Intertemporal Choice of Fuzzy Soft Sets

This paper first merges two noteworthy aspects of choice. On the one hand, soft sets and fuzzy soft sets are popular models that have been largely applied to decision making problems, such as real estate valuation, medical diagnosis (glaucoma, prostate cancer, etc.), data mining, or international trade. They provide crisp or fuzzy parameterized descriptions of the universe of alternatives. On the other hand, in many decisions, costs and benefits occur at different points in time. This brings about intertemporal choices, which may involve an indefinitely large number of periods. However, the literature does not provide a model, let alone a solution, to the intertemporal problem when the alternatives are described by (fuzzy) parameterizations. In this paper, we propose a novel soft set inspired model that applies to the intertemporal framework, hence it fills an important gap in the development of fuzzy soft set theory. An algorithm allows the selection of the optimal option in intertemporal choice problems with an infinite time horizon. We illustrate its application with a numerical example involving alternative portfolios of projects that a public administration may undertake. This allows us to establish a pioneering intertemporal model of choice in the framework of extended fuzzy set theorie

Evaluating strategies for implementing industry 4.0: a hybrid expert oriented approach of B.W.M. and interval valued intuitionistic fuzzy T.O.D.I.M.

open access articleDeveloping and accepting industry 4.0 influences the industry structure and customer willingness. To a successful transition to industry 4.0, implementation strategies should be selected with a systematic and comprehensive view to responding to the changes flexibly. This research aims to identify and prioritise the strategies for implementing industry 4.0. For this purpose, at first, evaluation attributes of strategies and also strategies to put industry 4.0 in practice are recognised. Then, the attributes are weighted to the experts’ opinion by using the Best Worst Method (BWM). Subsequently, the strategies for implementing industry 4.0 in Fara-Sanat Company, as a case study, have been ranked based on the Interval Valued Intuitionistic Fuzzy (IVIF) of the TODIM method. The results indicated that the attributes of ‘Technology’, ‘Quality’, and ‘Operation’ have respectively the highest importance. Furthermore, the strategies for “new business models development’, ‘Improving information systems’ and ‘Human resource management’ received a higher rank. Eventually, some research and executive recommendations are provided. Having strategies for implementing industry 4.0 is a very important solution. Accordingly, multi-criteria decision-making (MCDM) methods are a useful tool for adopting and selecting appropriate strategies. In this research, a novel and hybrid combination of BWM-TODIM is presented under IVIF information

A novel approach to multi-attribute group decision-making based on interval-valued intuitionistic fuzzy power Muirhead mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method

An approach to multiple attribute decision making based on the induced Choquet integral with fuzzy number intuitionistic fuzzy information

In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method

An interval-valued intuitionistic fuzzy multiattribute group decision making framework with incomplete preference over alternatives

This article proposes a framework to handle multiattribute group decision making problems with incomplete pairwise comparison preference over decision alternatives where qualitative and quantitative attribute values are furnished as linguistic variables and crisp numbers, respectively. Attribute assessments are then converted to interval-valued intuitionistic fuzzy numbers (IVIFNs) to characterize fuzziness and uncertainty in the evaluation process. Group consistency and inconsistency indices are introduced for incomplete pairwise comparison preference relations on alternatives provided by the decision-makers (DMs). By minimizing the group inconsistency index under certain constraints, an auxiliary linear programming model is developed to obtain unified attribute weights and an interval-valued intuitionistic fuzzy positive ideal solution (IVIFPIS). Attribute weights are subsequently employed to calculate distances between alternatives and the IVIFPIS for ranking alternatives. An illustrative example is provided to demonstrate the applicability and effectiveness of this method

An approach to multiattribute decision making with interval-valued intuitionistic fuzzy assessments and incomplete weights

This article proposes an approach to multiattribute decision making with incomplete attribute weight information where individual assessments are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). By employing a series of optimization models, the proposed approach derives a linear program for determining attribute weights. The weights are subsequently used to synthesize individual IVIFN assessments into an aggregated IVIFN value for each alternative. In order to rank alternatives based on their aggregated IVIFN values, a novel method is developed for comparing two IVIFNs by introducing two new functions: the membership uncertainty index and the hesitation uncertainty index. An illustrative investment decision problem is employed to demonstrate how to apply the proposed procedure and comparative studies are conducted to show its overall consistency with existing approaches