A new flexible and reliable interval valued fuzzy VIKOR method based on uncertainty risk reduction in decision making process: An application for determining a suitable location for digging some pits for municipal wet waste landfill

Facility location selection problem is one of the challenging and famous kinds of MCDM problems including both quantitative and qualitative criteria. For each Multiple Criteria Decision Making (MCDM) problem, when the ratings of alternatives with respect to the criteria and/or the values of criteria’s weights are presented by Interval Valued Fuzzy Numbers (IVFNs), the conventional fuzzy MCDM methods (Type-1 fuzzy MCDM methods) tend to be less effective. Therefore, the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be applied for solving such fuzzy MCDM problems. In this paper, we propose an IVF-VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) method based on uncertainty risk reduction in decision making process. By using such method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving two numerical examples that the former of which is a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The second numerical example is presented with an aim of comparing our method with the two other IVF-MCDM methods. As a result, we found out the proposed method is reliable and practical for the facility location selection problems and other MCDM problems. Moreover, the proposed method has a considerable accuracy and is flexible and easy to use.     

A new flexible and reliable IVF-TOPSIS method based on uncertainty risk reduction in decision making process

One of the challenging and famous types of MCDM (Multiple Criteria Decision Making) problems that includes both quantitative and qualitative criteria is Facility location selection problem. For the common fuzzy MCDM problems (Type-1 fuzzy MCDM problems), the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the common fuzzy numbers. However, in the majority of cases, determining the exact membership degree for each element of the fuzzy sets which are considered for the ratings of alternatives with respect to the criteria or/and the values of criteria weights as a number in interval [0,1], is difficult. In this situation, the ratings of alternatives with respect to the criteria or/and the values of criteria weights, are expressed by the IVFNs (Interval Valued Fuzzy Numbers) and thereby the IVF-MCDM (Interval Valued Fuzzy MCDM) methods should be used. In this paper, the authors propose an IVF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method based on uncertainty risk reduction in decision making process. By using this method, the reliability of the captured decisions in an IVF decision making problem is significantly increased. The proposed method is applied for solving a real application problem related to selecting a suitable location for digging some pits for municipal wet waste landfill in one of the largest cities in Iran. The proposed method is also compared with another IVF-TOPSIS method. As a result, the authors concluded that in addition to benefits such as simplicity and ease of use that exist in the previous IVF-TOPSIS methods, the proposed method has a significant reliability and flexibility and is practical for facility location selection problems and other IVF-MCDM problems.     

Optimal location selection for an international distribution center by using a new hybrid method

The selection of a location for an international distribution center (IDC) is a most important decision for international logistics managers owing to the need to consider various criteria that involve a complex decision process in which multiple requirements and uncertain conditions have to be taken into consideration simultaneously. Moreover, the criteria often exist simultaneously as independent and dependent characteristics when the problems of location selection have become very complex. A new hybrid method combining the concepts of fuzzy DEMATEL and a new method of fuzzy multiple criteria decision-making (MCDM) in a fuzzy environment is proposed to solve the problems of IDC location selection. In this paper, the fuzzy DEMATEL is proposed to arrange a suitable structure between criteria, and the analytic hierarchy/network process (AHP/ANP) is used to construct weights of all criteria. The linguistic terms characterized by triangular fuzzy numbers are used to denote the evaluation values of all alternatives versus various criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses an empirical case for optimal location selection for an IDC in Pacific Asia to illustrate the proposed method, and the results show that the method is an effective means for tackling fuzzy MCDM problems.     

Group decision making process for supplier selection with VIKOR under fuzzy environment

During recent years, how to determine suitable suppliers in the supply chain has become a key strategic consideration. However, the nature of supplier selection is a complex multi-criteria problem including both quantitative and qualitative factors which may be in conflict and may also be uncertain. The VIKOR method was developed to solve multiple criteria decision making (MCDM) problems with conflicting and non-commensurable (different units) 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 this paper, linguistic values are used to assess the ratings and weights for these factors. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchy MCDM model based on fuzzy sets theory and VIKOR method is proposed to deal with the supplier selection problems in the supply chain system. A numerical example is proposed to illustrate an application of the proposed model.     

