Case‐based approach for supporting strategy decision making

The practice of strategy decision making proves that when the management board is strongly limited in its capacity to take rational actions, specifically in the context of great decision complexity and uncertainty, it is considered good practice to refer to experience through reasoning by analogy. In this paper, we would like to concentrate on supporting strategic decisions in small and medium enterprises (SMEs). The complexity of analogy‐based reasoning has its roots in an attempt to solve new problems based on past cases from a different domain, while we will focus on case‐based approach for a single domain. Additionally, we have chosen case‐based reasoning as a suitable decision‐making paradigm because it is corresponds to managers’ decision‐making behaviour. We present the STRATEGOS case‐based reasoning system for supporting strategic decision making by SMEs management boards and then the system evaluation by the dozens of chief executive officers (CEOs) from SMEs is presented. The results of the survey are promising and show the remarkable correspondence of the proposed solution with expectations and strategic behaviour of CEOs.     

Interval‐valued probabilistic linguistic term sets in multi‐criteria group decision making

The theory of probabilistic linguistic term sets (PLTSs) is very useful in objectively dealing with the multi‐criteria group decision making (MCGDM) problems in which there is hesitancy in providing linguistic assessments; and PLTSs allow experts to express their preferences on one linguistic term over another. In order to reflect the uncertainty and inconsistency of decision‐makers and handle incomplete linguistic information, we propose a new PLTS called interval‐valued probabilistic linguistic term set (IVPLTS). In addition, the existing approaches associated with PLTSs are limited or highly complex in real applications. Therefore, new operations, comparison laws, and aggregation operators are developed for IVPLTS. Furthermore, we establish an efficient framework for MCGDM problems based on the proposed comparison method and the fuzzy preference relation. Then we apply it to a real‐life case under linguistic environment. The extended TOPSIS methods combined with PLTSs by using different operational laws are also included for comparison. The final results demonstrate the efficiency and practicality of the new framework.     

Triangular norm‐based cuts and possibility characteristics of triangular intuitionistic fuzzy numbers for decision making

Triangular intuitionistic fuzzy numbers (TIFNs) is one of the useful tools to manage the fuzziness and vagueness in expressing decision data and solving decision making problems. In this paper, triangular norm (t‐norm) based cuts of TIFNs are developed to synthesize the membership and nonmembership functions in describing the cut sets, then the possibility characteristics of TIFNs, i.e., the possibility mean, the possibility variance, and the possibility mean‐standard deviation ratio, are given. Thereby, on the ground of the possibility mean‐standard deviation ratio, a ranking method of TIFNs is introduced. With these elements, an approach to multiple attributes decision making (MADM) is proposed and illustrated by a numerical example. It is shown that the approach to MADM comprehensively considers both the membership and nonmembership functions and can lead to objective and reasonable results.     

Z‐uncertain probabilistic linguistic variables and its application in emergency decision making for treatment of COVID‐19 patients

Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z‐uncertain probabilistic linguistic variables (Z‐UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z‐UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z‐uncertain probabilistic linguistic (Z‐UPL) environment. Finally, an emergency decision‐making case of COVID‐19 patients and comparative analysis illustrate the necessity and effectiveness of this method.     

Interval‐valued Pythagorean fuzzy GRA method for multiple‐attribute decision making with incomplete weight information

In this paper, the concept of multiple‐attribute group decision‐making (MAGDM) problems with interval‐valued Pythagorean fuzzy information is developed, in which the attribute values are interval‐valued Pythagorean fuzzy numbers and the information about the attribute weight is incomplete. Since the concept of interval‐valued Pythagorean fuzzy sets is the generalization of interval‐valued intuitionistic fuzzy set. Thus, due the this motivation in this paper, the concept of interval‐valued Pythagorean fuzzy Choquet integral average (IVPFCIA) operator is introduced by generalizing the concept of interval‐valued intuitionistic fuzzy Choquet integral average operator. To illustrate the developed operator, a numerical example is also investigated. Extended the concept of traditional GRA method, a new extension of GRA method based on interval‐valued Pythagorean fuzzy information is introduced. First, utilize IVPFCIA operator to aggregate all the interval‐valued Pythagorean fuzzy decision matrices. Then, an optimization model based on the basic ideal of traditional grey relational analysis (GRA) method is established, to get the weight vector of the attributes. Based on the traditional GRA method, calculation steps for solving interval‐valued Pythagorean fuzzy MAGDM problems with incompletely known weight information are given. The degree of grey relation between every alternative and positive‐ideal solution and negative‐ideal solution is calculated. To determine the ranking order of all alternatives, a relative relational degree is defined by calculating the degree of grey relation to both the positive‐ideal solution and negative ideal solution simultaneously. Finally, to illustrate the developed approach a numerical example is to demonstrate its practicality and effectiveness.     

