Linguistic Fuzzy Numbers Research Articles

Selecting the Optimal Mine Ventilation System via a Decision Making Framework under Hesitant Linguistic Environment

Ventilation systems are amongst the most essential components of a mine. As the indicators of ventilation systems are in general of ambiguity or uncertainty, the selection of ventilation systems can therefore be regarded as a complex fuzzy decision making problem. In order to solve such problems, a decision making framework based on a new concept, the hesitant linguistic preference relation (HLPR), is constructed. The basic elements in the HLPR are hesitant fuzzy linguistic numbers (HFLNs). At first, new operational laws and aggregation operators of HFLNs are defined to overcome the limitations in existing literature. Subsequently, a novel comparison method based on likelihood is proposed to obtain the order relationship of two HFLNs. Then, a likelihood-based consistency index is introduced to represent the difference between two hesitant linguistic preference relations (HLPRs). It is a new way to express the consistency degree for the reason that the traditional consistency indices are almost exclusively based on distance measures. Meanwhile, a consistency-improving model is suggested to attain acceptable consistent HLPRs. In addition, a method to receive reasonable ranking results from HLPRs with acceptable consistency is presented. At last, this method is used to pick out the best mine ventilation system under uncertain linguistic decision conditions. A comparison and a discussion are conducted to demonstrate the validity of the presented approach. The results show that the proposed method is effective for selecting the optimal mine ventilation system, and provides references for the construction and management of mines.

Multi-attribute Group Decision Making Based on Cloud Aggregation Operators Under Interval-Valued Hesitant Fuzzy Linguistic Environment

Interval-valued hesitant fuzzy linguistic set, as an extension of linguistic term set and interval-valued hesitant fuzzy set, can effectively describe uncertainty, hesitancy, and inconsistency inherent in decision-making process. In this paper, a method based on comprehensive cloud aggregation operators is developed for solving multi-attribute group decision-making (MAGDM) problems with interval-valued hesitant fuzzy linguistic numbers (IVHFLNs). First, a comprehensive cloud of an IVHFLN is defined according to the cloud model. Using the comprehensive cloud, a distance measure between two comprehensive clouds is proposed and a distance measure for comprehensive cloud matrices is developed. Then, some generalized geometric aggregation operators of comprehensive clouds for IVHFLNs are introduced, including a comprehensive cloud generalized weighted geometric operator, a comprehensive cloud generalized ordered weighted geometric operator, and a comprehensive cloud generalized hybrid geometric operator. Subsequently, two approaches are presented to compute the deviations among attributes. Then, a programming model of maximizing deviation is established to derive the attribute weights objectively. To determine DMs’ weights, a technique for order preference by similarity to ideal solution-based approach is put forward in interval-valued hesitant fuzzy linguistic environment. The individual order of alternatives for each decision maker is obtained by the comprehensive cloud aggregation operator. To generate the collective order of alternatives, a multi-objective assignment model is constructed and transformed into a single-objective program to resolve. Thus, a method based on comprehensive cloud aggregation operators is proposed for MAGDM with IVHFLNs. Finally, two examples of application are given to demonstrate the applicability and effectiveness of the proposed method.

Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision-making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.

Distance Measures for Hesitant Fuzzy Linguistic Sets and Their Applications in Multiple Criteria Decision Making

Hesitant fuzzy linguistic term sets (HFLTSs) provide a linguistic and computational basis to increase the flexibility and richness of linguistic elicitation based on the fuzzy linguistic approach. Based on the traditional Hamming distance, Euclidean distance and generalized distance, some new class of distance measures for hesitant fuzzy linguistic numbers which include the hesitance degree of hesitant fuzzy element are provided and some linguistic scale functions are applied. We also define the continuous distance measure between two collections of HFLTSs. Furthermore, the proposed distance measures based on TOPSIS method for hesitant fuzzy linguistic multiple criteria decision making are developed, which calculate the distances between the alternatives and the positive ideal solution, the negative ideal solution, respectively. Then, the relative closeness degree to the ideal solution is calculated to rank all the alternatives. The main characteristics of the proposed distance measures are that it not only considers the hesitance of the hesitant fuzzy elements but also deals with linguistic transformation problem under different semantic situations, which efficiently avoid information loss and distortion. Finally, an example is provided to illustrate the feasibility and effectiveness of the developed method, which are then compared to the existing methods.

