Multiattribute decision making based on interval-valued intuitionistic fuzzy values, score function of connection numbers, and the set pair analysis theory

Decision support system based on bipolar complex fuzzy Hamy mean operators

The important feature of the multi-attribute decision-making (MADM) technique is to identify an ideal solution and aggregate collective cognitive fuzzy information of human opinion. To serve this purpose, we explore the concepts of the bipolar complex fuzzy set with positive and negative support terms. A few applications of the Hamy mean (HM) and Dual Hamy mean (DHM) models are also discussed to find out the relationship among input arguments or different preferences. For this, we derive a family of mathematical approaches by incorporating the theory of bipolar complex fuzzy information such as bipolar complex fuzzy Hamy mean (BCFHM), bipolar complex fuzzy weighted Hamy mean (BCFWHM), bipolar complex fuzzy Dual Hamy mean (BCFDHM), and bipolar complex fuzzy weighted Dual Hamy mean (BCFWDHM) operators. Derived mathematical approaches are more applicable and can express the influence of uncertain information due to the involvement of additional parameter values. Based on diagnosed research work and mathematical methodologies, we establish a decision algorithm for the MADM problem to resolve real-life dilemmas. An experimental case study demonstrates the compatibility of derived approaches and evaluates the investment policy's sustainability based on certain parameters. The advantages and consistency of the proposed research work are verified in the comparative study with various existing aggregation operators.

Location selection for offshore wind power station using interval-valued intuitionistic fuzzy distance measure-RANCOM-WISP method

The development opportunities and high-performance capacity of offshore wind energy project depends on the selection of the suitable offshore wind power station (OWPS) location. The present study aims to introduce a decision-making model for assessing the locations for OWPS from multiple criteria and uncertainty perspectives. In this regard, the concept of interval-valued intuitionistic fuzzy set (IVIFS) is utilized to express uncertain information. To quantify the degree of difference between IVIFSs, an improved distance measure is proposed and further utilized for deriving the objective weights of criteria. Numerical examples are discussed to illustrate the usefulness of introduced IVIF-distance measure. The RANking COMparison (RANCOM) based on interval-valued intuitionistic fuzzy information is presented to determine the subjective weights of criteria. With the combination of objective and subjective weights of criteria, an integrated weighting tool is presented to find the numeric weights of criteria under IVIFS environment. Further, a hybrid interval-valued intuitionistic fuzzy Weighted integrated Sum Product (WISP) approach is developed to prioritize the OWPS locations from multiple criteria and uncertainty perspectives. This approach combines the benefits of two normalization tools and four utility measures, which approves the effect of beneficial and non-beneficial criteria by means of weighted sum and weighted product measures. Further, the developed approach is applied to the OWPS location selection problem of Gujarat, India. Sensitivity and comparative analyses are presented to confirm the robustness and stability of the present WISP approach. This study provides an innovative decision analysis framework, which makes a significant contribution to the OWPS locations assessment problem under uncertain environment.

Interval-valued Pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and Choquet integral

This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment.

An integrated interval-valued intuitionistic fuzzy technique for resumption risk assessment amid COVID-19 prevention

Currently, China has achieved a remarkable achievement on the containment of COVID-19, which creates a favorable condition for the gradual resumption of normal life. However, COVID-19 infections continue to rise in many nations and some sporadic cases occur from time to time in China, which still poses some risks to the resumption. Hence, it is imperative to develop some reasonable techniques to assess the resumption risk. This paper aims to investigate an integrated interval-valued intuitionistic fuzzy (IVIF) technique to adroitly assess the resumption risk based on DEMATEL (decision making trial and evaluation laboratory), BWM (best-worst method) and SPA (set pair analysis). This integrated technique is called IVIF-DBWM-SPA, where the IVIF-DBWM (combined by the IVIF-DEMATEL and IVIF-BWM) is used to determine the global criteria weights and the IVIF-SPA is employed to generate the ranking order of the alternatives. The IVIF-DEMATEL and IVIF-BWM are used to determine the weights of dimensions and the weights of criteria under each dimension, respectively. In this IVIF-BWM, two bi-objective programming models are constructed by regarding experts' pessimistic and optimistic attitudes, respectively. Combined experts' intrapersonal and interpersonal uncertainties simultaneously, a bi-objective programming model is proposed to derive the dynamic weights of experts. Based on the determined weights of experts and criteria, an IVIF-SPA is developed to assess the risk levels of all alternatives. The validity of the proposed technique is demonstrated with a real case of college resumption risk assessment amid COVID-19. Some sensitivity and comparison analyses are provided to show the merits of the proposed technique.

Comprehensive risk assessment of algae and shellfish in the middle route of South-to-North Water Diversion Project

Since the main canal of the middle route of South-to-North Water Diversion Project was put into operation, the species, quantity, and biomass of algae and shellfish have responded quickly to the environment, and a single dominant species has appeared in the community, demonstrating the remarkably abnormal proliferation property of algae and shellfish. In order to evaluate the safety risk of abnormal proliferation of algae and shellfish in the middle route and realize dynamic analysis of all kinds of influencing factors, a comprehensive risk evaluation system of algae and shellfish in the middle route of South-to-North Water Diversion Project based on comprehensive weighting and four-element connection number was constructed by integrating the analytic hierarchy process (AHP) and the weight assignment theory of criteria importance through intercriteria (CRITIC). The system consists of 21 evaluation indexes selected from risk factors and carriers. Taking Henan section in the middle route as an example, comprehensive risk evaluation system of algae and shellfish in the middle route of South-to-North Water Diversion Project was applied to calculate the partial connection number of each order and obtain the risk development trend of each indicator. The results showed that algae and shellfish in the middle route were in a very safe state at the safety risk level of level I. Finally, reasonable measures to reduce the risks facing algae and shellfish in the middle route of South-to-North Water Diversion Project are given, which effectively make up the deficiency of existing evaluation methods.

