Trapezoidal Intuitionistic Fuzzy Multiattribute Decision Making Method Based on Cumulative Prospect Theory and Dempster-Shafer Theory

With respect to decision making problems under uncertainty, a trapezoidal intuitionistic fuzzy multiattribute decision making method based on cumulative prospect theory and Dempster-Shafer theory is developed. The proposed method reflects behavioral characteristics of decision makers, information fuzziness under uncertainty, and uncertain attribute weight information. Firstly, distance measurement and comparison rule of trapezoidal intuitionistic fuzzy numbers are used to derive value function under trapezoidal intuitionistic fuzzy environment. Secondly, the value function and decision weight function are used to calculate prospect values of attributes for each alternative. Then considering uncertain attribute weight information, Dempster-Shafer theory is used to aggregate prospect values for each alternative, and overall prospect values are obtained and thus the alternatives are sorted consequently. Finally, an illustrative example shows the feasibility of the proposed method

Risky multi-criteria group decision making on green capacity investment projects based on supply chain

Green capacity investment projects have rapidly emerged involving suppliers, customers, and manufacturing organizations in supply chain systems with environmental challenges. This paper focuses on and identifies both primary strategic and operational elements that will aid managers in evaluating and making risky multi-criteria decisions on green capacity investment projects. We propose a cloud prospect value consensus process consisting of feedback and adjustment mechanisms that provide modification instructions to the corresponding decision makers for a decision matrix based on the cloud model and prospect theory, which considers psychological behavior, disagreements between decision makers, and the ambiguity of linguistic variable assessment across multi-criteria risks. The new model increases the efficiency and accuracy of decision making. To verify the feasibility and validity of the Cloud Prospect Value Consensus Degree based on the Feedback adjustment mechanism, its performance is compared with three state-of-the-art multi-criteria group decision-making methods

Simplified models for multi-criteria decision analysis under uncertainty

Includes abstract.Includes bibliographical references.When facilitating decisions in which some performance evaluations are uncertain, a decision must be taken about how this uncertainty is to be modelled. This involves, in part, choosing an uncertainty format {a way of representing the possible outcomes that may occur. It seems reasonable to suggest {and is an aim of the thesis to show {that the choice of how uncertain quantities are represented will exert some influence over the decision-making process and the final decision taken. Many models exist for multi-criteria decision analysis (MCDA) under conditions of uncertainty; perhaps the most well-known are those based on multi-attribute utility theory [MAUT, e.g. 147], which uses probability distributions to represent uncertainty. The great strength of MAUT is its axiomatic foundation, but even in its simplest form its practical implementation is formidable, and although there are several practical applications of MAUT reported in the literature [e.g. 39, 270] the number is small relative to its theoretical standing. Practical applications often use simpler decision models to aid decision making under uncertainty, based on uncertainty formats that `simplify' the full probability distributions (e.g. using expected values, variances, quantiles, etc). The aim of this thesis is to identify decision models associated with these `simplified' uncertainty formats and to evaluate the potential usefulness of these models as decision aids for problems involving uncertainty. It is hoped that doing so provides some guidance to practitioners about the types of models that may be used for uncertain decision making. The performance of simplified models is evaluated using three distinct methodological approaches {computer simulation, `laboratory' choice experiments, and real-world applications of decision analysis {in the hope of providing an integrated assessment. Chapter 3 generates a number of hypothetical decision problems by simulation, and within each problem simulates the hypothetical application of MAUT and various simplified decision models. The findings allow one to assess how the simplification of MAUT models might impact results, but do not provide any general conclusions because they are based on hypothetical decision problems and cannot evaluate practical issues like ease-of-use or the ability to generate insight that are critical to good decision aid. Chapter 4 addresses some of these limitations by reporting an experimental study consisting of choice tasks presented to numerate but unfacilitated participants. Tasks involved subjects selecting one from a set of five alternatives with uncertain attribute evaluations, with the format used to represent uncertainty and the number of objectives for the choice varied as part of the experimental design. The study is limited by the focus on descriptive rather than real prescriptive decision making, but has implications for prescriptive decision making practice in that natural tendencies are identified which may need to be overcome in the course of a prescriptive analysis

Analysis of Decision Support Systems of Industrial Relevance: Application Potential of Fuzzy and Grey Set Theories

