Development of a multi-period multi-attribute group decision-making method using type- 2 fuzzy set of linguistic variables

Fuzzy set theory is particularly appropriate approach when data include imprecise. Type-2 fuzzy set theory captures ambiguity that associates the uncertainty of membership functions by incorporating footprints and models high level uncertainty. If the quality characteristic is a binary classification into conforming/non-conforming of product, this decision depends on human subjectivity that have ambiguity or vague. In this situation, monitoring the process with statistical control charts based on interval type-2 fuzzy sets, a special case of type-2 fuzzy sets, is more suitable due to the human imprecise judgments on quality characteristics. In this paper, interval type-2 fuzzy p-control chart is developed into the literature for the first time. Due to the interval type-2 fuzzy sets modelled more uncertainty for defining membership functions, in this paper interval type-2 fuzzy fraction nonconforming numbers used for handling more uncertainty in process. Real word application is implemented with developed fuzzy control chart.

A new fuzzy multi-attribute group decision-making method with generalized maximal consistent block and its application in emergency management

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes.

This chapter formally introduces type-1 fuzzy sets and fuzzy logic. It is the backbone for Chap. 3 and provides the foundation upon which type-2 fuzzy sets and systems are built in later chapters. Its coverage includes: crisp sets, type-1 fuzzy sets and associated concepts [including a short biography of Prof. Zadeh (the father of fuzzy sets and fuzzy logic)], type-1 fuzzy set defined, linguistic variables, returning to linguistic variables from a numerical value of a membership function, set theoretic operations for crisp and type-1 fuzzy sets, crisp and fuzzy relations and compositionson the same or different product spaces , compositions of a type-1 fuzzy set with a type-1 fuzzy relation, hedges, the Extension Principle (which is about functions of fuzzy sets), α-cuts (which are a powerful way to represent a type-1 fuzzy set in terms of intervals), functions of type-1 fuzzy sets computed by using α-cuts, multivariable membership functions and Cartesian products, crisp logic, going from crisp logic to fuzzy logic, Mamdani (engineering) implications, some final remarks, and an appendix about properties/laws of type-1 fuzzy sets. 35 examples are used to illustrate this chapter’s important concepts.

Multi-attribute group decision making method with dual comprehensive clouds under information environment of dual uncertain Z-numbers

Faced with the increasing complexity and uncertainty of decision-making information, interval-valued Fermatean hesitant fuzzy sets (IVFHFSs) were presented as a novel mathematical model that handled uncertain data more effectively. However, existing multi-attribute group decision-making (MAGDM) methods based on IVFHFSs do not thoroughly investigate the operational laws. Also, these existing MAGDM methods do not take into account the connections between attributes and are less flexible. To address these issues, this paper proposes a new MAGDM method based on Einstein Bonferroni operators under IVFHFSs. First, we thoroughly examine the operational laws of Einstein t-norms under the IVFHFSs to further extend the study of the operational laws. Then, we introduce the interval-valued Fermatean hesitant fuzzy Einstein Bonferroni mean operator and the interval-valued Fermatean hesitant fuzzy Einstein weighted Bonferroni mean operator under Einstein t-norms. Our suggested aggregation operators consider the relationship between attributes and are far more flexible in comparison to the current approaches. Later, a novel MAGDM method based on Einstein Bonferroni operators under the IVFHFSs is given. Finally, the practicality and validity of the proposed method are demonstrated by a cardiovascular disease diagnosis application.

Determination of best renewable energy sources in India using SWARA-ARAS in confidence level based interval-valued Fermatean fuzzy environment

The selection of appropriate suppliers in an uncertain environment influences the sustainability and the competitive advantage of the automotive industry and hence presents one of the significant management problems. In the literature, it is suggested that an acceptable supplier may be determined concerning many criteria. In this manuscript, criteria selection is based on the relevant literature. Handling of different uncertainties is performed by using the type-2 fuzzy sets that have the capability of handling more considered impreciseness and uncertainties. In the presented research, the two-state model is proposed. In the first stage, the relative importance of criteria and sub-criteria are described by pre-defined linguistic expressions which are modeled by the interval type-2 triangular fuzzy numbers (IT2TFNs). The fuzzy weights vectors are given by using the fuzzy Analytic Hierarchical Process with IT2TFNs (IT2FAHP). After that, the ranking of suppliers is based on the modified Multi-Attributive Border Approximation area Comparison method (MABAC) with IT2TFNs (IT2FMABAC). The extension of the conventional MABAC includes: (a) modeling of sub-criteria values of IT2TFNs, (b) the fuzzy criteria values are calculated by using fuzzy algebra rules, (c) belonging of each supplier to border approximation areas (BAAs) is given by using procedure, and (d) the distance of suppliers to BAAs is determined by using the normalized Euclidean distance formulas. The proposed model is tested on the real-life data from the automotive supply chain. Through the presented research, it is shown that the proposed IT2FMABAC is a useful and reliable tool for the rational purchasing decision-making process.

