Multicriteria Decision Making with Cognitive Limitations: A DS/AHP‐Based Approach

In real life, sometimes multicriteria decision making (MCDM) problems are dealt with inevitably under cognitive limitations of human's minds. However, few existing models can directly solve MCDM problems of this kind. Thus, to address the issue, this paper proposes a novel approach, which can: (i) handle the cognitive limitations in MCDM problems by distinguishing the case of complete criteria (i.e., there are no hidden cognitive factors that can deviate rational decisions) from the case of incomplete criteria (i.e., there are some hidden cognitive factors that can deviate rational decisions); (ii) differentiate incomplete and complete relative ranking of the groups of decision alternatives (DAs) over a criterion; and (iii) solve the imprecise and uncertain evaluation of criterion weight as well as the ambiguous evaluations of the groups of DAs regarding a given criterion. Hence, we give a measure to consider the influence of cognitive limitations and give two methods to reduce the influence of cognitive limitations when a decision making needs more rational. Moreover, we illustrate our approach by solving a real‐life problem of estate investment. Finally, we give some experimental results about the reduction of the required number of knowledge judgments in our method compared with the previous methods.     

Hybrid MCDM based methodology for selecting the optimum maintenance strategy for ship machinery systems

The key to achieving optimum ship system reliability and safety is to have a sound maintenance management system in place for mitigating or eliminating equipment/component failures. Maintenance has three key elements; risk assessment, maintenance strategy selection and the process of determining the optimal interval for the maintenance task. The optimisation of these three main elements of maintenance is what constitute a sound maintenance management system. One of the challenges that marine maintenance practitioners are faced with is the problem of maintenance selection for each equipment item of the ship machinery system. The decision making process involves utilising different conflicting decision criteria in selecting the optimum maintenance strategy from among multiple maintenance alternatives. In tackling such decision making problems the application of a multi-criteria decision making (MCDM) method is appropriate. Hence in this paper two hybrid MCDM methods; Delphi-AHP and Delphi-AHP-PROMETHEE, are presented for the selection of appropriate maintenance strategies for ship machinery systems and other related ship systems. A case study of a ship machinery system maintenance strategy selection problem is used to demonstrate the suitability of the proposed methods.     

Data transformation in the evidential reasoning-based decision making process

This paper describes the application of an evidential reasoning (ER)‐based decision making process to multiple‐criteria decision making (MCDM) problems having both quantitative and qualitative criteria. The ER approach is based on the decision theory and the theory of evidence and it uses the concept of ‘degree of belief’ to assess decision alternatives on each attribute. When faced with MCDM problems, evaluation and selection or ranking of alternatives appear to be both challenging and vital to arrive at a rational and robust decision. In the presence of both qualitative and quantitative evaluations in an MCDM problem, it is necessary, when using the ER‐based decision making process, to transform or convert quantitative data into a belief structure using a number of grades so that the converted belief structure and the original quantitative data are equivalent in values or utilities. This paper suggests three scenarios for data transformation and examines how the ranking of decision alternatives is changed when different scenarios of data transformation are used. Ranking of UK universities using the ER approach is illustrated as an example.     

Proposing a new integrated model based on sustainability balanced scorecard (SBSC) and MCDM approaches by using linguistic variables for the performance evaluation of oil producing companies

Using the balanced scorecard approach based on sustainable development parameters is a powerful and useful methodology to evaluate the sustainable performance of organization or company. In this paper, a new approach based on sustainability balanced scorecard (SBSC) and multi criteria decision making (MCDM) approaches is developed for evaluating the performance of oil producing companies in Iran. For reflecting the interdependent relationships among factors influencing the problem under consideration, analytical network process (ANP), a branch of the MCDM techniques, is employed. However, using the ANP method for calculating the preference ratings of alternatives is a time-consuming and bothersome process; therefore, COPRAS (COmplex PRoportional ASsessment) technique is adopted to prioritize the feasible alternatives in terms of linguistic variables. Based on this study, the results demonstrate the effectiveness of the proposed model. The performance evaluation model proposed by using a combination of the MCDM methods and the SBSC approach helps authorities to make an attempt for achieving a competitive advantage.     