A Novel Picture Fuzzy Linguistic Aggregation Operator and Its Application to Group Decision-making

The intuitionistic fuzzy set (IFS) is an effective tool to express uncertain and incomplete cognitive information with the membership, non-membership, and hesitance degrees. The picture fuzzy set (PFS) is an extension of IFS, and it can contain more information than IFS. Linguistic variables (LVs) can easily describe the complex cognitive information provided by the decision makers. So it is necessary to combine the PFS with the linguistic term and define the picture fuzzy linguistic set (PFLS), then extend Archimedean triangular norms (t-norms) and triangular conorms (s-norms), which are the generalizations of a number of other t-norms and s-norms, such as Einstein, Hamacher, and Frank s-norms and t-norms, to process PFLS. By combining the PFS and the linguistic term, we define the picture fuzzy linguistic set (PFLS) and the operations of the picture fuzzy linguistic numbers (PFLNs). Further, we develop the Archimedean picture fuzzy linguistic weighted arithmetic averaging (A-PFLWAA) operator and discuss a number of properties and special cases of this operator. Besides, we propose an approach to deal with multiple attributes group decision-making (MAGDM) problem on the basis of the developed A-PFLWAA operator. An approach to solve MAGDM problem is proposed on the basis of the A-PFLWAA operator, and the validity and reliability of the proposed method are proven by an illustrative example. The PFLNs are the generalizations of the intuitionistic linguistic numbers (ILNs), and they contain more information than ILNs. In addition, our method cannot only be utilized to solve the problems with ILNs but also be used to deal with the problems with PFLNs, and it is a generalization of a number of the existing methods.

Multiple criteria decision analysis based on Shapley fuzzy measures and interval-valued hesitant fuzzy linguistic numbers

Hesitant fuzzy sets (HFSs) are powerful tools in managing simultaneous sources of vagueness. Inspired by HFSs, interval-valued hesitant fuzzy linguistic sets (IVHFLSs) combine linguistic term sets and interval-valued hesitant fuzzy sets (IVHFSs) together to flexibly characterize uncertain information from simultaneous sources. The purpose of this paper is to investigate effective ways to aggregate such uncertain information and then apply them to multiple criteria decision analysis (MCDA). First, two interval-valued hesitant fuzzy linguistic Choquet integrals are proposed to characterize the interdependent characteristics between criteria. Then, based on the Shapley fuzzy measures, we develop two kinds of generalized interval-valued hesitant fuzzy linguistic Shapley Choquet integrals to globally characterize interactions between criteria combinations. A model designed to obtain the optimal Shapley fuzzy measures is then constructed. Furthermore, an approach to interval-valued hesitant fuzzy linguistic MCDA is developed based on the proposed aggregation operators. Finally, a numerical example and a detailed discussion are provided to illustrate the application of the proposed approach and to demonstrate its practicality and effectiveness, respectively.

Analysis of socioeconomic development by intuitionistic linguistic fuzzy numbers

In this paper by using fuzzy intuitionistic linguistic fuzzy operators has been analyzed the influence of external factors to economic state, social consequences and government responses. The analysis is investigated on the basis of Azerbaijan and international information in 2010-2015.

A new hybrid decision making system for supplier selection

The objective of this paper is to develop a hybrid decision making system using Data Envelopment Analysis (DEA) and linguistic fuzzy models for selecting the best supplier in the presence of multiple decision makers. In this hybrid system, first the weights of selected criteria are obtained from each of the decision makers as linguistic fuzzy numbers within the framework of group decision making. Then, to select the best supplier, absolute weight restriction (AWR) model is incorporated into the DEA model. A real case study demonstrates the application of the model.

Assessment of the Innovative Capacity of Intellectual Property

This article is dedicated to development of methods for assessment of the intellectual property’s innovative capacity based on the mathematical tools of fuzzy sets. It shows that the structure of the intellectual property’s innovative capacity is determined by sets of factors affecting its formation and the criteria related to these factors. The structure of innovative capacity is represented by the following components: competitiveness, available resources, economic efficiency, feasibility and external investment risks. The indicator tree illustrates the structure of the intellectual property’s innovative capacity. The multi-component method of assessment of the intellectual property’s innovative capacity implies application of basic methods for finding the components of the innovative capacity and objective function of components’ consolidation. The author suggests to combine the components of the intellectual property’s innovative capacity through fuzzification with subsequent reverse procedure of defuzzification. Fuzzification implies transformation of components of the core of the intellectual property’s innovative capacity into linguistic variables using production rules of fuzzy logics, and external investment risks are fuzzificated by means of minimax functions. Defuzzification of components of the core of innovative capacity and external investment risks is defined by the functions with input parameters in the form of linguistic variables and fuzzy trapezoidal numbers. Use of these methods focuses on improvement in the approach to assessment of the potential economic efficiency of intellectual property in innovations. The article considers the opportunities for extension of the structure and modification of approaches to assessment of the intellectual property’s innovative capacity. The author suggests to apply expert systems in management of the innovative capacity in various economic activities. DOI: 10.5901/mjss.2015.v6n4s4p325

Multi-criteria decision-making methods based on the Hausdorff distance of hesitant fuzzy linguistic numbers

A hesitant fuzzy linguistic set is an extension of both a linguistic term set and a hesitant fuzzy set. It combines a quantitative evaluation with a qualitative evaluation, which can describe the real preferences of decision makers and reflect their uncertainty, hesitancy and inconsistency. The focus of this paper is those multi-criteria decision-making (MCDM) problems in which the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). Having reviewed the relevant literature, the Hausdorff distance for HFLNs is provided and some linguistic scale functions are applied. Subsequently, two hesitant fuzzy linguistic MCDM methods are proposed, which are based on the proposed distance measure and the TOPSIS and TODIM methods. The first of these MCDM methods is based on complete rationality, whilst the second is based on bounded rationality. Finally, an illustrative example is provided to verify the proposed methods, which are then compared to the existing approaches.

