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A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input–output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman's rank correlation test assesses the statistical significance of two rankings sets. [ABSTRACT FROM AUTHOR]

As a new conception of IFS (Intuitionistic Fuzzy Sets), Pythagorean Fuzzy Sets can manage conflicted details more fexibly in decision-making. This extension has been used repeatedly for decision making. This is an important trend in decision making that is worth further study in combination with the study of entropy properties. This paper proposes a new entropy for the Pythagorean Fuzzy Sets and an application measure using the TOPSIS method. The new entropy approach was used to estimate the objective weights in the decision-making procedure. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) technique is presumed that the optimum alternative has the least distance from the positive and farthest from the negative ideal solution. This approach has been widely adopted to solve MCDM issues in multiple fields. We present a simple study case where we use TOPSIS and new entropy to solve the group decision-making problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present the use of an innovative approach based on MCDM methods as the main component of a consumer Decision Support System (DSS) by recommending the most suitable products among a given set of alternatives. This system provides a reliable recommendation to the consumer in the form of a compromise ranking constructed from the five MCDM methods: the hybrid approach TOPSIS-COMET, COCOSO, EDAS, MAIRCA, and MABAC. Each of the methods used contributes significantly to the final compromise ranking built with the Copeland strategy. Chosen MCDM methods were combined with the objective CRITIC weighting method, and their performance was presented on the illustrative example of choosing the most suitable mobile phone. A sensitivity analysis involving the rw and WS correlation coefficients was performed to determine the match between the compromise ranking of the candidates and the rankings provided by each MCDM method. Sensitivity analysis demonstrated that all investigated compromise candidate rankings show high convergence with the rankings provided by the particular MCDM methods. Thus, the performed study proved that the proposed approach shows high potential to be successfully used as a central component of DSS for recommending the most suitable product. Such DSS could be a universal and future-proof solution for e-commerce sites and websites, providing advanced product comparison capabilities in delivering a recommendation to the user as a final ranking of alternatives. [ABSTRACT FROM AUTHOR]

The paper introduces the modular approach in the Characteristic Objects method for the reduction of the rules base and thereby avoiding the curse of dimensionality. In this way, the required number of comparisons, between characteristic objects, is highly reduced. The modular approach decomposes a decisional model to related submodels, where each submodel aggregates correlated criteria. In the result, the modular solution consists of several fuzzy modules, which create a hierarchical structure of the considered problem. The proposed approach is compared with the conventional approach by using two exemplary decision functions. For this purpose, three and six-dimensional reference functions are used. Performed experiments enabled the comparison of an accuracy a proposed approach. [ABSTRACT FROM AUTHOR]

This paper introduces the Characteristic Objects Method (COMET) as a useful multi-criteria decision-making (MCDM) method for use in medical applications. The author presents an assessment of the risk of hard arteriosclerotic cardiovascular disease (ASCVD) events. First, an MCDM mini model will be obtained using the COMET, this mini model is the easiest to identify but has the lowest accuracy. The mini model uses only two values for each criterion as characteristic values. For the ASCVD problem, the following four criteria will be used: age, total cholesterol, HDL cholesterol and systolic blood pressure. The author assumes that a white, male patient who is nonsmoker and is free of diabetes or hypertension. The model will next be used to build a ranking for example patients. Finally, the obtained results will be verified using the statistical data (ACC/AHA model) to check the accuracy of the COMET procedure. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-making (MCDM) methods are associated with the ranking of alternatives based on expert judgments made using a number of criteria. In the MCDM field, the distance-based approach is one popular method for receiving a final ranking. One of the newest MCDM method, which uses the distance-based approach, is the Characteristic Objects Method (COMET). In this method, the preferences of each alternative are obtained on the basis of the distance from the nearest characteristic objects and their values. For this purpose, the domain and fuzzy numbers set for all the considered criteria are determined. The characteristic objects are obtained as the combination of the crisp values of all the fuzzy numbers. The preference values of all the characteristic object are determined based on the tournament method and the principle of indifference. Finally, the fuzzy model is constructed and is used to calculate preference values of the alternatives. In this way, a multi-criteria model is created and it is free of rank reversal phenomenon. In this approach, the matrix of expert judgment is necessary to create. For this purpose, an expert has to compare all the characteristic objects with each other. The number of necessary comparisons depends squarely to the number of objects. This study proposes the improvement of the COMET method by using the transitivity of pairwise comparisons. Three numerical examples are used to illustrate the efficiency of the proposed improvement with respect to results from the original approach. The proposed improvement reduces significantly the number of necessary comparisons to create the matrix of expert judgment. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance. The Complex Proportional Assessment (COPRAS) method identifies the preferences and ranking of decisional variants. It also allows for a more comprehensive analysis of complex decision-making problems, where many opposite criteria are observed. This approach allows us to minimize cost and maximize profit in the finally chosen decision (alternative). This paper presents a new entropy measurement for fuzzy intuitionistic sets and an application example using the IFS COPRAS method. The new entropy method was used in the decision-making process to calculate the objective weights. In addition, other entropy methods determining objective weights were also compared with the proposed approach. The presented results allow us to conclude that the new entropy measure can be applied to decision problems in uncertain data environments since the proposed entropy measure is stable and unambiguous. [ABSTRACT FROM AUTHOR]

An expert may experience difficulties in decision making when evaluating alternatives through a single assessment value in a hesitant environment. A fuzzy linear regression model (FLRM) is used for decision-making purposes, but this model is entirely unreasonable in the presence of hesitant fuzzy information. In order to overcome this issue, in this paper, we define a hesitant fuzzy linear regression model (HFLRM) to account for multicriteria decision-making (MCDM) problems in a hesitant environment. The HFLRM provides an alternative approach to statistical regression for modelling situations where input–output variables are observed as hesitant fuzzy elements (HFEs). The parameters of HFLRM are symmetric triangular fuzzy numbers (STFNs) estimated through solving the linear programming (LP) model. An application example is presented to measure the effectiveness and significance of our proposed methodology by solving a MCDM problem. Moreover, the results obtained employing HFLRM are compared with the MCDM tool called technique for order preference by similarity to ideal solution (TOPSIS). Finally, Spearman's rank correlation test is used to measure the significance for two sets of ranking. [ABSTRACT FROM AUTHOR]

This paper aims to present an innovative approach based on two newly developed Multi-Criteria Decision-Making (MCDM) methods: COMET combined with TOPSIS and SPOTIS, which could be the basis for a decision support system (DSS) in the problem of selecting solar panels. Solar energy is one of the most promising and environmentally friendly energy sources because of the enormous potential of directly converting available solar radiation everywhere into electricity. Furthermore, ever-lower prices for photovoltaic systems make solar electricity more competitive with power from conventional energy sources, increasing interest in solar panels among companies and households. This fact generates the need for a user-friendly, objective, fully automated DSS to support the multi-criteria selection of solar panels. Both MCDM methods chosen for this purpose are rank-reversal-free and precise. First, the objective entropy weighting method was applied for determining criteria weights. Final rankings were compared by two ranking correlation coefficients: symmetrical r w and asymmetrical W S . Then the sensitivity analysis providing local weights of alternatives for decision criteria was performed. The obtained results prove the adequacy and practical usefulness of the presented approach in solving the problem of solar panels selection. [ABSTRACT FROM AUTHOR]