Uncertain linguistic hesitant fuzzy sets and their application in multi‐attribute decision making

To denote the quantitative and qualitative fuzzy information simultaneously, this paper introduces a new type of fuzzy sets called uncertain linguistic hesitant fuzzy sets, which are denoted by an uncertain linguistic variable with several possible interval membership degrees. Considering the application of this type of fuzzy sets, several basic operational laws are defined, and several properties are studied. Meanwhile, an ordered relationship is introduced. Then, two types of uncertain linguistic hesitant fuzzy aggregation operators are defined. One uses additive measures, and the other is based on λ‐fuzzy measures. Then, a similarity measure is presented, by which models for the optimal weight vector are constructed. After that, an approach to uncertain linguistic hesitant fuzzy multi‐attribute decision making is developed. Finally, an illustrative example for evaluating corporate environmental performance is offered to show the concrete practicality of the procedure.     

Weighted‐selective aggregated majority‐OWA operator and its application in linguistic group decision making

This paper focuses on the aggregation operations in the group decision‐making model based on the concept of majority opinion. The weighted‐selective aggregated majority‐OWA (WSAM‐OWA) operator is proposed as an extension of the SAM‐OWA operator, where the reliability of information sources is considered in the formulation. The WSAM‐OWA operator is generalized to the quantified WSAM‐OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM‐IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision‐making model under the linguistic domain, which consists of two‐stage aggregation processes, is developed in order to fuse the experts’ judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model.     

Parameter reductions in N‐soft sets and their applications in decision‐making

Parameter reduction is an important operation for improving the performance of decision‐making processes in various uncertainty theories. The theory of N‐soft sets is emerging as a powerful mathematical tool for dealing with uncertainties beyond the standard formulation of the soft set theory. In this research article, we extend the notion of parameter reduction to N‐soft set theory, and we also justify its practical calculation. To this purpose, we define related theoretical concepts (e.g. N‐soft subset, reduct N‐soft set and redundant parameter) and examine some of their fundamental properties. Then, we argue that the idea of attributes reduction from the rough set theory cannot be employed in the N‐soft set theory in order to reduce the number of parameters. Consequently, we take an original position in order to adequately define and compute parameter reductions in N‐soft sets. Finally, we develop an application of parameter reduction of N‐soft sets.     

A ranking function based on principal‐value Pythagorean fuzzy set in multicriteria decision making

Multicriteria decision making (MCDM) has been attracting attention in recent years. There are two essential directions in the research territory, one direction is the research of representation of evaluation information and another is the construction of ranking function. In this paper, we consider some nonstandard fuzzy sets, intuitionistic, and interval‐valued fuzzy sets. Especially, the Pythagorean membership grade and Pythagorean fuzzy set receive much attention. Then, to reflect the importance of principal value, we shall propose the principal‐value Pythagorean fuzzy number (p‐PFN) and principal‐value Pythagorean fuzzy set. Furthermore, a novel ranking function is constructed to select the ideal alternative(s) based on p‐PFNs in MCDM. Finally, an investment strategy decision‐making problem is proposed to reveal the availability and practicability of the function under the new environment.     