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 Model for Decision Making with Missing,Imprecise, and Uncertain Evaluations of Multiple Criteria

In real‐life multicriteria decision making (MCDM) problems, the evaluations against some criteria are often missing, inaccurate, and even uncertain, but the existing theories and models cannot handle such evaluations well. To address the issue, this paper extends the Dempster–Shafer (DS)/analytic hierarchy process (DS/AHP) approach of MCDM to handle three types of ambiguous evaluations: missing, interval‐valued, and ambiguous lottery evaluations. In our extension, the aggregation of criteria's evaluation takes the following six steps: (i) calculate the expected evaluation interval and the ambiguity degree of each group of decision alternatives regarding each criterion, (ii) from them to obtain the preference degree of each group of decision alternatives, (iii) apply the DS/AHP method to obtain the mass function distribution of each group of decision alternatives, (iv) use the Dempster's rule of combination to get the overall mass function of each group of decision alternatives with respect to all criteria, (v) according to the overall mass function to count the belief function and the plausibility function of each decision alternative, and (vi) set the overall preference ordering of decision alternatives by our regret‐avoid ambiguous principle and then find the optimal solution. Finally, we give an example of real estate investment to illustrate how our approach is employed to deal with real‐life MCDM problems.     

Combining prospect theory and fuzzy numbers to multi-criteria decision making

Many multi-criteria decision making (MCDM) methods have been proposed to handle uncertain decision making problems. Most of them are based on fuzzy numbers and they are not able to cope with risk in decision making. In recent years, some MCDM methods based on prospect theory to handle risk MCDM problems have been developed. In this paper, we propose a hybrid approach combining prospect theory and fuzzy numbers to handle risk and uncertainty in MCDM problems. So, it is possible to tackle more challenging MCDM problems. A case study involving oil spill in the sea illustrates the application of the novel method.     

Prioritized multi-criteria decision making based on preference relations

There may exist priority relationships among criteria in multi-criteria decision making (MCDM) problems. This kind of problems, which we focus on in this paper, are called prioritized MCDM ones. In order to aggregate the evaluation values of criteria for an alternative, we first develop some weighted prioritized aggregation operators based on triangular norms (t-norms) together with the weights of criteria by extending the prioritized aggregation operators proposed by Yager (Yager, R. R. (2004). Modeling prioritized multi-criteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 34, 2396–2404). After discussing the influence of the concentration degrees of the evaluation values with respect to each criterion to the priority relationships, we further develop a method for handling the prioritized MCDM problems. Through a simple example, we validate that this method can be used in more wide situations than the existing prioritized MCDM methods. At length, the relationships between the weights associated with criteria and the preference relations among alternatives are explored, and then two quadratic programming models for determining weights based on multiplicative and fuzzy preference relations are developed.     

Finding the numerical compensation in multiple criteria decision-making problems under fuzzy environment

In this paper, we have developed a methodology to derive the level of compensation numerically in multiple criteria decision-making (MCDM) problems under fuzzy environment. The degree of compensation is dependent on the tranquility and anxiety level experienced by the decision-maker while taking the decision. Higher tranquility leads to the higher realisation of the compensation whereas the increased level of anxiety reduces the amount of compensation in the decision process. This work determines the level of tranquility (or anxiety) using the concept of fuzzy sets and its various level sets. The concepts of indexing of fuzzy numbers, the risk barriers and the tranquility level of the decision-maker are used to derive his/her risk prone or risk averse attitude of decision-maker in each criterion. The aggregation of the risk levels in each criterion gives us the amount of compensation in the entire MCDM problem. Inclusion of the compensation leads us to model the MCDM problem as binary integer programming problem (BIP). The solution to BIP gives us the compensatory decision to MCDM. The proposed methodology is illustrated through a numerical example.     

