Yan-Lai Li

Proportional hesitant fuzzy linguistic term set for multiple criteria group decision making

We propose the general concept of PHFLTS.We define the negation, union, and intersection operations on PHFLTSs.We present the PHFLWA and PHFLOWA operators.A transformation algorithm is proposed to convert the proportional comparative linguistic pairs into PHFLTSs.We develop a proportional hesitant fuzzy linguistic MCGDM model. The theory of hesitant fuzzy linguistic term sets (HFLTSs) is a powerful technique used to describe hesitant situations, which are typically assessed by experts using several possible linguistic values or rich expressions instead of a single term. The union of HFLTSs with respect to each expert, that is, an extended HFLTS (EHFLTS), further facilitates the elicitation of linguistic assessments for addressing group decision-making problems because EHFLTSs can deal with generalized (either consecutive or non-consecutive) linguistic terms. In this study, we propose proportional HFLTSs (PHFLTSs), which include the proportional information of each generalized linguistic term. The mathematical form for a PHFLTS is consistent with that for a linguistic distribution assessment. However, the underlying meanings of the proportions associated with generalized linguistic terms are different. PHFLTSs can be viewed as a special method for performing linguistic distribution assessments. PHFLTSs are recognized as a useful extension of HFLTSs and a possibility distribution for HFLTSs under different assumptions. We define the basic operations with closed properties among PHFLTSs on the basis of t-norms and t-conorms. We then propose a probability theory-based outranking method for PHFLTSs by providing possibility degree formulas. We also study two fundamental aggregation operators for PHFLTSs, namely, the proportional hesitant fuzzy linguistic weighted averaging operator and the proportional hesitant fuzzy linguistic ordered weighted averaging operator. Several important properties of these aggregation operators are investigated. Finally, we use the proposed multiple criteria group decision-making model in practical applications.

Determining the final priority ratings of customer requirements in product planning by MDBM and BSC

Quality function deployment (QFD) has been widely used to translate customer requirements (CRs) into engineering characteristics (ECs) in product planning and improvement. Product planning house of quality (PPHOQ) is of fundamental and strategic importance in the QFD system. Correctly determining the final priority ratings of CRs is essential in the process of constructing PPHOQ, because it will largely affect the target value of ECs for product improvement. This paper present a systematic and operational method based on the integration of a minimal deviation based method (MDBM), balanced scorecard (BSC), analytic hierarchy process (AHP) and scale method to determine the final priority ratings of CRs. To exploit the competition and preference information of product improvement, the MDBM is developed to determine the CPRs of CRs. A concept of the total output of achieving the ITPE of a CR is introduced and analyzed by using the integration of BSC, AHP and scale method in a qualitative and quantitative way, and then the priority rating of achieving the ITPE of this CR is determined. Finally, a case study is provided to illustrate the effectiveness of the proposed method.

A rough set approach for estimating correlation measures in quality function deployment

Quality function deployment (QFD) is a planning and problem-solving methodology used to translate customer requirements (CRs) into engineering characteristics (ECs) in the course of new product development (NPD). Estimating the correlation measures among ECs is a crucial step in the product planning house of quality (PPHOQ) construction process because these measures seriously affect the planning of development efforts. This study presents a rough set-based approach used to estimate the correlation measures by revealing the knowledge of a QFD team. The approach involves introducing the category factor of a correlation to express the influences of the correlation categories on the corresponding correlation measures. A case study of a two-cylinder washing machine is used to illustrate the proposed approach. The result shows that the novel approach is effective in revealing the related knowledge of the QFD team and facilitating NPD decision making.

A Note on Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets

In this note, we point out an error to the proof of Theorem 3.4 in Zhang and Xu (Int J Intell Syst 2014;29(12):1061–1078) by a counterexample. We find that the inequality (i.e., |(πβ1)2−(πβ2)2|≤|(πβ1)2−(πβ3)2| ) with respect to the degrees of indeterminacy of any three Pythagorean fuzzy numbers in the proof of Theorem 3.4 in Zhang and Xus paper is not valid. A new proof is provided in this note.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.

Rough set-based approach for modeling relationship measures in product planning

Quality function deployment (QFD) provides a planning and problem-solving methodology that is widely renowned for translating customer requirements (CRs) into engineering characteristics (ECs) for new product development. As the first phase of QFD, product planning house of quality (PPHOQ) plays a very important role in this process. The degrees and directions of the relationship measures between CRs and ECs have serious effects on the special planning of ECs, modeling the relationship measures is an important step in constructing PPHOQ. The current paper presents a rough set (RS)-based approach for modeling relationship measures by determining the knowledge and experience of the QFD team, aided by the introduction of the type factor of a relationship used to express the effects of the relationship types. A study of general cases is used to demonstrate the performances and limitations of the proposed RS-based approach. The results show that the novel approach effectively determines the relative knowledge of the QFD team and facilitates decision-making in new product development.