Some new Pythagorean fuzzy Choquet–Frank aggregation operators for multi‐attribute decision making

Pythagorean fuzzy set (PFS) whose main feature is that the square sum of the membership degree and the non‐membership degree is equal to or less than one, is a powerful tool to express fuzziness and uncertainty. The aim of this paper is to investigate aggregation operators of Pythagorean fuzzy numbers (PFNs) based on Frank t‐conorm and t‐norm. We first extend the Frank t‐conorm and t‐norm to Pythagorean fuzzy environments and develop several new operational laws of PFNs, based on which we propose two new Pythagorean fuzzy aggregation operators, such as Pythagorean fuzzy Choquet–Frank averaging operator (PFCFA) and Pythagorean fuzzy Choquet–Frank geometric operator (PFCFG). Moreover, some desirable properties and special cases of the operators are also investigated and discussed. Then, a novel approach to multi‐attribute decision making (MADM) in Pythagorean fuzzy context is proposed based on these operators. Finally, a practical example is provided to illustrate the validity of the proposed method. The result shows effectiveness and flexible of the new method. A comparative analysis is also presented.     

Study on the ranking problems in multiple attribute decision making based on interval‐valued intuitionistic fuzzy numbers

This paper puts forward a new ranking method for multiple attribute decision‐making problems based on interval‐valued intuitionistic fuzzy set (IIFS) theory. First, the composed ordered weighted arithmetic averaging operator and composed ordered weighted geometric averaging operator are extended to the IIFSs in which they are, respectively, named interval‐valued intuitionistic fuzzy composed ordered weighted arithmetic averaging (IIFCOWA) operator and interval‐valued intuitionistic composed ordered weighted geometric averaging (IIFCOWG) operator. Afterwards, to compare interval‐valued intuitionistic fuzzy numbers, we define the concepts of the maximum, the minimum, and ranking function. Some properties associated with the concepts are investigated. Using the IIFCOWA or IIFCOWG operator, we establish the detailed steps of ranking alternatives (or attributes) in multiple attribute decision making. Finally, an illustrative example is provided to show that the proposed ranking method is feasible in multiple attribute decision making.     

Social facilitation effect in search and decision‐making components of visual inspection

This study aimed to examine the effect of social presence on the performance of the search and decision‐making components of visual inspection. A within‐subject design experiment was conducted. Participants performed easy and difficult search and decision‐making tasks in alone and audience‐present conditions with search time, decision time, decision accuracy rates, and subjective arousal level in both components measured. Results indicated that the presence of an audience shortened (lengthened) the response time in easy (difficult) search and decision‐making components but did not influence decision accuracy rates. The social facilitation intensity in the search component was stronger than that in the decision‐making component. For both components, the performance impairment in difficult tasks was stronger than the performance improvement in easy tasks, and arousal was greater in the audience‐present condition than when working alone. The findings helped clarify the influential mechanisms of the social facilitation effect in visual inspection tasks.     

A consensus‐ and harmony‐based feedback mechanism for multiple attribute group decision making with correlated intuitionistic fuzzy sets

In this study, an interactive consensus model is proposed for correlated multiple attribute group decision making (MAGDM) problems with intuitionistic triangular fuzzy numbers (ITFNs). The harmony degree (HD) is investigated to determine the degree of maintaining experts' original information while the consensus level is defined as the proximity degree (PD) between an expert and other experts on three levels: evaluation elements of alternatives, alternatives, and decision matrices. Combining HD and PD, a three‐dimensional feedback mechanism is proposed to identify discordant experts, alternatives, and corresponding preference values that contribute less to consensus, and provides advice to reach a higher consensus level. Additionally, visual representation of experts' consensus position within the group is provided. Furthermore, a graphical simulation of future consensus and harmony status, if the recommended values were to be implemented, is also provided. Therefore, our proposed feedback mechanism guarantees that it increases the consensus level of the set of experts while maintaining, as much as possible, experts' original information. Then, the PD‐induced intuitionistic triangular fuzzy correlated averaging (PD‐IITFCA) operator is investigated to aggregate the interactive individual opinions between experts. Finally, the intuitionistic triangular fuzzy correlated averaging (ITFCA) operator is developed to aggregate the evaluation elements of alternatives under correlative attributes. Based on the score and accurate functions of ITFNs, an order relation is proposed to obtain the final solution of alternatives.     

