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An alternative theory of linguistic variables is introduced based on voting model semantics. This theory is then applied to computing with words whereby a calculus is introduced for inference from linguistic facts and rules.

The aim of this paper is to develop a fuzzy linear programming technique for multidimensional analysis of preference (FLINMAP) in multiattribute group decision making problems with linguistic variables and incomplete preference information. In this paper, linguistic variables are used to assess an alternative on qualitative attributes using fuzzy ratings corresponding to some triangular fuzzy numbers. Each alternative is assessed on the basis of its distance to a fuzzy positive ideal solution (FPIS) which is unknown a priori. The FPIS and the weights of attributes are calculated by constructing a new linear programming model based on the group consistency and inconsistency indices defined on the basis of preferences between alternatives given by the decision makers. The distance of each alternative to the FPIS can be calculated to determine the ranking order of all alternatives. The implementation process of this methodology is demonstrated with an example.

The urban rail system in Istanbul carries in total more than 700.000 passengers per a day on different types of lines which require well organized risk governance. This paper evaluates the urban rail systems in Istanbul under different risk factors using Fuzzy Analytic Hierarchy Process (FAHP) to uncover the critical risk criteria of these systems and to make a multi-criteria evaluation of existing rail systems for the assignment of the scarce resources. Linguistic variables are used in the pairwise comparisons of criteria and alternatives. The risk factors considered are regional criticality, line characteristics, line safety and station structure. The evaluation results imply that the most risky critical urban rail system in Istanbul is the subway line from Sishane to Darussafaka.

In this paper some limitations of the conventional IF — THEN fuzzy rules due to the context dependency and rule structure are discussed. To overcome those limitations, the operational definition of a linguistic variable proposed by Zadeh is extended in such a way that a fuzzy value of a linguistic variable may take several meanings depending on the context. Applied to fuzzy controllers and models, this new operational definition leads to a new class of fuzzy controllers and models. To show its applicability this concept is applied to model the gear selection of two human drivers with different characteristics.

People use natural languages to think, to reason, to deduce conclusions, and to make decisions. Fuzzy set theory introduced by L. A. Zadeh has been intensively developed and founded a computational foundation for modeling human reasoning processs. The contribution of this theory both in the theoretical and the applied aspects is well recognized. However, the traditional fuzzy set theory cannot handle linguistic terms directly. In our approach, we have constructed algebraic structures to model linguistic domains, and developed a method of linguistic reasoning, which directly manipulates linguistic terms, In particular, our approach can be applied to fuzzy control problems.

In many applications of expert systems or fuzzy control, there exist numerous fuzzy reasoning methods. Intuitively, the effectiveness of each method depends on how well this method satisfies the following criterion: the similarity degree between the conclusion (the output) of the method and the consequence of an if-then sentence (in the given fuzzy model) should be the "same" as that between the input of the method and the antecedent of this if-then sentence. To formalize this idea, we introduce a "measure function" to measure the similarity between linguistic terms in a domain of any linguistic variable and to build approximate reasoning methods. The resulting comparison between our method and some other methods shows that our method is simple and more effective.

Identification of important design requirements for product development is critical because it leads to successful products with shorter development time. Quality Function Deployment (QFD) is a tool to help the product development team to systematically determine the design requirements for developing a product with higher customer satisfaction. Therefore, determining the Importance rating of Engineering Characteristics should be robust and reliable. Generally, in QFD charts the relationships between Customer Attributes and Engineering Characteristics can be defined using linguistic variables that have three values: Weak, Medium and Strong. Reversing priority of results (rank reversing) is possible when various scales such as 1-3-5 or 1-3-9 are employed. In this paper, the effect of using fuzzy numbers in rank reverse reduction is studied. For this study a statistical experiment for measuring rank reverse with fuzzy numbers was designed. This experiment was replicated for 7 sets, which included symmetrical and non-symmetrical triangular and trapezoidal fuzzy sets with various degrees of fuzziness. This experiment was extended for cases involving relative importance for Customer Attributes with various fuzzy sets used for weights of importance. The results showed a major reduction in rank reversal using symmetrical membership functions. Furthermore, results did not depend on system fuzziness, and there were not any major differences between the use of triangular and trapezoidal membership functions.

