Scenario 2). An extension has also been included for multi-valued goal programming problem and numerical illustrations have been done with the help of LINGO software. Result: Numerical study reveals that the GWI takes maximum and minimum values in a decreasing manner as time increases. It is seen that for scenario 1, the global environmental system will attain its stability after 30 years by degrading 31% of GWI with respect to present base line. For scenario 2, after the same time the global environmental system will attain its stability quite slowly by degrading 28% of GWI with respect to present base line. Conclusion: Here we have studied a mathematical model of global warming first time using fuzzy system. No other mathematical models have been existed in the literature. Thus, the basic novelty lies in a robust decision-making approach which shows the expected time of extinction of major species in this world. However, extensive study on data analytics over major environmental components can tell the stability of the global warming indicator and hence the future fate of the globe also.