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The weighted evaluation function method with normalized objective functions is used to transform the proposed multi-objective model into a single objective one, which reflects the investors' preference for returns, risks and social responsibility by adjusting the weights. Finally, an example is given to illustrate the solution steps of the model and the effectiveness of the algorithm.

Based on the possibility theory, assuming that the future returns of each asset are trapezoidal fuzzy numbers, a mean-variance-Yager entropy-social responsibility model is constructed including piecewise linear transaction costs and risk-free assets. The model proposed in this paper includes six constraints, the investment proportion sum, the non-negativity proportion, the ceiling and floor, the pre-assignment, the cardinality and the round lot constraints. In addition, considering the special round lot constraint, the proposed model is transformed into an integer programming problem.

The effects of different constraints and transaction costs on the effective frontier of the portfolio are analyzed, which not only assists investors to make decisions close to their expectations by setting appropriate parameters but also provides constructive suggestions through the overall performance of each asset.

There are two improvements in the improved particle swarm optimization algorithm: one is that the complex constraints are specifically satisfied by using a renewable 0–1 random constraint matrix and random scaling factors instead of fixed ones; the other is eliminating the particles with poor fitness and randomly adding some new particles that satisfy all the constraints to achieve the goal of global search as much as possible.

Achieving a zero-carbon city requires a long-term strategic perspective. The authors propose a decision-making model which would take into account the economic, environmental and social impacts for prioritizing the zero-carbon measures for sustainable urban transportation.

An integrated intuitionistic fuzzy gained and lost dominance score (IF-GLDS) model is introduced based on intuitionistic fuzzy Yager weighted aggregation (IFYWA) operators and proposed weight-determining IF-SPC procedure. In addition, a weighting tool is presented to obtain the weights of decision experts. Further, the feasibility and efficacy of developed IF-SPC-GLDS model is implemented on a multi-criteria investment company selection problem under IFS context.

The results of the developed model, “introducing zero-emission zones” should be considered as the first measure to implement. The preference of this initiative offers sustainable transport in India to achieve a zero-carbon transport by having the greatest impact on the modal shift from cars to sustainable mobility modes with a lower operational and implementation cost as well as having greater public support. The developed model utilized can be relocated to other smart cities which aim to achieve a zero-carbon transport. Sensitivity and comparative analyses are discussed to reveal the robustness of obtained result. The outcomes show the feasibility of the developed methodology which yields second company as the suitable choice, when compared to and validated using the other MCDA methods from the literature, including TOPSIS, COPRAS, WASPAS and CoCoSo with intuitionistic fuzzy information.

A new intuitionistic fuzzy symmetry point of criterion (IF-SPC) approach is presented to find weights of criteria under IFSs setting. Then, an IF-GLDS model is introduced using IFYWA operators to rank the options in the realistic multi-criteria decision analysis (MCDA) procedure. For this purpose, the IFYWA operators and their properties are developed to combine the IFNs. These operators can offer a flexible way to deal with the realistic MCDA problems with IFS context.

Most decision-making problems in construction are complex and difficult to solve, as they involve multiple criteria and multiple decision makers in addition to subjective uncertainties, imprecisions and vagueness surrounding the decision-making process. In many instances, the decision-making process is based on linguistic terms rather than numerical values. Hence, structured fuzzy consensus-reaching processes and fuzzy aggregation methods are instrumental in multi-criteria group decision-making (MCGDM) problems for capturing the point of view of a group of experts. This chapter outlines different fuzzy consensus-reaching processes and fuzzy aggregation methods. It presents the background of the basic theory and formulation of these processes and methods, as well as numerical examples that illustrate their theory and formulation. Application areas of fuzzy consensus reaching and fuzzy aggregation in the construction domain are identified, and an overview of previously developed frameworks for fuzzy consensus reaching and fuzzy aggregation is provided. Finally, areas for future work are presented that highlight emerging trends and the imminent needs of fuzzy consensus reaching and fuzzy aggregation in the construction domain.

Focuses on the applications of fuzzy set theory as a tool for the construction of multi‐criteria decision functions from specifications expressed in natural language. Starting with the ability to represent individual criteria satisfactions in terms of membership of fuzzy subsets, shows how different types of linguistic specifications are implemented. Consideration is given to the representation of trade‐offs between criteria, quantifier‐guided aggregations, conditioned criteria and possibilistically qualified criteria.

This paper proposes a fuzzy random multi-objective portfolio model with different entropy measures and designs a hybrid algorithm to solve the proposed model.

Because random uncertainty and fuzzy uncertainty are often combined in a real-world setting, the security returns are considered as fuzzy random numbers. In the model, the authors also consider the effects of different entropy measures, including Yager's entropy, Shannon's entropy and min-max entropy. During the process of solving the model, the authors use a ranking method to convert the expected return into a crisp number. To find the optimal solution efficiently, a fuzzy programming technique based on artificial bee colony (ABC) algorithm is also proposed.

