Interval-valued Fuzzy Set Theory Research Articles

Fuzzy and rough approach to the problem of missing data in fall detection system

Two new methods for mining incomplete data based on interval-valued fuzzy set theory and rough set theory, particularly maximal consistent blocks were proposed, and their application to the fall detection system, exactly to the posture detection system. The suggested methods are based on interval-valued aggregation operators supporting decision-making involving uncertainty. Additionally, the new measure of knowledge was used in two aspects: in the imputation of missing data and during the inference process. The usage of the knowledge measure allowed for a reduction of the uncertainty due to incompleteness and imprecision of data, while increasing the efficiency of the decision-making process, through the additional selection of objects for which the degree of the information measure is the highest. The developed hybrid approach to mining incomplete data and its application in a real decision-making problem yield stable performance despite the increase in missing data.

Green multiple-criteria decision-making method of selection of diamond cutting tool for promoting cleaner production in the natural stone industry

Selection of a reasonable diamond cutting tool (DCT) is a crucial Multiple Criteria Decision-Making (MCDM) problem for promoting cleaner production for a natural stone company. It has severe uncertainties in the decision information, complex interdependences among the DM criteria and needs to balance stakeholders' opinions and adopt the non-complete compensation idea in the DM process. This paper establishes a specialized index system with changing the evaluation object from ontology of DCT to the ‘stone machining system’ within the boundary demarcated by LCA. Decision-Making Trial and Evaluation Laboratory (DEMATEL) method is applied to analyze the interdependence relationships existing in the index system and then the indicators' weights can be obtained by Analytic Network Process (ANP) method. In order to avoid complete compensation among indicators, Preference Ranking Organization Method for Enrichment Evaluations II (PROMETHEE II) method is used to prioritize the alternatives and identify the most reasonable DCT. The new developed MCDM algorithm is expressed based on interval-valued fuzzy set (IVFS) theory to handle the uncertain information in DM process. Integration of IVFS theory with MCDM method allows the decision-maker to use linguistic variables which correspond to interval-valued fuzzy numbers to describe their judgments and ensures all the stakeholders' preferences can be trade-off in the DM process. In the case application, the proposed method has been applied to select a suitable DCT to cut the Lotus red granite (G3768) for a stone processing company in China. As a result, the iron-based DCT (TJ-15) obtained the highest priority net flow (0.373) among five DCT alternatives and it was identified as the most reasonable DCT for the case company. The application study demonstrates the effectiveness and robustness of the developed method and indicates that pursuit of matching DCT with the characteristics of natural stone is more rational than blindly adopting more advanced and expensive DCT.

A Novel Multi-Criteria Decision-Making Approach for Intellectual Property Risk Assessment in Crowdsourcing Design

Crowdsourcing design is a knowledge-intensive innovative design mode, in which there are various intellectual property risks. This paper proposes a novel multi-criteria decision-making approach for intellectual property risk assessment in crowdsourcing design. First, domain experts are invited to identify and evaluate various risk factors in the given crowdsourcing design environment, and the interval-valued Pythagorean fuzzy sets theory (IVPF) is used to eliminate the vagueness and ambiguity of risk assessment opinions from experts. A combination weight method based on the Decision Making Trial and Evaluation Laboratory (DEMATEL) and entropy weight (EW) is designed to measure the importance degree of risk evaluation parameters, which includes risk probability (P), risk frequency (F) and risk severity (S). Then, a TODIM method is used to calculate the risk value of various factors to identify the largest intellectual property risk. Finally, the feasibility and effectiveness of the proposed approach are verified by a case. The experimental results show that the proposed approach can effectively evaluate the intellectual property risks in crowdsourcing design.