Soft computing based on new interval-valued fuzzy modified multi-criteria decision-making method

In this paper, a new interval-valued fuzzy modified TOPSIS (IVFM-TOPSIS) method is proposed that can reflect both subjective judgment and objective information in real life situations. This proposed method is based on concepts of the positive ideal and negative ideal solutions for solving multi-criteria decision-making (MCDM) problems in a fuzzy environment. The performance rating values and weights of criteria are linguistic variables expressed as triangular interval-valued fuzzy numbers. Furthermore, we appraise the performance of alternatives against both subjective and objective criteria with multi-judges for decision-making problems. Finally, for the purpose of proving the validity of the proposed method a numerical example is presented for a robot selection problem.     

A new method selection approach for fuzzy group multicriteria decision making

Fuzzy multicriteria decision making (MCDM) has been widely used in ranking a finite number of decision alternatives characterized by fuzzy assessments with respect to multiple criteria. In group decision settings, different fuzzy group MCDM methods often produce inconsistent ranking outcomes for the same problem. To address the ranking inconsistency problem in fuzzy group MCDM, this paper develops a new method selection approach for selecting a fuzzy group MCDM method that produces the most preferred group ranking outcome for a given problem. Based on two group averaging methods, three aggregation procedures and three defuzzification methods, 18 fuzzy group MCDM methods are developed as an illustration to solve the general fuzzy MCDM problem that requires cardinal ranking of the decision alternatives. The approach selects the group ranking outcome of a fuzzy MCDM method which has the highest consistency degree with its corresponding ranking outcomes of individual decision makers. An empirical study on the green bus fuel technology selection problem is used to illustrate how the approach works. The approach is applicable to large-scale group multicriteria decision problems where inconsistent ranking outcomes often exist between different fuzzy MCDM methods.     

Extension of the ELECTRE method based on interval-valued fuzzy sets

Decision-making is the process of finding the best option among the feasible alternatives. In classical multiple criteria decision-making (MCDM) methods, the ratings and the weights of the criteria are known precisely. However, if decision makers cannot reach an agreement on the method of defining linguistic variables based on the fuzzy sets, the interval-valued fuzzy set theory can provide a more accurate modeling. In this paper, the interval-valued fuzzy ELECTRE method is presented aiming at solving MCDM problems in which the weights of criteria are unequal, using interval-valued fuzzy set concepts. For the purpose of proving the validity of the proposed model, we present a numerical example and build a practical maintenance strategy selection problem.     

Parting curve selection and evaluation using an extension of fuzzy MCDM approach

Parting curve selection and evaluation plays an important role in mold design. Multiple criteria decision-making (MCDM) is an effective tool for evaluating and ranking problems involving multiple criteria. In order to select suitable parting curve, several criteria need to be taken into account. Therefore, this paper proposes an extension of fuzzy MCDM approach to solve parting curve selection problem. In the proposed model, the ratings of alternatives and importance weights of criteria for parting curve selection are expressed in linguistic terms. The membership functions of the final fuzzy evaluation value in the proposed model are developed based on the linguistic expressions. To make the procedure easier and more practical, the normalized weighted ratings are defuzzified into crisp values by using a new maximizing set and minimizing set ranking approach to determine the ranking order of alternatives. An example of parting curve evaluation and selection is given. The results show that the proposed approach is very effective in selecting the optimal parting curve for the molded part. Finally, this paper compares the proposed approach with another fuzzy MCDM approach to demonstrate its advantages and applicability.     