The aim of this paper is to develop a new fuzzy linear programming technique for solving multi-attribute decision-making (MADM) problems with incomplete weight preference information under fuzzy environments. In this methodology, linguistic variables are used to capture fuzziness in decision information and decision-making processes by means of a fuzzy decision matrix. Consistency and inconsistency indices are defined on the basis of preference relations between alternatives given by the decision maker under uncertain environments. Each alternative is assessed on the basis of its distance to a fuzzy ideal solution (FIS) which is unknown a priori. Then the FIS and the weights of attributes are estimated using a new linear programming model based upon the consistency and inconsistency indices defined. The fuzzy distance of each alternative to the FIS can be calculated to determine the ranking order of all alternatives. An extended illustrative example on the selection of air-fighters is presented to demonstrate the implementation process of this methodology. The methodology proposed in this paper can deal with MADM problems under not only fuzzy environments but also crisp environments. Also it has been proven that different weight information structures may result in different final decision results.

Multi-criteria decision-making (MCDM) is one of the most widely used decision methodologies. Because every kind of MCDM approach has unique strengths and weaknesses, it is difficult to determine which kind of MCDM approach is best suited to a specific problem. Therefore, a new decision-making method is proposed herein, based on linguistic information and intersection concepts; it is called the linguistic intersection method (LIM). Notably, the linguistic variables are more suited to expressing the opinion of each decision maker. There are four MCDM methods: TOPSIS, ELECTRE, PROMETHEE and VIKOR which are included in the LIM. First, each MCDM approach is used to determine the ranking order of all alternatives in accordance with the linguistic evaluations of decision makers. Then, the intersection set is determined with regard to the better alternatives of all methods. Third, the final ranking order of alternatives in the intersection set can be determined by the proposed method. Lastly, an example is given to describe the procedure of the proposed method. In order to verify the effectiveness of the proposed method, a simulation test is provided to compare the LIM with the linguistic MCDM method. According to the comparison results, the proposed method is more stable in determining the ranking order of all decision alternatives.

Neutrosophic matrices are more logical and feasible for the decision-makers, and they play a vital role in addressing multi-criteria decision making problems and dealing with indeterminacy. In this paper, we defined the multi-valued neutrosophic fuzzy matrix as well as its determinant, adjoint, and various operations. Under those operations, we defined several propositions. We prove that multi-valued neutrosophic matrices may not have to satisfy all of the properties of regular neutrosophic matrices but their application to multi-criteria decision-making problems is highly efficient. We introduced new linguistic variables for corresponding multi-valued neutrosophic numbers. The application of the proposed linguistic variable was numerically demonstrated by using the neutrosophic simplified-TOPSIS approach. The shown problem decides which sim card is best for the phone, which is evaluated by a team of decision-makers and the result is graphically displayed.

Biological systems are complex, consisting of many elements of different nature. As a whole, they are robust, and a general system description can be done in a semi-quantitative way when it comes to phenotype behaviors. We used these properties earlier¹ to develop a new systems biology method, causal mapping (CMAP). In this paper, we pinpoint some problems with the earlier version of CMAP, and develop it further. CMAP used linguistic variables (LV) to describe the behaviour of biological systems, and here we use the procedure of fuzzyfications to improve CMAP. The numerical methods to calculate the ranges of LV are agreeable to reality in a very intuitive manner. The new version of CMAP reproduced the physical data on cortical oscillations² in spreading cells with depolymerized microtubules. Further, predictions were made on the dependency of the myosin activity on the period of oscillations.

The presented development lies on the way to a more general approach that should be able to address questions of biological robustness, modularity and hierarchy.

The purpose of this paper is to develop a nonlinear programming model and method for solving fuzzy multi-attribute group decision making (FMAGDM) problems with linguistic variables. In this methodology, alternatives are assessed on qualitative attributes using linguistic terms from the designated linguistic term set, which can be expressed with the triangular fuzzy number set designated a priori. Alternatives for decision makers are assessed on the basis of the distances between the ordered weighted averaging (OWA) comprehensive value and the group best alternative which is unknown a priori. The group best alternative is then estimated through solving an auxiliary nonlinear programming model based on the concept that the sum of the distances of alternatives from the group best alternative for the decision makers should be as small as possible. The obtained group best alternative can be expressed using the designated triangular fuzzy numbers, which are corresponding to the designated linguistic terms. A numerical example is examined to demonstrate the difference between the proposed method and the generalized induced OWA operator method.

Generally, the health status can be measured by means of specific or generic questionnaires that let identify if an illness, a complication or a treatment affect the quality of life. In the existing literature the health status concept is a subjective impression, and patient is only person capable to define it. There are a lot of indexes to measure the health status degree, one of them is the EQ-5D where health information is expressed by means of numerical values, although the evaluated indicators are qualitative and subjective. This contribution proposes a linguistic EQ-5D where health information is modelled by means of linguistic information provided by patients in order to manage the uncertainty and subjectivity of such assessments.