A Novel Approach to Decision Making Based on Interval-Valued Fuzzy Soft Set

Interval-valued fuzzy soft set theory is a powerful tool that can provide the uncertain data processing capacity in an imprecise environment. The two existing methods for decision making based on this model were proposed. However, when there are some extreme values or outliers on the datasets based on interval-valued fuzzy soft set for making decisions, the existing methods are not reasonable and efficient, which may ignore some excellent candidates. In order to solve this problem, we give a novel approach to decision making based on interval-valued fuzzy soft set by means of the contrast table. Here, the contrast table has symmetry between the objects. Our proposed algorithm makes decisions based on the number of superior parameter values rather than score values, which is a new perspective to make decisions. The comparison results of three methods on two real-life cases show that, the proposed algorithm has superiority to the existing algorithms for the feasibility and efficiency when we face up to the extreme values of the uncertain datasets. Our proposed algorithm can also examine some extreme or unbalanced values for decision making if we regard this method as supplement of the existing algorithms.

New Score and Accuracy Function for IVIF Sets and Their Applications to AHP for MCGDM

Multi-criteria group decision making (MCGDM) is an important part of decision science and widely applied in several fields. To cope with the vagueness and ambiguity of the human evaluation in the MCGDM process, interval-valued intuitionistic fuzzy set (IVIFS) theory is introduced. In this study, the AHP method whose traditional form is frequently used in MCGDM problems is improved in the IVIF environment. Since the aim of AHP is to choose the most suitable criterion/alternative by making a rank from the most important to the least important, the improved IVIF-AHP method is based on the ranking functions. Some existing score and accuracy functions are analyzed and it is seen that these functions have some limitations to rank IVIF numbers. So, new score and accuracy functions of IVIFS are developed to overcome their limitations and these new functions are integrated into the IVIF-AHP method. The comparative results show that the improved IVIF-AHP method gives a consistent ranking for the criteria. Moreover, the proposed method steps are illustrated with a case study about prioritizing some technical and soft skills over industrial engineering and electrical engineering.

Parameter reduction analysis under interval-valued m-polar fuzzy soft information

This paper formalizes a novel model that is able to use both interval representations, parameterizations, partial memberships and multi-polarity. These are differing modalities of uncertain knowledge that are supported by many models in the literature. The new structure that embraces all these features simultaneously is called interval-valued multi-polar fuzzy soft set (IVmFSS, for short). An enhanced combination of interval-valued m-polar fuzzy (IVmF) sets and soft sets produces this model. As such, the theory of IVmFSSs constitutes both an interval-valued multipolar-fuzzy generalization of soft set theory; a multipolar generalization of interval-valued fuzzy soft set theory; and an interval-valued generalization of multi-polar fuzzy set theory. Some fundamental operations for IVmFSSs, including intersection, union, complement, “OR”, “AND”, are explored and investigated through examples. An algorithm is developed to solve decision-making problems having data in interval-valued m-polar fuzzy soft form. It is applied to two numerical examples. In addition, three parameter reduction approaches and their algorithmic formulation are proposed for IVmFSSs. They are respectively called parameter reduction based on optimal choice, rank based parameter reduction, and normal parameter reduction. Moreover, these outcomes are compared with existing interval-valued fuzzy methods; relatedly, a comparative analysis among reduction approaches is investigated. Two real case studies for the selection of best site for an airport construction and best rotavator are studied.

A new parameter reduction algorithm for interval-valued fuzzy soft sets based on Pearson’s product moment coefficient

Interval-valued fuzzy soft set theory is a newly emerging mathematical tool for dealing with uncertain problems. Parameter reduction abandons redundant parameters meanwhile holds the powerful ability to support decision making Ma et al. (2014) expressed four diverse parameter reduction approaches which are appropriate for the different scenarios. Optimal choice considered parameter reduction approach is not effective to support the additive parameters. The other three methods provide the support for the newly additive parameters but possess very low rate of success. And the four methods are computationally complicated. In this paper, we propose Pearson’s product moment coefficient based parameter reduction algorithm for an interval-valued fuzzy soft sets. By comparison with four algorithms, this approach not only is carried out before getting the scores, give attention to the newly additive parameters, and has much higher probability to find parameter reduction, but also is not more computationally complicated. Therefore, this algorithm is the most efficient to support extension and combination of multiple evaluation systems based on interval-valued fuzzy soft set in the down-to-earth applications environment. The superiority and effectiveness of the proposed approach is demonstrated by this means of a suitable practical application case of on-line reservation for accommodation and twenty synthetic generated datasets.