A new method for multiple attribute group decision-making with intuitionistic trapezoid fuzzy linguistic information

With respect to multi-attribute group decision-making (MAGDM) problems in which the attribute values take form of intuitionistic trapezoid fuzzy linguistic numbers, some new aggregation operators are proposed, such as intuitionistic trapezoid fuzzy linguistic weighted geometric operator, intuitionistic trapezoid fuzzy linguistic ordered weighted geometric operator, intuitionistic trapezoid fuzzy linguistic hybrid weighted geometric operator, intuitionistic trapezoid fuzzy linguistic generalized weighted averaging operator, intuitionistic trapezoid fuzzy linguistic generalized ordered weighted averaging operator and intuitionistic trapezoid fuzzy linguistic generalized hybrid weighted averaging operator are proposed at first. Then, some desirable properties of these proposed operators are discussed, including monotonicity, idempotency, commutativity and boundedness. Furthermore, based on the proposed operators, some novel methods are developed to solve MAGDM problems with intuitionistic trapezoid fuzzy linguistic information under different cases. Finally, an illustrative example of emergency response capability evaluation is provided to illustrate the applicability and effectiveness of the proposed methods.

Interval-valued hesitant fuzzy linguistic sets and their applications in multi-criteria decision-making problems

An interval-valued hesitant fuzzy linguistic set (IVHFLS) can serve as an extension of both a linguistic term set and an interval-valued hesitant fuzzy set. This new set combines quantitative evaluation with qualitative evaluation; these can describe the real preferences of decision-makers and reflect their uncertainty, hesitancy, and inconsistency. This work focuses on multi-criteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of interval-valued hesitant fuzzy linguistic numbers (IVHFLNs). The new approach to solving these problems is based on the prioritized aggregation operators of IVHFLNs. Having reviewed the relevant literature, we provide interval-valued hesitant fuzzy linguistic operations and apply some linguistic scale functions, which have been improved on the basis of psychological theory and prospect theory. Ultimately, two kinds of prioritized aggregation operators of IVHFLNs are developed, which extend to a grouping prioritized situation and are applied to MCDM problems. Finally, an example is provided to illustrate and verify the proposed approach in two separate situations, which are then compared to other representative methods.

Fuzzy risk analysis based on the novel fuzzy ranking with new arithmetic operations of linguistic fuzzy numbers

The project of managing risk analysis problems plays an important task in present world. The arithmetic operations of some fuzzy risk analysis methods do not satisfy some properties of linguistic fuzzy numbers and the comparison of the trapezoidal fuzzy numbers does not coincide with the perception of the individual. In this paper, we present a new ranking on generalized fuzzy numbers and new arithmetic operations such as fuzzy addition, fuzzy multiplication, and fuzzy division on linguistic fuzzy numbers. Also, we present an efficient approach for fuzzy risk analysis based on new arithmetic operators of the linguistic trapezoidal fuzzy numbers and new fuzzy ranking.

Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making

The paper proposes the concepts of an interval neutrosophic linguistic set (INLS) and an interval neutrosophic linguistic number (INLN) as a further generalization of the concepts of an intuitionistic linguistic set (ILS) and an intuitionistic linguistic fuzzy number (ILFN). Then, we introduce basic operational rules of INLNs and define the score function, accuracy function, and certainty function of an INLN. Furthermore, we propose an interval neutrosophic linguistic weighted arithmetic average (INLWAA) operator and an interval neutrosophic linguistic weighted geometric average (INLWGA) operator and investigate their properties, and then establish a decision-making method based on the INLWAA and INLWGA operators to handle multiple attribute decision-making problems with interval neutrosophic linguistic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

Hesitant fuzzy linguistic multicriteria decision-making method based on generalized prioritized aggregation operator.

Based on linguistic term sets and hesitant fuzzy sets, the concept of hesitant fuzzy linguistic sets was introduced. The focus of this paper is the multicriteria decision-making (MCDM) problems in which the criteria are in different priority levels and the criteria values take the form of hesitant fuzzy linguistic numbers (HFLNs). A new approach to solving these problems is proposed, which is based on the generalized prioritized aggregation operator of HFLNs. Firstly, the new operations and comparison method for HFLNs are provided and some linguistic scale functions are applied. Subsequently, two prioritized aggregation operators and a generalized prioritized aggregation operator of HFLNs are developed and applied to MCDM problems. Finally, an illustrative example is given to illustrate the effectiveness and feasibility of the proposed method, which are then compared to the existing approach.