A combined fuzzy approach to determine the best region for a nuclear power plant in Turkey

When increase in energy needs of developing countries cannot be met by conventional energy sources, alternative energy sources are considered to substitute them. Nuclear energy that meets the needs of a greater proportion of energy demands for countries is one of effective alternative energy types. In this context, after deciding on the use of nuclear energy, the selection of the most suitable location for the production of nuclear power is one of the important decision making problems. In this paper, we performed a facility location selection model for Turkey in meeting the needs of energy with using new and unused source of nuclear energy. For this aim, a combined fuzzy multi criteria decision making (MCDM) methodology that consists of Interval type-2 fuzzy analytical hierarchy process (AHP) that is applied to determine weights of criteria and interval type-2 fuzzy TOPSIS that is applied for ranking alternatives is used to determine the best location alternative for the nuclear power plant. By the way, the obtained results have been analyzed depending upon the criteria that used for the evaluation process. The obtained results are compared with existing nuclear power plants location selection policy for Turkey and some suggestions have been made for the plants where would be the located are not decided. By the way, a sensitivity analysis has been conducted to analyze effects of changes in decision's parameters.     

An analytical solution to fuzzy TOPSIS and its application in personnel selection for knowledge-intensive enterprise

Personnel selection is a critical enterprise strategic problem in knowledge-intensive enterprise. Fuzzy number which can be described as triangular (trapezoid) fuzzy number is an adequate way to assess the evaluation and weights for the alternatives. In that case, fuzzy TOPSIS, as a classic fuzzy multiple criteria decision making (MCDM) methods, has been applied in personnel selection problems. Currently, all the researches on this topic either apply crisp relative closeness but causing information loss, or employ fuzzy relative closeness estimate but with complicated computation to rank the alternatives. In this paper, based on Karnik–Mendel (KM) algorithm, we propose an analytical solution to fuzzy TOPSIS method. Some properties are discussed, and the computation procedure for the proposed analytical solution is given as well. Compared with the existing TOPSIS method for personnel selection problem, it obtains accurate fuzzy relative closeness instead of the crisp point or approximate fuzzy relative closeness estimate. It can both avoid information loss and keep computational efficiency in some extent. Moreover, the global picture of fuzzy relative closeness provides a way to further discuss the inner properties of fuzzy TOPSIS method. Detailed comparisons with approximate fuzzy relative closeness method are provided in personnel selection application.     

Combining fuzzy weight average with fuzzy inference system for material substitution selection in electric industry

Material selection is a very important issue for an electronics company as it includes many qualitative or quantification factors. The material selection problem is associated with design and manufacturing problems which have been widely investigated. This study develops a hybrid fuzzy decision-making model which combines the fuzzy weight average (FWA) with the fuzzy inference system (FIS) for material substitution selection in the electronics industry. FWA is employed to select a substitute material in an uncertain environment, while FIS is used for reasoning purposes. FWA with α-cuts arithmetic (FWA_α-cut) is a popularly technology in decision-making problems. However, FWA_α-cut may result in the following unanticipated situations: (1) unclear decision situations; (2) undecided results expressed by fuzzy membership functions; and (3) high computational complexity. Therefore, a fuzzy weight average with the weakest t-norm (FWA_Tω) is designed as an alternative method for group decision making. In contrast to traditional FWA methods, FWA_Tω obtains more visible fuzzy results for decision makers with lower computational complexity, and can provide exacter estimation by the weakest t-norm operations in uncertain environment. Thus, the proposed hybrid fuzzy decision-making model imitates an expert’s experiences and can estimate substitution purchasing in various statuses. A real material substitution selection case is employed to examine the feasibility of the proposed model; experimental results reveal that the proposed model performs better than the traditional FWA model in coping with material substitution selection problems.     

Multi-criteria decision-making using interval-valued hesitant fuzzy QUALIFLEX methods based on a likelihood-based comparison approach