The present work articulates few case empirical studies on decision making in industrial context. Development of variety of Decision Support System (DSS) under uncertainty and vague information is attempted herein. The study emphases on five important decision making domains where effective decision making may surely enhance overall performance of the organization. The focused territories of this work are i) robot selection, ii) g-resilient supplier selection, iii) third party logistics (3PL) service provider selection, iv) assessment of supply chain’s g-resilient index and v) risk assessment in e-commerce exercises. Firstly, decision support systems in relation to robot selection are conceptualized through adaptation to fuzzy set theory in integration with TODIM and PROMETHEE approach, Grey set theory is also found useful in this regard; and is combined with TODIM approach to identify the best robot alternative. In this work, an attempt is also made to tackle subjective (qualitative) and objective (quantitative) evaluation information simultaneously, towards effective decision making. Supplier selection is a key strategic concern for the large-scale organizations. In view of this, a novel decision support framework is proposed to address g-resilient (green and resilient) supplier selection issues. Green capability of suppliers’ ensures the pollution free operation; while, resiliency deals with unexpected system disruptions. A comparative analysis of the results is also carried out by applying well-known decision making approaches like Fuzzy- TOPSIS and Fuzzy-VIKOR. In relation to 3PL service provider selection, this dissertation proposes a novel ‘Dominance- Based’ model in combination with grey set theory to deal with 3PL provider selection, considering linguistic preferences of the Decision-Makers (DMs). An empirical case study is articulated to demonstrate application potential of the proposed model. The results, obtained thereof, have been compared to that of grey-TOPSIS approach. Another part of this dissertation is to provide an integrated framework in order to assess gresilient (ecosilient) performance of the supply chain of a case automotive company. The overall g-resilient supply chain performance is determined by computing a unique ecosilient (g-resilient) index. The concepts of Fuzzy Performance Importance Index (FPII) along with Degree of Similarity (DOS) (obtained from fuzzy set theory) are applied to rank different gresilient criteria in accordance to their current status of performance. The study is further extended to analyze, and thereby, to mitigate various risk factors (risk sources) involved in e-commerce exercises. A total forty eight major e-commerce risks are recognized and evaluated in a decision making perspective by utilizing the knowledge acquired from the fuzzy set theory. Risk is evaluated as a product of two risk quantifying parameters viz. (i) Likelihood of occurrence and, (ii) Impact. Aforesaid two risk quantifying parameters are assessed in a subjective manner (linguistic human judgment), rather than exploring probabilistic approach of risk analysis. The ‘crisp risk extent’ corresponding to various risk factors are figured out through the proposed fuzzy risk analysis approach. The risk factor possessing high ‘crisp risk extent’ score is said be more critical for the current problem context (toward e-commerce success). Risks are now categorized into different levels of severity (adverse consequences) (i.e. negligible, minor, marginal, critical and catastrophic). Amongst forty eight risk sources, top five risk sources which are supposed to adversely affect the company’s e-commerce performance are recognized through such categorization. The overall risk extent is determined by aggregating individual risks (under ‘critical’ level of severity) using Fuzzy Inference System (FIS). Interpretive Structural Modeling (ISM) is then used to obtain structural relationship amongst aforementioned five risk sources. An appropriate action requirement plan is also suggested, to control and minimize risks associated with e-commerce exercises

Decision support for selecting a shortlist of electricity-saving options: a modified SMAA approach

This paper describes an application providing decision support for generating a shortlist of promising electricity-saving options for households in South Africa. The decision problem is characterised by constraints on time and other resources, and by substantial uncertainty around the preferences for energy-related attributes and the performance of alternatives on those attributes. We use a stochastic multi-criteria acceptability analysis model to incorporate preferential uncertainties, and adapt this for use with quantiles and other "simplified" formats for representing uncertain attribute evaluations

Interval Type-2 Fuzzy Programming Method for Risky Multicriteria Decision-Making with Heterogeneous Relationship

We propose a new interval type-2 fuzzy (IT2F) programming method for risky multicriteria decision-making (MCDM) problems with IT2F truth degrees, where the criteria exhibit a heterogeneous relationship and decision-makers behave according to bounded rationality. First, we develop a technique to calculate the Banzhaf-based overall perceived utility values of alternatives based on 2-additive fuzzy measures and regret theory. Subsequently, considering pairwise comparisons of alternatives with IT2F truth degrees, we define the Banzhaf-based IT2F risky consistency index (BIT2FRCI) and the Banzhaf-based IT2F risky inconsistency index (BIT2FRII). Next, to identify the optimal weights, an IT2F programming model is established based on the concept that BIT2FRII must be minimized and must not exceed the BIT2FRCI using a fixed IT2F set. Furthermore, we design an effective algorithm using an external archive-based constrained state transition algorithm to solve the established model. Accordingly, the ranking order of alternatives is derived using the Banzhaf-based overall perceived utility values. Experimental studies pertaining to investment selection problems demonstrate the state-of-the-art performance of the proposed method, that is, its strong capability in addressing risky MCDM problems

A novel TODIM based on prospect theory to select green supplier with q-rung orthopair fuzzy set

The authors would like to acknowledge the financial support by the Fundamental Research Funds for the Central Universities (#JBK2001043, and #JBK190969), the FEDER funds provided in the National Spanish project PID2019-103880RB-I00 and also it has been partially supported by grant from the National Natural Science Foundation of China (#71910107002).Green supply chain has developed rapidly due to the advocacy of ecological civilization, and choosing a proper green supplier is a crucial issue. Considering the fuzziness of evaluation information and the psychological states of decision makers (DMs) in selecting process, a novel TODIM based on prospect theory with q-rung orthopair fuzzy set (q-ROFS) is proposed. The novel TODIM concerns both the perceived transformed probability weighting function and the differences in risk attitudes. A new distance, which concerns the herd mentality, is carried out to measure the perceived difference of the q-ROFS. Besides, a new systematic evaluation index system, named as PCEM (Product, Cooperation ability, Environment, Market), has been established. A case related to pork supplier companies is presented and fully demonstrates the effectiveness of the novel TODIM when compared with the extended one, the intuitionistic fuzzy TODIM, the Pythagorean fuzzy TODIM as well as the TOPSIS with q-ROFS. Finally, a series of comparative analyses illustrate the advantages of the proposed TODIM.Fundamental Research Funds for the Central Universities JBK2001043 JBK190969FEDER funds provided in the National Spanish project PID2019-103880RB-I00National Natural Science Foundation of China (NSFC) 7191010700