Application Research of Two-Tuple Linguistic Theory in Warship Battle Damage Assessment

With respect to the problems of losing dates and information distorting, which may cause false decision in battle damage assessment, a warship optimized model was put forth on the basis of two-tuple linguistic theory and triangular fuzzy number. In the end, a reasonable conclusion is used for battle decision and repair according to simulating.

Multi-attribute group decision-making (MAGDM) for supplier selection using fuzzy linguistic modelling integrated with VIKOR method

Supplier selection is a multi-attribute decision-making (MADM) problem with the involvement of conflicting and non-commensurable criteria, assuming that compromising is acceptable for conflict resolution, the decision-maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. In the present reporting, VIKOR method has been adopted in a fuzzy environment to assess multi-criteria attributes on suppliers’ performance and to select the best supplier among a group of alternative suppliers. Individual attribute weights as well as supplier’s attribute measures have been expressed in terms of linguistic fuzzy numbers, then a hierarchy MADM model based on fuzzy sets theory and VIKOR method has been applied to deal with such a supplier selection problem. A numerical illustration has been represented to focus application feasibility of the aforesaid methodology.

Refitting Sites Selection of Ocean Trawler Based on Fuzzy Matter-Element Model and Information Entropy Theory

Refitting sites selection of ocean trawler in wartime, is affected by a variety of technical factors and other factors such as organization, planning, management, and so on. The index system is given by detailed analysis of the influence factors. A fuzzy matter-element model is built up in view of the fuzziness and incompatibility of the indexes, combining quantitative analysis with qualitative analysis, with quantifying the qualitative indexes by linguistic variables and fuzzy numbers. The information entropy theory is used to calculate the value of index weights, to reduce the subjective randomness. The multi-objective selection problem is transformed into the single-object decision by Euclid approach degree. The example shows that the method is very practical and the result is objective.

Fuzzy MCDM approach to R&D project evaluation in Taiwan's public sectors

PurposeEstablishing a performance‐oriented evaluation in public sectors is the key to successful administrations. However, because of lacking relative comparable measuring standards, it is difficult to measure the relative performance of one unit while comparing to other units with regard to the multiple criteria decision making (MCDM) of performance evaluation. This paper aims to focus on the performance ranking of research and development (R&D) projects in Taiwan's public sectors.Design/methodology/approachThe algorithm in this paper is based on the concept of fuzzy set theory and the hierarchical structure analysis. The analyzing method adopts the methods of standard normal distribution, linear transformation, and fuzzy MCDM, carrying on the analysis of multiple criteria of the performance evaluation.FindingsThis paper constructs linguistic values to the subjective judgments and analyzes the ranking results of the performance evaluation with respect to 45 R&D projects of one of Taiwan's electric power companies. Thus, the paper demonstrates a successful way of evaluating R&D projects in the public sector.Originality/valueIn this paper, a decision algorithm based on the fuzzy set theory is proposed to solve the performance evaluation of R&D projects in public sectors. In order to solve the difficulties of measuring one unit of the relative performance of quantitative criteria comparing to the other units, the method of standard normal distribution is adopted while measuring the quantitative criteria. The concept of linguistic values and fuzzy numbers are used in this paper since they could easily be used to describe the subjective measurement of the appropriateness of alternatives and the importance weightings of criteria.

Selection among ERP outsourcing alternatives using a fuzzy multi-criteria decision making methodology

Outsourcing can be seen as a strategic way to align technology initiatives and business goals, as a strategy for managing technology operations in today's difficult business environment, and as a way to reduce operating costs. Often, companies begin the process by outsourcing non-core business operations, which may include applications, assets, people and other resources. The outsourcing decision is important since the correct selection can dramatically increase a firm's performance. When companies outsource a significant part of their business and become more dependent on outsourcers, the consequences of poor decision making becomes more severe. Since enterprise resource planning (ERP) is one of the vital systems, if not the one, that integrates all functions including planning, manufacturing, distribution, and accounting into a single system, its outsourcing is a very important multi-attribute decision problem for the firms. In the literature, outsourcing decisions are often based on multi-criteria approaches. In this paper, a fuzzy multi-criteria decision making methodology is suggested for the selection among ERP outsourcing alternatives. The methodology is based on the analytic hierarchy process (AHP) under fuzziness. It allows decision-makers to express their evaluations in linguistic expressions, crisp or fuzzy numbers. In the application of the proposed methodology, an automotive firm selects the best alternative among three ERP outsourcing firms.