Triangular intuitionistic fuzzy random decision making based on combination of parametric estimation, score functions, and prospect theory

This study investigates and improves the operational laws of triangular intuitionistic fuzzy numbers. The triangular intuitionistic fuzzy random variable (TIFRV) is introduced on the basis of the concepts of the triangular intuitionistic fuzzy number and triangular fuzzy random variable. Related properties of a TIFRV are also proposed and verified. To solve the problem of multi-criteria decision making on aspiration levels—a situation in which criterion weights are unknown and criterion values are given in terms of TIFRVs—this study proposes a triangular intuitionistic fuzzy random decision- making method based on a combination of parametric estimation, score functions, and prospect theory. In this method, the decision maker evaluates alternatives with triangular intuitionistic fuzzy numbers in different periods of decision making and thus enables the estimation of the parameters of the triangular intuitionistic fuzzy population and the creation of an intuitionistic triangular fuzzy random matrix. An expectation-variance intuitionistic fuzzy matrix is constructed on the basis of mean-variance analysis, and a fuzzy random score function is then defined to transform a normalized expectation-variance intuitionistic fuzzy matrix into a score function matrix. Prospect theory is used to calculate the values of prospect score functions, and the information entropy method is used to determine criterion weights. This procedure generates comprehensive prospect score function values that determine the final ranking of alternatives. A practical example is presented to show the feasibility and effectiveness of the proposed approach.

On Generalized Extended Bonferroni Means for Decision Making

The extended Bonferroni mean (EBM) recently proposed differs from the classical Bonferroni mean, as it aims to capture the heterogeneous interrelationship among the attributes instead of presupposing a homogeneous relation among them. In this study, we generalize the EBM to explicitly and profoundly understand its aggregation mechanism by defining a composite aggregation function. We adopt the approach of optimizing the choice of weighting vectors for the generalized EBM (GEBM) with respect to the least absolute deviation of residuals. We also investigate several desirable properties of the GEBM. Our special interest in this study is to investigate the ability of the GEBM to model mandatory requirements. Finally, the influence of replacing the conjunctive of the GEBM is analyzed to show how the change of the conjunctive affects the global andness and orness of the GEBM. Meanwhile, the aggregation mechanism of the EBM is specified and provided with quite intuitive interpretations for application.

A Framework for Triangular Fuzzy Random Multiple-Criteria Decision Making

Most real-world decisions practically occur in extremely complex environments characterized by both fuzziness and randomness. This phenomenon highlights the requirement for new evaluation methods in a fuzzy random environment and new ways to address fuzzy random multiple-criteria decision-making (MCDM) problems. This study reviews fuzzy random variable (FRV) to evaluate fuzzy random decision-making environment. Given the inaccuracy of certain precision formulas proposed in previous studies for the variance of a triangular FRV, this work presents the detailed process of calculating precision variance formulas and discusses several properties of the expectation and variance of triangular FRVs (TFRVs). The united variance of a TFRV vector is also proven to possess non-additive properties. Thus, an ordered weighted averaging (OWA) operator is extended to aggregate fuzzy random data by proposing a triangular fuzzy random OWA operator. Motivated by the idea of mean–variance analysis, an expectation-variance-based method is employed to rank TFRVs. Furthermore, a novel triangular fuzzy random MCDM method is developed, and certain numerical examples are provided to demonstrate the ability of TFRVs to comprehensively assess the performance of a specific alternative. This work also illustrates how the triangular fuzzy random MCDM framework can be extended to any fuzzy random decision-making process.

Shuffled Frog Leaping Algorithm for Preemptive Project Scheduling Problems with Resource Vacations Based on Patterson Set

This paper presents a shuffled frog leaping algorithm (SFLA) for the single-mode resource-constrained project scheduling problem where activities can be divided into equant units and interrupted during processing. Each activity consumes 0–3 types of resources which are renewable and temporarily not available due to resource vacations in each period. The presence of scarce resources and precedence relations between activities makes project scheduling a difficult and important task in project management. A recent popular metaheuristic shuffled frog leaping algorithm, which is enlightened by the predatory habit of frog group in a small pond, is adopted to investigate the project makespan improvement on Patterson benchmark sets which is composed of different small and medium size projects. Computational results demonstrate the effectiveness and efficiency of SFLA in reducing project makespan and minimizing activity splitting number within an average CPU runtime, 0.521 second. This paper exposes all the scheduling sequences for each project and shows that of the 23 best known solutions have been improved.