A method to multi-attribute decision making with picture fuzzy information based on Muirhead mean

The recently proposed picture fuzzy set (PFS) is a powerful tool for handling fuzziness and uncertainty. PFS is character-ized by a positive membership degree, a neutral membership degree, and a negative membership degree, making it more suitable and useful than the intuitionistic fuzzy set (IFS) when dealing with multi-attribute decision making (MADM). The aim of this paper is to develop some aggregation operators for fusing picture fuzzy information. Considering the Muirhead mean (MM) is an aggregation technology which can consider the interrelationship among all aggregated ar-guments, we extend MM to picture fuzzy context and propose a family of picture fuzzy Muirhead mean operators. In addition, we investigate some properties and special cases of the proposed operators. Further, we develop a novel meth-od to MADM in which the attribute values take the form of picture fuzzy numbers (PFNs). Finally, a numerical example is provided to illustrate the validity of the proposed method

Power of Continuous Triangular Norms with Application to Intuitionistic Fuzzy Information Aggregation

The paper aims to investigate the power operation of continuous triangular norms (t-norms) and develop some intuitionistic fuzzy information aggregation methods. It is proved that a continuous t-norm is power stable if and only if every point is a power stable point, and if and only if it is the minimum t-norm, or it is strict, or it is an ordinal sum of strict t-norms. Moreover, the representation theorem of continuous t-norms is used to obtain the computational formula for the power of continuous t-norms. Based on the power operation of t-norms, four fundamental operations induced by a continuous t-norm for the intuitionistic fuzzy (IF) sets are introduced. Furthermore, various aggregation operators, namely the IF weighted average (IFWA), IF weighted geometric (IFWG), and IF mean weighted average and geometric (IFMWAG) operators, are defined, and their properties are analyzed. Finally, a new decision-making algorithm is designed based on the IFMWAG operator, which can remove the hindrance of indiscernibility on the boundaries of some classical aggregation operators. The practical applicability, comparative analysis, and advantages of the study with other decision-making methods are furnished to ascertain the efficacy of the designed method

Simplified neutrosophic indeterminate decision making method with decision makers’ indeterminate ranges

There exists the indeterminate situations of truth, falsity, indeterminacy degrees due to the uncertainty and inconsistency of decision makers’ arguments in a complicated decision making (DM) problem. Then, existing neutrosophic set cannot describe the indeterminate information of truth, falsity, indeterminacy degrees. It is noted that the simplified neutrosophic set (SNS) is depicted by truth, falsity, indeterminacy degrees, while a neutrosophic number (NN) can be flexibly depicted by its determinate part and its indeterminate part. Regarding the indeterminate situations of truth, falsity, indeterminacy degrees in indeterminate DM problems, this study first presents a simplified neutrosophic indeterminate set (SNIS) to express the hybrid information of SNS and NN and defines the score, accuracy, and certainty functions of simplified neutrosophic indeterminate elements (SNIEs) with indeterminate ranges to compare SNIEs. Then, we introduce a SNIE weighted arithmetic averaging (SNIEWAA) operator and a SNIE weighted geometric averaging (SNIEWGA) operator to aggregate simplified neutrosophic indeterminate information. Next, a multi-attribute DM approach with decision makers’ indeterminate ranges is established regarding the SNIEWAA and SNIEWGA operators in SNIS setting. Finally, the proposed DM approach is applied in a DM example on choosing a suitable slope design scheme to indicate the applicability and suitability of the proposed approach

A group decision-making model for wastewater treatment plans selection based on intuitionistic fuzzy sets

As the need for environmental protection and resource sustainability has increased in recent times, wastewater treatment has become increasingly important. In this paper, a group decision-making model for plans selection in wastewater treatment is proposed. In order to deal with uncertainties and multiple attributes in wastewater treatment, an intuitionistic fuzzy set is employed to evaluate wastewater treatment plans effectively. A distance measure is defined to obtain an objective weight measuring the expert’s judgment. More specifically, experts first use group decision-making on the various plans with an intuitionistic fuzzy set. Meanwhile, Due to the decision-makers psychological behavior, the prospect theory is applied. Next, the various plans are ranked by The Order of Preference by Similarity to Ideal Solution (TOPSIS) method and prospect theory. Finally, an illustrative example of wastewater treatment plans selection is used to verify the proposed model