(1) The return of optimal portfolio increases while the level of investor risk aversion increases. (2) The difference of the investment weights of the optimal portfolio obtained with Yager's entropy are much smaller than that of the min–max entropy. (3) The performance of the ABC algorithm on solving the proposed model is superior than other intelligent algorithms such as the genetic algorithm, differential evolution and particle swarm optimization.

To the best of the authors' knowledge, no effect has been made to consider a fuzzy random portfolio model with different entropy measures. Thus, the novelty of the research is constructing a fuzzy random multi-objective portfolio model with different entropy measures and designing a hybrid fuzzy programming-ABC algorithm to solve the proposed model.

Green innovation in human-centric smart manufacturing (HSM-GI) has emerged as a new paradigm in innovation management for Industry 5.0. The evaluation analysis method is crucial for measuring the development progress and guiding continual improvements of HSM-GI. Since this process of HSM-GI can be regarded as complex and interactive, a holistic picture is often required to describe the interrelations of its antecedents and consequences. In this respect, this study aims to construct a causality network indicator system and proposes a synergy evaluation method for HSM-GI.

Firstly, based on the Driver force-State-Response (DSR) causal-effect framework, this study constructs a holistic indicator system to analyze the interactions between environmental and human concerns of HSM-GI. Secondly, owing to the imprecision of human cognition and synergy interaction in the evaluation process, a flexible hesitant fuzzy (HF) superiority-inferiority synergetic evaluation method is presented. This method quantifies the strengths of causal relationships and expresses the incentives and constraints attitudes of humans. Finally, the proposed framework is applied to six HSMs in the electronic technology industry.

The driving force and state of the HSM-GI system exhibit an upward trend, while the response continues to decline due to changing market demands. The order and synergy degree have shown an increasing trend during 2021–2023, particularly significant for BOE and Haier Smart Home. HSM-GI systems with higher scores mostly have functional coordination and a coherent synergy structure.

This study demonstrates the proposed approach’s applicability and assists policymakers in formulating targeted strategies for green innovation systems.

Pharmaceutical supply chains (PSCs) need a well-operating and faultless logistics system to successfully store and distribute their medicines. Hospitals, health institutes, and pharmacies must maintain extra stock to respond requirements of the patients. Nevertheless, there is an inverse correlation between the level of medicine stock and logistics service level. The high stock level held by health institutions indicates that we have not sufficiently excellent logistics systems presently. As such, selecting appropriate logistics service providers (drug distributors) is crucial and strategic for PSCs. However, this is difficult for decision-makers, as highly complex situations and conflicting criteria influence such evaluation processes. So, a robust, applicable, and strong methodological frame is required to solve these decision-making problems.

To achieve this challenging issue, the authors develop and apply an integrated entropy-WASPAS methodology with Fermatean fuzzy sets for the first time in the literature. The evaluation process takes place in two stages, as in traditional multi-criteria problems. In the first stage, the importance levels of the criteria are determined by the FF-entropy method. Afterwards, the FF-WASPAS approach ranks the alternatives.

The feasibility of the proposed model is also supported by a case study where six companies are evaluated comprehensively regarding ten criteria. Herewith, total warehouse capacity, number of refrigerated vehicles, and personnel are the top three criteria that significantly influence the evaluation of pharmaceutical distribution and warehousing companies. Further, a comprehensive sensitivity analysis proves the robustness and effectiveness of the proposed approach.

The proposed multi-attribute decision model quantitatively aids managers in selecting logistics service providers considering imprecisions in the multi-criteria decision-making process.

A new model has been developed to present a sound mathematical model for selecting logistics service providers consisting of Fermatean fuzzy entropy and WASPAS methods. The paper's main contribution is presenting a comprehensive and more robust model for the ex ante evaluation and ranking of providers.

Examines the problem of fuzzification in situations in which in addition to the usual fuzzy output of the controller there exists some ancillary restriction on the allowable defuzzified values. Provides two basic approaches to address this problem. In the first approach, enforces the restriction by selecting the defuzzified value through a random experiment in which the values which have non‐zero probabilities are in the allowable region; this method is based on the RAGE defuzzification procedure and makes use of a non‐monotonic conjunction operator. The second approach, which, in the spirit of the commonly used methods, is a kind of expected value, converts the problem to a constraint optimization problem.

The aim of this study as to find out an approach for emergency program selection.

The authors have generated six aggregation operators (AOs), namely picture fuzzy Yager weighted average (PFYWA), picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, picture fuzzy Yager weighted geometric (PFYWG), picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.

First of all, the authors defined the score and accuracy function for picture fuzzy set (FS), and some fundamental operational laws for picture FS using the Yager aggregation operation. After that, using the developed operational laws, developed some AOs, namely PFYWA, picture fuzzy Yager ordered weighted average, picture fuzzy Yager hybrid weighted average, PFYWG, picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators, have been proposed along with their desirable properties. A decision-making (DM) approach based on these operators has also been presented. An illustrative example has been given for demonstrating the approach. Finally, discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.

To find the best alternative for emergency program selection.

In constructing intelligent machines we must at times include the capability to perform precise actions in the face of imprecise information. Using fuzzy subset theory we show how to build algorithms to meet this task.