Probabilistic Fuzzy Environment Research Articles

Reliability appraisal of a system using interval-valued probabilistic dual hesitant fuzzy element

Here, under probabilistic fuzzy environment, we introduce a new technique for reliability appraisal of a system, where the reliability of a component/unit of a system is represented by interval-valued probabilistic dual hesitant fuzzy element (IVPDHFE). In present work, we evaluate the reliability for some complex systems (series configuration, parallel configuration and bridge configuration) using score function and deviation degree which is very useful in decision making, measurement theory, optimization problems and risk analysis. In addition, a numerical example is included to better illustrate the current technique.

Multi-attribute group decision making method based on prospect theory under hesitant probabilistic fuzzy environment

The hesitant fuzzy element (HFE), as an extension of fuzzy numbers, has received much attention and the occurrence probabilities of each membership in the HFEs are assumed to be equal, i.e., the decision makers (DMs) share the same preference for each membership. Anecdotal observations suggest otherwise. To address this issue, the hesitant probabilistic fuzzy set (HPFS) is proposed, which is more suitable for depicting the DMs’ preferences in decision making. Research reports that psychological behavior matters in the decision-making process. Consequently, this paper proposes a multi-attribute group decision making method under a hesitant probabilistic fuzzy environment that considers the DMs’ psychological state in the decision-making process. A weights determination model is constructed, incorporating objective decision-making information and the subjective preferences of the DMs based on a score function and the minimum relative entropy principle. Finally, an established case example is applied to validate the applicability of the proposed method, and comparative analysis is also completed to verify the validity of the proposed method.

Hesitant Probabilistic Fuzzy Preference Relations in Decision Making

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

Multi-criteria Outranking Methods with Hesitant Probabilistic Fuzzy Sets

Due to the defects of hesitant fuzzy sets (HFSs) in the actual decision-making process, it is necessary to add the probabilities corresponding to decision maker’s preferences to the values in HFSs. Hesitant probabilistic fuzzy sets (HPFSs) are suitable for presenting this kind of information and contribute positively to the efficiency of depicting decision maker’s preferences in practice. However, some important issues in HPFSs utilization remain to be addressed. In this paper, the qualitative flexible multiple criteria method (QUALIFLEX) and the preference ranking organization method for enrichment evaluations II (PROMETHEE II) are extended to HPFSs. First, we provide a comparison method for hesitant probabilistic fuzzy elements (HPFEs). Second, we propose a novel possibility degree depicting the relations between two HPFEs, and then, employ the possibility degree to extend the QUALIFLEX and PROMETHEE II methods to hesitant probabilistic fuzzy environments based on the proposed possibility degree. Third, an information integration method is introduced to simplify the processing of HPFE evaluation information. Finally, we provide an example to demonstrate the usefulness of the proposed methods. An illustrative example in conjunction with comparative analyses is employed to demonstrate that our proposed methods are feasible for practical multi-criteria decision-making (MCDM) problems, and the final ranking results show that the proposed methods are more accurate than the compared methods in an actual decision-making processes. HPFSs are more practical than HFSs due to their efficiency in comprehensively representing uncertain, vague, and probabilistic information. The proposed methods are effective for solving hesitant probabilistic MCDM problems and are expected to contribute to the solution of MCDM problems involving uncertain or vague information.

A Dynamic Reference Point Method for Emergency Response Under Hesitant Probabilistic Fuzzy Environment

According to the characteristics of emergency decision-making in crisis management, this paper proposes a dynamic decision-making method using the hesitant probabilistic fuzzy set to deal with the inadequate information, uncertainty and dynamic trends. This method is suitable for emergency decision-making as it provides supports for the dynamic and evolutionary characteristics of emergency responses and the uncertain probability about external environment is also considered. In order to make a continuous adjustment with the development of situations, we give a definition of the expectation level, based on which the dynamic reference point method is proposed to obtain the optimal emergency response plan under the hesitant probabilistic fuzzy environment. We also analyze the probability of different situations that may occur in the process of emergency decision-making and provide an algorithm for solving this problem. Finally, a practical case of hazardous goods leakage pollution accident is given to illustrate our method, and then, the optimal decision alternative chain is obtained.

Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment

As a generalized fuzzy number, the hesitant fuzzy element (HFE) has been receiving increased attention and has recently become a popular topic. However, we find that the occurring probabilities of the possible values in the HFE are equal, which is obviously impractical. Consequently, in this paper, we propose a hesitant fuzzy number with probabilities, called the hesitant probabilistic fuzzy number, and construct its score function, deviation function, comparison laws, and its basic operations. It is well known that in the context of a group of decision makers (DMs), one of the basic approaches to built consensus is to aggregate individual evaluations or individual priorities. Thus, to use the hesitant fuzzy numbers for consensus building with a group of DMs, we further propose a method called maximizing score deviation method to obtain the DMs’ weights under the HPFE environment, based on which two extended and four new ordered weighted operators are provided to fuse the HPFE information and build the consensus of the DMs. We also analyze the differences among these ordered weighted operators and provide their application scopes. Finally, a practical case is provided to demonstrate consensus building with a group of DMs under the HPFE environment using the proposed approaches.

Multi-criteria decision making by means of fuzzy and probabilistic sets

The paper deals with the methods of multi-criteria decision making in a probabilistic fuzzy environment. It is assumed that over the set of alternatives (elements) there exists a finite set of criteria represented by the respective probabilistic sets. Aggregating the criteria the final decision set is obtained. Various choice criteria are used to get the final ordering of the alternatives. The ideas are illustrated by means of numerical examples.

On the choice of optimal alternatives for decision making in probabilistic fuzzy environment

A type of dominance of alternatives called stochastic dominance is presented in this paper, whose purpose is the choice of optimal alternatives in uncertain and imprecise environment. For the decision set (in addition to the sets representing goals and constraints) the concept of probabilistic set as introduced by Hirota is used. The ideas are illustrated by means of numerical examples.

Decision making in uncertain environments

In the paper some problems of decision making in fuzzy and probabilistic fuzzy environments are formulated. The goals and constraints in such decision situations may be simultaneously fuzzy and random by their nature. Looking for a decision set which should be any reasonable function of goals and constraints, it leads to operations on probabilistic sets which are also of interest in that work. Some numerical examples of decision making are illustrating the theoretical considerations presented in this paper.

The aggregation operations for decision making in probabilistic fuzzy environment

This paper deals with some important classes of aggregation operations on various kinds of sets applied to decision making problems. These operations are mainly based on general concepts such as triangular norms ( t- and s-norms). In this paper we focus particularly on operations on probabilistic sets and their distribution function representation. The considerations are illustrated by means of numerical examples.