New Trends in Neutrosophic Theory and Applications Volume II

Neutrosophic set has been derived from a new branch of philosophy, namely Neutrosophy. Neutrosophic set is capable of dealing with uncertainty, indeterminacy and inconsistent information. Neutrosophic set approaches are suitable to modeling problems with uncertainty, indeterminacy and inconsistent information in which human knowledge is necessary, and human evaluation is needed. Neutrosophic set theory was proposed in 1998 by Florentin Smarandache, who also developed the concept of single valued neutrosophic set, oriented towards real world scientific and engineering applications. Since then, the single valued neutrosophic set theory has been extensively studied in books and monographs introducing neutrosophic sets and its applications, by many authors around the world. Also, an international journal - Neutrosophic Sets and Systems started its journey in 2013. Single valued neutrosophic sets have found their way into several hybrid systems, such as neutrosophic soft set, rough neutrosophic set, neutrosophic bipolar set, neutrosophic expert set, rough bipolar neutrosophic set, neutrosophic hesitant fuzzy set, etc. Successful applications of single valued neutrosophic sets have been developed in multiple criteria and multiple attribute decision making. This second volume collects original research and application papers from different perspectives covering different areas of neutrosophic studies, such as decision making, graph theory, image processing, probability theory, topology, and some theoretical papers. This volume contains four sections: DECISION MAKING, NEUTROSOPHIC GRAPH THEORY, IMAGE PROCESSING, ALGEBRA AND OTHER PAPERS. First paper (Pu Ji, Peng-fei Cheng, Hongyu Zhang, Jianqiang Wang. Interval valued neutrosophic Bonferroni mean operators and the application in the selection of renewable energy) aims to construct selection approaches for renewable energy considering the interrelationships among criteria. To do that, Bonferroni mean (BM) and geometric BM (GBM) are employed

Integrated Frameworks for Effective Multi-criteria Decision Making in Reliability Centred Maintenance of Industrial Machines

No abstract availabl

Fuzzy Techniques for Decision Making 2018

Zadeh's fuzzy set theory incorporates the impreciseness of data and evaluations, by imputting the degrees by which each object belongs to a set. Its success fostered theories that codify the subjectivity, uncertainty, imprecision, or roughness of the evaluations. Their rationale is to produce new flexible methodologies in order to model a variety of concrete decision problems more realistically. This Special Issue garners contributions addressing novel tools, techniques and methodologies for decision making (inclusive of both individual and group, single- or multi-criteria decision making) in the context of these theories. It contains 38 research articles that contribute to a variety of setups that combine fuzziness, hesitancy, roughness, covering sets, and linguistic approaches. Their ranges vary from fundamental or technical to applied approaches

A SPHERICAL FUZZY BASED DECISION MAKING FRAMEWORK WITH EINSTEIN AGGREGATION FOR COMPARING PREPAREDNESS OF SMEs IN QUALITY 4.0

Researchers work hard to embrace technological changes and redefine the quality management as Quality 4.0 (Q 4.0). In this context, the purpose of the current work is twofold. First, it aims to compare the preparedness of the small and medium enterprises (SMEs) for sustaining in Q4. Second, it intends to propose a novel hybrid spherical fuzzy based multi-criteria group decision-making (MAGDM) framework with Einstein aggregation (EA). A real-life case study on six SMEs is carried out with the help of three experts. For aggregating the individual responses (using spherical fuzzy numbers or SFNs), EA is used. Then two very recent models such as Simple Ranking Process (SRP) and Symmetry Point of Criterion (SPC) are extended using SFN to rank the SMEs. Finally, the validation tests and sensitivity analysis are carried out. It is noted that the application of analytical tools, knowledge management and use of technology under the support and mentorship of visionary leadership are the key criteria for building up the capability to embrace Q 4.0. Interestingly, it is noted that medium scale firms are better prepared than small-scale enterprises. This work is apparently a first of its kind that focuses on SMEs for assessing their quality management practices in Industry 4.0 era

A hybrid power heronian function-based multi-criteria decision-making model for workplace charging scheduling algorithms.

This study proposes a new multi-criteria decision-making model to determine the best smart charging scheduling that meets electric vehicle (EV) user considerations at work-places. An optimal charging station model is incorporated into the decision-making for a quantitative evaluation. The proposed model is based on a hybrid Power Heronian functions in which the linear normalization method is improved by applying the inverse sorting algorithm for rational and objective decision-making. This enables EV users to specify and evaluate multi-criteria for considering their aspects at workplaces. Five different charging scheduling algorithms with AC dual port L2 and DC fast charging electric vehicle supply equipment (EVSE) are investigated. Based on EV users from the field, the required charging time, EVSE occupancy, the number of EVSE units, and user flexibility are found to have the highest importance degree, while charging cost has the lowest importance degree. The experimental results show that, in terms of meeting EV users' considerations at workplaces, scheduling EVs based on their charging energy needs performs better as compared to scheduling them by their arrival and departure times. While the scheduling alternatives display similar ranking behavior for both EVSE types, the best alternative may differ for the EVSE type. To validate the proposed model, a comparison against three traditional models is performed. It is demonstrated that the proposed model yields the same ranking order as the alternative approaches. Sensitivity analysis validates the best and worst scheduling alternatives