Multiattribute group decision making based on intuitionistic 2-tuple linguistic information

The recruitment of university researchers can be considered a multi-attribute group decision-making (MAGDM) problem. MAGDM is a familiar issue with uncertainty and fuzziness in the decision-making field. Generalized hesitation fuzzy numbers (GHFNs) as a new expanded form of hesitation fuzzy numbers (HFNs) can better express the uncertain information in MAGDM. The TODIM is a very classical and widely used method to deal with the MAGDM issue. In this paper, we integrate cumulative prospect theory (CPT) into TODIM to consider not only decision makers’ subjective risk preferences but also their confidence level to obtain more reasonable choices under risk conditions. Therefore, we propose the GHF CPT-TODIM approach to tackle the MAGDM issue. Meanwhile, in the GHF environment, it is proposed to use the volatility of attribute information (entropy weighting method) to obtain the importance of attributes, obtain the unknown attribute weight, and enhance the rationality of weight information. Finally, the validity and usefulness of the technique are verified by applying the GHF CPT-TODIM technique to the recruitment of university researchers and comparing it with the existing GHF MAGDM method, which offers a new way to solve the MAGDM problem with GHFNs.

Application of Type-2 Interval Fuzzy Sets to Contractor Qualification Process

Nowadays, most people can get enough energy to maintain one-day activity, while few people know whether they eat healthily or not. It is quite important to analyze nutritional facts of foods eaten for those who are losing weight or suffering chronic diseases such as diabetes. However, diet is a problem with a high uncertainty, and it is widely pointed out that classical ontology is not sufficient to deal with imprecise and vague knowledge for some real-world applications like diet. On the other hand, a fuzzy ontology can effectively help handle and process uncertain data and knowledge. This chapter proposes a type-2 fuzzy set and fuzzy ontology for diet application and uses the type-2 fuzzy markup language (T2FML) to describe the knowledge base and rule base of the diet, including ingredients and the contained servings of six food categories of some common foods in Taiwan. The experimental results show that type-2 fuzzy logic system (FLS) performs better than type-1 FLS, proving that type-2 FLS can provide a powerful paradigm to handle the high level of uncertainties present in diet.

A type-2 fuzzy set, which is characterized by a fuzzy membership function, involves more uncertainties than the type-1 fuzzy set. As the most widely used type-2 fuzzy set, interval type-2 fuzzy set is a very useful tool to model the uncertainty in the process of decision making. As a special case of interval type-2 fuzzy set, trapezoidal interval type-2 fuzzy set can express linguistic assessments by transforming them into numerical variables objectively. The aim of this paper is to investigate the multiple attribute group decision-making problems in which the attribute values and the weights take the form of trapezoidal interval type-2 fuzzy sets. First, we introduce the concept of trapezoidal interval type-2 fuzzy sets and some arithmetic operations between them. Then, we develop several trapezoidal interval type-2 fuzzy aggregation operators for aggregating trapezoidal interval type-2 fuzzy sets and examine several useful properties of the developed operators. Furthermore, based on the proposed operators, we develop two approaches to multiple attribute group decision making with linguistic information. Finally, a practical example is given to illustrate the feasibility and effectiveness of the developed approach.

Finite-interval-valued Type-2 Gaussian fuzzy numbers applied to fuzzy TODIM in a healthcare problem

Type-2 fuzzy sets (T2FSs) exhibit evident merits when it comes to representing the complex and high uncertainty, which has been encountered in fuzzy optimization and multiple criteria decision making (MCDM) problems. Since T2FSs theory was proposed by Zadeh in 1975, then a series of theories and methods were investigated by more scholars. Type-2 fuzzy aggregation operators, contributing to the fundamental information fusion theory, have been paid more attention and applied to different areas during the last two decades. In this paper, a survey of type-2 fuzzy aggregation and application for MCDM is carried out. We first review some basic knowledge including definitions, operations, type reduction and ranking methods of T2FSs. Then the definitions and properties of some main aggregation operators are introduced. Furthermore, some application categories under type-2 fuzzy environment are given. Finally, we identify some existing shortcomings and point at future research directions on this topic.