Some q‐rung orthopair fuzzy Heronian mean operators in multiple attribute decision making

The generalized Heronian mean and geometric Heronian mean operators provide two aggregation operators that consider the interdependent phenomena among the aggregated arguments. In this paper, the generalized Heronian mean operator and geometric Heronian mean operator under the q‐rung orthopair fuzzy sets is studied. First, the q‐rung orthopair fuzzy generalized Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy geometric Heronian mean (q‐ROFGHM) operator, q‐rung orthopair fuzzy generalized weighted Heronian mean (q‐ROFGWHM) operator, and q‐rung orthopair fuzzy weighted geometric Heronian mean (q‐ROFWGHM) operator are proposed, and some of their desirable properties are investigated in detail. Furthermore, we extend these operators to q‐rung orthopair 2‐tuple linguistic sets (q‐RO2TLSs). Then, an approach to multiple attribute decision making based on q‐ROFGWHM (q‐ROFWGHM) operator is proposed. Finally, a practical example for enterprise resource planning system selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

New exponential operational laws and their aggregation operators for interval‐valued Pythagorean fuzzy multicriteria decision‐making

In this article, we define two new exponential operational laws about the interval‐valued Pythagorean fuzzy set (IVPFS) and their corresponding aggregation operators. However, the exponential parameters (weights) of all the existing operational laws of IVPFSs are crisp values in IVPFS decision‐making problems. As a supplement, this paper first introduces new exponential operational laws of IVPFS, where bases are crisp values or interval numbers and exponents are interval‐valued Pythagorean fuzzy numbers. The prominent characteristic of these proposed operations is studied. Based on these laws, we develop some new weighted aggregation operators, namely the interval‐valued Pythagorean fuzzy weighted exponential averaging operator and the dual interval‐valued Pythagorean fuzzy weighted exponential averaging. Finally, a decision‐making approach is presented based on these operators and illustrated with some numerical examples to validate the developed approach.     

Fuzzy rough set on probabilistic approximation space over two universes and its application to emergency decision‐making

Probabilistic approaches to rough sets are still an important issue in rough set theory. Although many studies have been written on this topic, they focus on approximating a crisp concept in the universe of discourse, with less effort on approximating a fuzzy concept in the universe of discourse. This article investigates the rough approximation of a fuzzy concept on a probabilistic approximation space over two universes. We first present the definition of a lower and upper approximation of a fuzzy set with respect to a probabilistic approximation space over two universes by defining the conditional probability of a fuzzy event. That is, we define the rough fuzzy set on a probabilistic approximation space over two universes. We then define the fuzzy probabilistic approximation over two universes by introducing a probability measure to the approximation space over two universes. Then, we establish the fuzzy rough set model on the probabilistic approximation space over two universes. Meanwhile, we study some properties of both rough fuzzy sets and fuzzy rough sets on the probabilistic approximation space over two universes. Also, we compare the proposed model with the existing models to show the superiority of the model given in this paper. Furthermore, we apply the fuzzy rough set on the probabilistic approximation over two universes to emergency decision‐making in unconventional emergency management. We establish an approach to online emergency decision‐making by using the fuzzy rough set model on the probabilistic approximation over two universes. Finally, we apply our approach to a numerical example of emergency decision‐making in order to illustrate the validity of the proposed method.     

Multiple attribute decision‐making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q‐rung orthopair fuzzy environment

A Q‐rung orthopair fuzzy set (q‐ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision‐making problems with q‐rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q‐rung orthopair fuzzy extended Bonferroni mean (q‐ROFEBM) operator and its weighted form (q‐ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q‐ROFEBM and q‐ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge‐based entropy measure for q‐ROFSs is also proposed to obtain the attribute weights. Based on the proposed q‐ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q‐ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.     

A novel tree‐shaped antenna with wideband and end‐fire properties designed by competitive algorithm of simulating natural tree growth

This article presents a novel tree‐shaped antenna with wideband and end‐fire properties designed by the Competitive Algorithm of Simulating Natural Tree Growth. The antenna has an impedance bandwidth of 27.2% for S11 < ?10dB, maintains end‐fire radiation pattern and achieves a high gain over the entire frequency band from 5.4 GHz to 7.1 GHz. © 2010 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2010.