QUALIFLEX is a very efficient outranking method to handle multi-criteria decision-making (MCDM) involving cardinal and ordinal preference information. Based on a likelihood-based comparison approach, this paper develops two interval-valued hesitant fuzzy QUALIFLEX outranking methods to handle MCDM problems within the interval-valued hesitant fuzzy context. First, we define the likelihoods of interval-valued hesitant fuzzy preference relations that compare two interval-valued hesitant fuzzy elements (IVHFEs). Then, we propose the concepts of the concordance/discordance index, the weighted concordance/discordance index and the comprehensive concordance/discordance index. Moreover, an interval-valued hesitant fuzzy QUALIFLEX model is developed to solve MCDM problems where the evaluative ratings of the alternatives and the weights of the criteria take the form of IVHFEs. Additionally, this paper propounds another likelihood-based interval-valued hesitant fuzzy QUALIFLEX method to accommodate the IVHFEs’ evaluative ratings of alternatives and non-fuzzy criterion weights with incomplete information. Finally, a numerical example concerning the selection of green suppliers is provided to demonstrate the practicability of the proposed methods, and a comparison analysis is given to illustrate the advantages of the proposed methods.

     

Soft computing based on interval valued fuzzy ANP-A novel methodology

Analytic Network Process (ANP) is the multi-criteria decision making (MCDM) tool which takes into account such a complex relationship among parameters. In this paper, we develop the interval-valued fuzzy ANP (IVF-ANP) to solve MCDM problems since it allows interdependent influences specified in the model and generalizes on the supermatrix approach. Furthermore, performance rating values as well as the weights of criteria are linguistics terms which can be expressed in IVF numbers (IVFN). Moreover, we present a novel methodology proposed for solving MCDM problems. In proposed methodology by applying IVF-ANP method determined weights of criteria. Then, we appraise the performance of alternatives against criteria via linguistic variables which are expressed as triangular interval-valued fuzzy numbers. Afterward, by utilizing IVF-weights which are obtained from IVF-ANP and applying IVF-TOPSIS and IVF-VIKOR methods achieve final rank for alternatives. Additionally, to demonstrate the procedural implementation of the proposed model and its effectiveness, we apply it on a case study regarding to assessment the performance of property responsibility insurance companies.     

A note on “Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets”

In a recent paper in this journal, Ashtiani et al. [1] proposed a fuzzy TOPSIS method based on interval-valued fuzzy sets. They changed the information of example that expressed by Chen [2] for the purpose of adjustment with their method and applied their method for solving the changed example. When we investigated their method, we found that Although, Ashtiani et al.’s method is really interesting, but applying it for some fuzzy MCDM problems leads to the incorrect solution and results. In other words, Ashtiani et al.’s method is not applicable to some fuzzy MCDM problems. In this paper we try to eliminate this problem.     

A fuzzy VIKOR method for supplier selection based on entropy measure for objective weighting

Recently, resolving the problem of evaluation and ranking the potential suppliers has become as a key strategic factor for business firms. With the development of intelligent and automated information systems in the information era, the need for more efficient decision making methods is growing. The VIKOR method was developed to solve multiple criteria decision making (MCDM) problems with conflicting and non-commensurable criteria assuming that compromising is acceptable to resolve conflicts. On the other side objective weights based on Shannon entropy concept could be used to regulate subjective weights assigned by decision makers or even taking into account the end-users’ opinions. In this paper, we treat supplier selection as a group multiple criteria decision making (GMCDM) problem and obtain decision makers’ opinions in the form of linguistic terms. Then, these linguistic terms are converted to trapezoidal fuzzy numbers. We extended the VIKOR method with a mechanism to extract and deploy objective weights based on Shannon entropy concept. The final result is obtained through next steps based on factors R, S and Q. A numerical example is proposed to illustrate an application of the proposed method.     

Vendor selection by integrated fuzzy MCDM techniques with independent and interdependent relationships

Vendor selection is an evaluation process that is based on many criteria that uses inaccurate or uncertain data. But while the criteria are often numerous and the relationships between higher-level criteria and lower-level sub-criteria are complex, most conventional decision models cannot help us clarify the interrelationships among the sub-criteria. Our proposed integrated fuzzy multiple criteria decision making (MCDM) method addresses this issue within the context of the vendor selection problem. First, we use triangular fuzzy numbers to express the subjective preferences of evaluators. Second, we use interpretive structural modeling (ISM) to map out the relationships among the sub-criteria. Third, we use the fuzzy analytical hierarchy process (AHP) method to compute the relative weights for each criterion, and we use non-additive fuzzy integral to obtain the fuzzy synthetic performance of each common criterion. Fourth, the best vendor is determined according to the overall aggregating score of each vendor using the fuzzy weights with fuzzy synthetic utilities. Fifth, we use an empirical example to show that our proposed method is preferred to the traditional method, especially when the sub-criteria are interdependent. Finally, our results provide valuable suggestions to vendors on how to improve each sub-criterion so that they can bridge the gap between actual and aspired performance values in the future.     