Microcomputer based multiple criteria decision support system for strategic planning

There are two major approaches currently used for developing Decision support Systems (DSS) for strategic planning, especially in the objective formulation stage. Several mathematical models have been developed to abstract the decision situation. However, they do not take into account either behavioral aspects of decision making or the presence of multiple and conflicting objectives. A second approach is to consider the several qualitative factors that go into decision making; such considerations are normally situation-dependent and hence it is difficult to provide a system for general managerial situations.The Multiple Criteria Decision Making (MCDM) approach combines the advantages of both the approaches and, therefore, is an excellent alternative for designing DSS. This paper develops an MCDM approach to strategic planning. The model is applied to such a problem in a simulated environment and the problem is solved interactively. Our experience shows that the proposed methodology is a viable approach for solving practical decision problems in strategic planning.     

Pythagorean fuzzy TODIM approach to multi-criteria decision making

Recently, the TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach, which can characterize the decision makers’ psychological behaviours under risk, has been introduced to handle multi-criteria decision making (MCDM) problems. Moreover, Pythagorean fuzzy set is an effective tool for depicting uncertainty of the MCDM problems. In this paper, based on the prospect theory, we first extend the TODIM approach to solve the MCDM problems with Pythagorean fuzzy information. Then, we conduct simulation tests to analyze how the risk attitudes of the decision makers exert the influence on the results of MCDM under uncertainty. Finally, a case study on selecting the governor of Asian Infrastructure Investment Bank is made to show the applicability of the proposed approach.     

A model based on 2-tuple fuzzy linguistic representation and Analytic Hierarchy Process for supplier segmentation using qualitative and quantitative criteria

The literature on supply base segmentation has increasingly adopted multi-criteria decision making (MCDM) techniques into recently proposed models. However, most proposals segment the supply base from the standpoint of the purchased item, which prevents them from providing guidelines that are specific to each supplier. Some authors have attempted to overcome these limitations by putting forward portfolio models based on the relationship with suppliers. These approaches use fuzzy variables and MCDM methods that take qualitative judgements by experts as the only input for decision making. However, many companies have databases with historical data about the performance of past transactions with suppliers that should be considered by expert systems that aim to comprehensively evaluate suppliers’ performance. This paper seeks to address this gap by proposing a segmentation model based on the relationship with suppliers capable of aggregating quantitative and qualitative criteria. Analytic Hierarchy Process (AHP) was used to determine the relative importance of each criteria. Fuzzy 2-tuple, a prominent computing with word (CWW) approach, was used to evaluate suppliers with a mixture of historical quantitative data and qualitative judgements by purchasing experts. An illustrative application of the proposed model was carried out in the pharmaceutical supply center (PSC) of a teaching hospital. The proposed model can be viewed as a decision support system capable of aggregating the qualitative judgements of experts and quantitative historical performance measures, thus providing guidelines to improve the relationship between suppliers and the buyer firm.     

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.     

An extended GRA method for MCDM with interval-valued triangular fuzzy assessments and unknown weights

Multiple criteria decision making (MCDM) is the process of ranking the feasible alternatives and selecting the best one by considering multiple criteria. Owing to the complexity, fuzziness and uncertainties of the objective things, the criterion values often take the form of linguistic variables, which can be expressed in interval-valued triangular fuzzy numbers. The purpose of this paper is to develop an extended grey relational analysis (GRA) method for solving MCDM problems with interval-valued triangular fuzzy numbers and unknown information on criterion weights. In order to determine the criterion weights, some optimization models based on the basic idea of traditional GRA method are established. Then, calculation steps of extended GRA method for MCDM are given. Finally, a numerical example is shown to verify the developed method and to demonstrate its practicality and feasibility.     

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.     