An Approach for the Analysis of Energy Resource Selection Based on Attributes by Using Dombi T-Norm Based Aggregation Operators

Dombi t-norm (DTN) and t-conorm (TCN) are among the most effective triangular norms in fuzzy systems for aggregation purposes. The environment of interval-valued intuitionistic fuzzy (IVIF) set gives us precision in expressing uncertain information by using a membership grade (MG) and non-membership grade (NMG) in the form of closed subintervals of 0, 1. The goal of this paper is to introduce DTN-based aggregation operators (AOs) for IVIF numbers (IVIFNs) and study their performance in the evaluation of the worth of energy recourses to be opted in Pakistan to deal with the energy crises situation. We first introduced some DTN and TCN-based operations for IVIFNs and developed two new AOs known as IVIF Dombi weighted averaging (IVIFDWA) and IVIF Dombi weighted geometric (IVIFDWG) operators. The validity and fitness of the proposed operators are tested. A case study is presented where the energy resources of Pakistan are discussed and the problem of the selection of sustainable energy resources in the context of Pakistan is investigated. The sensitivity analysis of the proposed IVIFDWA and IVIFDWG operators is studied and a comparative analysis of the current work with previous studies is established.

Research on the optimal aggregation method of fuzzy preference information based on spatial Steiner-Weber point

In view of the present situation that most aggregation methods of fuzzy preference information are extended or mixed by classical aggregation operators, which leads to the aggregation accuracy is not high. The purpose of this paper is to develop a novel method for spatial aggregation of fuzzy preference information. Thus we map the fuzzy preference information to a set of three-dimensional coordinate and construct the spatial aggregation model based on Steiner-Weber point. Then, the plant growth simulation algorithm (PGSA) algorithm is used to find the spatial aggregation point. According to the comparison and analysis of the numerical example, the aggregation matrix established by our method is closer to the group preference matrices. Therefore, the optimal aggregation point obtained by using the optimal aggregation method based on spatial Steiner-Weber point can best represent the comprehensive opinion of the decision makers.

Distance-Based Knowledge Measure for Intuitionistic Fuzzy Sets with Its Application in Decision Making

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov's intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

Multiattribute decision-making under Fermatean fuzzy bipolar soft framework

Fermatean fuzzy set theory is emerging as a novel mathematical tool to handle uncertainties in different domains of real world. Fermatean fuzzy sets were presented in order that uncertain information from quite general real-world decision-making situations could be mathematically tractable. To that purpose, these sets are more flexible and reliable than intuitionistic and Pythagorean fuzzy sets. This paper presents a novel hybrid model, namely, the Fermatean fuzzy bipolar soft set (FFBSS, in short) model as a general extension of two powerful existing models, that is, fuzzy bipolar soft set and Pythagorean fuzzy bipolar soft set models. Some fundamental properties of the proposed FFBSS model, namely, subset-hood, equal FFBSSs, relative null and relative absolute FFBSSs, restricted intersection and union, extended intersection and union, AND operation and OR operation are investigated along with numerical examples. In addition, certain basic operations, including Fermatean fuzzy weighted average and score function of FFBSSs are proposed. Furthermore, two applications of FFBSS are explored to deal with different multiattribute decision-making situations, that is, selection of best surgeon robot and analysis of most affected country due to COVID-19 ('CO' stands for corona, 'VI' for virus, 'D' for disease, and '19' stands for its year of emergence, that is, 2019). The proposed methodology is supported by an algorithm. At the end, a comparison analysis of the proposed hybrid model with some existing models, including Pythagorean fuzzy bipolar soft sets is provided.

Coupling Fuzzy Multi-Criteria Decision-Making and Clustering Algorithm for MSW Landfill Site Selection (Case Study: Lanzhou, China)

The siting of Municipal Solid Waste (MSW) landfills is a complex decision process. Existing siting methods utilize expert scores to determine criteria weights, however, they ignore the uncertainty of data and criterion weights and the efficacy of results. In this study, a coupled fuzzy Multi-Criteria Decision-Making (MCDM) approach was employed to site landfills in Lanzhou, a semi-arid valley basin city in China, to enhance the spatial decision-making process. Primarily, 21 criteria were identified in five groups through the Delphi method at 30 m resolution, then criteria weights were obtained by DEMATEL and ANP, and the optimal fuzzy membership function was determined for each evaluation criterion. Combined with GIS spatial analysis and the clustering algorithm, candidate sites that satisfied the landfill conditions were identified, and the spatial distribution characteristics were analyzed. These sites were subsequently ranked utilizing the MOORA, WASPAS, COPRAS, and TOPSIS methods to verify the reliability of the results by conducting sensitivity analysis. This study is different from the previous research that applied the MCDM approach in that fuzzy MCDM for weighting criteria is more reliable compared to the other common methods.