On interval-valued fuzzy soft set theory applied to semigroups

In this paper, we focus on combining the theories of interval-valued fuzzy soft sets over semigroups, and establishing a new framework for interval-valued fuzzy soft semigroups. The aim of this manuscript is to apply interval-valued fuzzy soft set for dealing with several kinds of theories in semigroups. First, we present the concepts of interval-valued fuzzy soft sets, interval-valued fuzzy soft semigroups, interval-valued fuzzy soft ideals, interval-valued fuzzy soft quasi-ideals, interval-valued fuzzy soft interior ideals and interval-valued fuzzy soft bi-ideals. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in this paper. Also, we prove that a non-empty subset of a semigroup S is a subsemigroup (left ideal, right ideal, ideal) of S if and only if the interval-valued fuzzy soft set over S is the interval-valued fuzzy soft subsemigroup (interval-valued fuzzy soft left ideal, interval-valued fuzzy soft right ideal, interval-valued fuzzy soft ideal) over S. Second, several new kinds of generalized fuzzy soft sets over semigroups are proposed, and related properties and mutual relationships are also investigated. Moreover, we study relation between quasi-ideals and interval-valued fuzzy soft quasi-ideals over semigroups. Finally, we obtain necessary and sufficient conditions of an interval-valued fuzzy soft ideal in order to be an interval-valued fuzzy soft interior ideal.

Data Analysis Approaches of Interval-Valued Fuzzy Soft Sets Under Incomplete Information

Interval-valued fuzzy soft set theory is a new and developing mathematical tool, which figures out a creative way aiming at dealing with uncertain and fuzzy data. Studies on decision making approaches and parameter reduction based on the complete interval-valued fuzzy soft sets became very active. However, we have to face up to a mount of incomplete data in real applications of interval-valued fuzzy soft sets. In this paper, we propose data analysis approaches of interval-valued fuzzy soft sets under incomplete information, which involves ignoring incomplete data when the percentage of missing entries is higher than the threshold and a filling approach for incomplete information while the percentage of missing entries is lower than the threshold. A suitable and practical case study demonstrates the implementation and validation of the proposed analysis approaches. The experimental results show that the overall accuracy estimation of the filling approach is up to 96.11%.

Negations With Respect to Admissible Orders in the Interval-Valued Fuzzy Set Theory

Admissible orders have brought the structure of chains in the framework of interval-valued fuzzy sets. However, a deeper study of functions monotone with respect to admissible orders is still missing in the literature. In this work, we consider the construction of negations and strong negations on intervals with respect to admissible orders, in particular, for the Xu and Yager and lexicographical orders, as well as for those based on $K_\alpha$ operators. We introduce and discuss an approach to the construction of strong negations on intervals with respect to $K_{\alpha,\beta }$ orders based on an arbitrary couple of strong negations defined over the standard real interval $[0,1]$ . The introduced strong negations have a deep impact on all fields exploiting fuzzy methods dealing with intervals, allowing to introduce complements, dual aggregations, implications, entropies, etc.

FUZZY RECURSIVE RELATIONSHIPS IN RELATIONAL DATABASES

Recursive relationships are used for modelling problems coming from the real life, such as, for example, a relationship describing formal dependencies between employees of an enterprise, where creation of work groups and teams requires analysis of many elements. In conventional database systems, the precision of data is assumed. If our knowledge of the fragment of reality to be modelled is imperfect one should apply tools for describing uncertain or imprecise information. One of them is the fuzzy set theory. The paper deals with recursive relationships in fuzzy databases. The analysis is performed with the use of the theory of interval-valued fuzzy sets. A definition of a fuzzy interval recursive relationship has been presented. The paper defines different connections of entities which participate in such relationships. Op-erations of the extended relational algebra are also discussed.