Discriminative aggregation operators for multi criteria decision making

A general aggregation formalism for multi criteria decision making (MCDM) applications is presented. Using this formalism, we derive the existing aggregation operators, and also develop some new ones. The proposed general formalism is further extended to develop discriminative class of aggregation operators for aiding MCDM. The proposed discriminative aggregation operators are based on the consideration of the variability in the various evaluations of a criterion. Four families of discriminative aggregation operators are developed using the extended formalism. These operators and applied in a managerial real world case-study.     

Determining of stock investments with grey relational analysis

Selecting stock is important problem for investors. Investors can use related financial ratios in stock selection. These kind of worthy financial ratios can be obtained from financial statements. The investors can use these ratios as criteria while they are selecting the stocks. Since dealing with more than one financial ratio, the investing issue becomes multi-criteria decision making (MCDM) problem for the investors. There are various techniques for solving MCDM problems in literature. In this study grey relational analysis (GRA) is used for ordering some financial firms’ stocks which are in Financial Sector Index of Istanbul Stock Exchange (ISE). Besides, because of the importance of criteria weights in decision making, three different approaches – heuristic, Analytic Hierarchy Process, learning via sample – were experimented to find best values of criteria weights in GRA process.     

TOPSIS with fuzzy belief structure for group belief multiple criteria decision making

TOPSIS is one of the major techniques in dealing with multiple criteria decision making (MCDM) problems, and Belief Structure (BS) model and Fuzzy BS model have been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with Fuzzy BS model is proposed to solve Group Belief MCDM problems. Firstly, the Group Belief MCDM problem is structured as a fuzzy belief decision matrix in which the judgments of each decision maker are described as Fuzzy BS models, and then the Evidential Reasoning approach is used for aggregating the multiple decision makers’ judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. In order to measure the separation from the ideal belief solutions, the concept and algorithm of Belief Distance Measure are introduced to compare the difference between Fuzzy BS models. Using the Belief Distance Measure, the relative closeness and ranking index can be calculated for ranking the alternatives. A numerical example is finally given to illustrate the proposed method.     

Developing a fuzzy TOPSIS approach based on subjective weights and objective weights

Multiple criteria decision making (MCDM) is widely used in ranking one or more alternatives from a set of available alternatives with respect to multiple criteria. Inspired by MCDM to systematically evaluate alternatives under various criteria, we propose a new fuzzy TOPSIS for evaluating alternatives by integrating using subjective and objective weights. Most MCDM approaches consider only decision maker’s subjective weights. However, the end-user attitude can be a key factor. We propose a novel approach that involves end-user into the whole decision making process. In this proposed approach, the subjective weights assigned by decision makers (DM) are normalized into a comparable scale. In addition, we also adopt end-user ratings as an objective weight based on Shannon’s entropy theory. A closeness coefficient is defined to determine the ranking order of alternatives by calculating the distances to both ideal and negative-ideal solutions. A case study is performed showing how the propose method can be used for a software outsourcing problem. With our method, we provide decision makers more information to make more subtle decisions.     

TOPSIS with belief structure for group belief multiple criteria decision making

The technique for order performance by similarity to ideal solution(TOPSIS)is one of the major techniques in dealing with multiple criteria decision making(MCDM)problems, and the belief structure(BS)model has been used successfully for uncertain MCDM with incompleteness, impreciseness or ignorance. In this paper, the TOPSIS method with BS model is proposed to solve group belief MCDM problems. Firstly, the group belief MCDM problem is structured as a belief decision matrix in which the judgments of each decision maker are described as BS models, and then the evidential reasoning approach is used for aggregating the multiple decision makers' judgments. Subsequently, the positive and negative ideal belief solutions are defined with the principle of TOPSIS. To measure the separation from ideal solutions, the concept and algorithm of belief distance measure are defined, which can be used for comparing the difference between BS models. Finally, the relative closeness and ranking index are calculated for ranking the alternatives. A numerical example is given to illustrate the proposed method.