Weapon selection using the AHP and TOPSIS methods under fuzzy environment

The weapon selection problem is a strategic issue and has a significant impact on the efficiency of defense systems. On the other hand, selecting the optimal weapon among many alternatives is a multi-criteria decision-making (MCDM) problem. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and the technique for order performance by similarity to ideal solution (TOPSIS), to help the actors in defence industries for the selection of optimal weapon in a fuzzy environment where the vagueness and subjectivity are handled with linguistic values parameterized by triangular fuzzy numbers. The AHP is used to analyze the structure of the weapon selection problem and to determine weights of the criteria, and fuzzy TOPSIS method is used to obtain final ranking. A real world application is conducted to illustrate the utilization of the model for the weapon selection problem. The application could be interpreted as demonstrating the effectiveness and feasibility of the proposed model.     

An integrated supplier selection methodology incorporating QFD and DEA with imprecise data

Supplier evaluation and selection is an important group decision making problem that involves not only quantitative criteria but also qualitative factors incorporating vagueness and imprecision. This paper proposes a novel fuzzy multi-criteria group decision making framework for supplier selection integrating quality function deployment (QFD) and data envelopment analysis (DEA). The proposed methodology allows for considering the impacts of inner dependence among supplier assessment criteria through constructing a house of quality (HOQ). The lower and upper bounds of the weights of supplier assessment criteria are identified by adopting fuzzy weighted average (FWA) method that enables the fusion of imprecise and subjective information expressed as linguistic variables. An imprecise DEA methodology is implemented for supplier selection, which employs the weights of supplier assessment criteria computed by FWA utilizing the data from the HOQ and the supplier ratings with respect to supplier assessment criteria. The application of the proposed framework is demonstrated through a case study in a private hospital in Istanbul.     

A consensus based group decision making methodology for strategic selection problems of supply chain coordination

In a supply chain (SC), the partners often make collective decisions to solve a number of problems which are characterized by various quantitative and qualitative criteria. This article presents a fuzzy TOPSIS and soft consensus based group decision making methodology to solve the multi-criteria decision making (MCDM) problems in supply chain coordination, i.e., selection problems. This methodology is proposed to improve the coordination in decentralized supply chains, i.e., supply chains that comprise several independent, legally separated entities with their own decision authorities. In order to address the imprecision of supply chain partners in formulating the preference value of various criteria, a fuzzy TOPSIS based methodology is proposed. Moreover, a soft consensus based group decision making approach is used for consensus forming among the supply chain partners, regarding the preference values of various criteria for different alternatives. Correlation coefficient and standard deviation (CCSD) based objective weight determination method is also used for enumeration of the weights of the criterion for fuzzy TOPSIS. To demonstrate the applicability of proposed methodology, an illustrative example has been presented.     

Trapezoidal fuzzy multi-number and its application to multi-criteria decision-making problems

In this paper, the concept of trapezoidal fuzzy multi-number (TFM-number) is proposed and some desired operational laws with properties are introduced. In the TFM-number, the occurrences are more than one with the possibility of the same or the different membership functions and the TFM-number is an extension of both fuzzy number set and fuzzy set, allowing the repeated occurrences of any element. Also, aim of this paper is to investigate a multiple criteria decision-making (MCDM) method under TFM-number environment. To construct this method, we first introduce some operational laws on TFM-number based on t-norm and s-norm. Then, TFM-number arithmetic and geometric operators are proposed. Finally, we develop an MCDM method and apply to an MCDM problem to verify the introduced decision-making methods.