Waste-to-energy, municipal solid waste treatment, and best available technology: Comprehensive evaluation by an interval-valued fuzzy multi-criteria decision making method

The treatment of municipal solid waste (MSW) has become an urgently important task of many countries. This objective of this study is to present a novel group multi-attribute decision analysis method for prioritizing the MSW treatment alternatives based on the interval-valued fuzzy set theory. This study allows multiple stakeholders to participate in the process of decision-making and they are also allowed to use linguistic variables to rate the alternatives and determine the weights of the evaluation criteria. The interval-valued fuzzy group decision making trail and evaluation laboratory (DEMATEL) method was developed to determine the weights of the evaluation criteria by considering the independent relationships among these criteria. The multi-actor interval-valued fuzzy grey relational analysis was developed to rank the waste-to-energy scenarios. Four alternative processes for MSW treatment including landfill, anaerobic digestion, incineration, and gasification were studied by the developed model, and the results reveal that the developed model can successfully help the stakeholders to determine the priority sequence of the alternative MSW treatment scenarios.

BI-IDEALS OF ORDERED SEMIGROUPS BASED ON THE INTERVAL-VALUED FUZZY POINT

Interval-valued fuzzy set theory (advanced generalization of Zadeh's fuzzy sets) is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, we introduce the notion of generalized quasi-coincident with () relation of an interval-valued fuzzy point with an interval-valued fuzzy set. In fact, this new concept is a more generalized form of quasi-coincident with relation of an interval-valued fuzzy point with an interval-valued fuzzy set. Applying this newly defined idea, the notion of an interval-valued -fuzzy bi-ideal is introduced. Moreover, some characterizations of interval-valued -fuzzy bi-ideals are described. It is shown that an interval-valued -fuzzy bi-ideal is an interval-valued fuzzy bi-ideal by imposing a condition on interval-valued fuzzy subset. Finally, the concept of implication-based interval-valued fuzzy bi-ideals, characterizations of an interval-valued fuzzy bi-ideal and an interval-valued -fuzzy bi-ideal are considered.

Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.

Interval-valued hesitant fuzzy Einstein prioritized aggregation operators and their applications to multi-attribute group decision making

Interval-valued hesitant fuzzy information aggregation plays an important role in interval-valued hesitant fuzzy set theory, which has received more and more attention in recent years. In this paper, we investigate interval-valued hesitant fuzzy multi-attribute group decision-making problems in which there exists a prioritization relationship among the attributes. Firstly, we introduce some Einstein operational laws on interval-valued hesitant fuzzy sets, and discuss some relations of these operations. Then, we develop two interval-valued hesitant fuzzy prioritized aggregation operators with the help of Einstein operations, such as the interval-valued hesitant fuzzy Einstein prioritized weighted average (IVHFEPWA) operator and the interval-valued hesitant fuzzy Einstein prioritized weighted geometric (IVHFEPWG) operator, whose desirable properties are investigated in detail. We further analyze the relationship between these proposed operators and the existing interval-valued hesitant fuzzy prioritized aggregation operators. Moreover, an approach to interval-valued hesitant fuzzy multi-attribute group decision making is given on the basis of the proposed operators. Finally, a numerical example is provided to demonstrate their effectiveness.

A risk-based decision support framework for selection of appropriate safety measure system for underground coal mines

In the context of underground coal mining industry, the increased economic issues regarding implementation of additional safety measure systems, along with growing public awareness to ensure high level of workers safety, have put great pressure on the managers towards finding the best solution to ensure safe as well as economically viable alternative selection. Risk-based decision support system plays an important role in finding such solutions amongst candidate alternatives with respect to multiple decision criteria. Therefore, in this paper, a unified risk-based decision-making methodology has been proposed for selecting an appropriate safety measure system in relation to an underground coal mining industry with respect to multiple risk criteria such as financial risk, operating risk, and maintenance risk. The proposed methodology uses interval-valued fuzzy set theory for modelling vagueness and subjectivity in the estimates of fuzzy risk ratings for making appropriate decision. The methodology is based on the aggregative fuzzy risk analysis and multi-criteria decision making. The selection decisions are made within the context of understanding the total integrated risk that is likely to incur while adapting the particular safety system alternative. Effectiveness of the proposed methodology has been validated through a real-time case study. The result in the context of final priority ranking is seemed fairly consistent.

Generalized Interval-Valued Fuzzy Rough Set and its Application in Decision Making

This paper presents a general study of generalized interval-valued fuzzy rough sets integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. In the constructive approach, by employing an interval-valued fuzzy residual implicator and its dual operator, generalized upper and lower interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy approximation space are first defined. Then properties of generalized interval-valued fuzzy rough approximation operators are discussed. Furthermore, connections between special types of interval-valued fuzzy relations and properties of generalized interval-valued fuzzy approximation operator are also established. In the axiomatic approach, generalized interval-valued fuzzy rough approximation operators are defined by axioms. We prove that different axiom sets can characterize the essential properties of generalized interval-valued fuzzy rough approximation operators. Also the composition of two approximation spaces is explored. Finally, a practical application is provided to illustrate the efficiency of the generalized interval-valued fuzzy rough set model.

The Parameter Reduction of the Interval-Valued Fuzzy Soft Sets and Its Related Algorithms

There has been a rapid growth of interest in developing approaches that are capable of dealing with imprecision and uncertainty. To this end, an interval-valued fuzzy soft set (IVFSS) that combines soft set theory with interval-valued fuzzy set theory has been proposed to handle imprecision and uncertainty in applications such as decision-making problems. However, there has been little focus on parameter reduction of the interval-valued fuzzy soft sets, which is significant in decision-making problems. In this paper, we introduce four different definitions of parameter reduction in interval-valued fuzzy soft sets to satisfy different the needs of decision makers. We propose four heuristic algorithms of parameter reduction. Finally, the algorithms are compared and summarized from the aspects of easy degree of finding reduction, applicability, reduction result, exact level for reduction, multiusability, applied situation, and computational complexity. The results of the experiment show that the methods reduce the redundant parameters while preserving certain decision abilities.

Fuzzy multi-objective group decision making based on interval-valued intuitionistic fuzzy set

In order to improve the accuracy of data decision making,an optimization approach was proposed for the algorithm of multi-objectives group decision making.By the interval-valued intuitionistic fuzzy set theory,the optimization was approached by the method of iterative computation gradually in the situation that the part weight information was incomplete usually.Results of the simulation indicate that the algorithm has low time complexity,and can be implemented in the computer easily;moreover,it also shows the effectiveness and accuracy of the algorithm.

An integrated approach to evaluate module partition schemes of complex products and systems based on interval-valued intuitionistic fuzzy sets

Modularisation strategy can effectively shorten the lead time and reduce the cost of complex products and systems (CoPS) development. A few schemes are usually obtained through module partition because of the multidimensional complexity of CoPS. Unfortunately, research has rarely been conducted on the module partition schemes evaluation (MPSE) that is a complicated multiple attribute decision-making (MADM) problem under fuzzy and uncertain environment. The interval-valued intuitionistic fuzzy set (IVIFS) theory has distinct advantage on dealing with the imprecise and uncertain information in decision-making. In this article, an integrated MPSE approach is developed based on IVIFS. First, the evaluation measures are provided in the form of interval-valued intuitionistic fuzzy numbers (IVIFNs). Then the aggregation operators of IVIFSs utilised to construct the fuzzy synthetic decision matrix (FSDM) are obtained based on Karnik–Mendel algorithms. Finally, the interval-valued intuitionistic fuzzy (IVIF) cross-entropy integrated with the TOPSIS framework is developed to rank the candidate alternatives. The MPSE methods have been used to the design of a large tonnage crawler crane to illustrate that proposed approach is effective and systematic to solve the MPSE problem of CoPS.