The vague sum (product) of a finite number of real numbers and the vague integral multiples (powers) of real numbers based on a perfect vague addition (multiplication) operation are introduced, and some of their fundamental properties are pointed out. Furthermore, some examples are designed to show how they can be practically implemented. Keyword: Fuzzy arithmetic, Vague arithmetic, Vague arith...

The correlation between the performance of attributes and the overallsatisfaction such as they are perceived by the customers is often used tocalculate the importance of attributes in the crisp case. Recently, the methodwas extended, based on the standard Zadeh extension principle, to the fuzzycase, taking into account the specificity of the human thinking. Thedifficulties of calculation are im...

We have presented trapezoidal intuitionistic fuzzy number. Arithmetic operations of trapezoidal intuitionistic fuzzy number is presented based on (α, β)-cuts. We have presented intuitionistic fuzzy fault tree analysis using trapezoidal intuitionistic fuzzy number. In application of intuitionistic fuzzy fault tree analysis, we have computed failure of fire protection system taking failure of eac...

We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of interval-valued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. Based on these main results of the paper, the methods or procedures elaborated for interval-valued trapezoidal or triangular fuzz...

In group decision making with linguistic information, the decision makers (DMs) usually provide their assessment information by means of linguistic variables. In some situations, however, the DMs may provide fuzzy linguistic information because of time pressure, lack of knowledge, and their limited attention and information processing capabilities. In this paper, we introduce the concepts of tr...

Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their ...

In this paper, we develop a new approach to deal with neutrosphic shortest path problem in a network in which each edge weight (or length) is represented as triangular fuzzy neutrosophic number. The proposed algorithm also gives the shortest path length from source node to destination node using ranking function. Finally, an illustrative example is also included to demonstrate our proposed appr...

This research addresses system reliability analysis using weakest t-norm based approximate intuitionistic fuzzy arithmetic operations, where failure probabilities of all components are represented by different types of intuitionistic fuzzy numbers. Due to the incomplete, imprecise, vague and conflicting information about the component of system, the present study evaluates the reliability of sy...

This paper presents solution technique of geometric programming with fuzzy parameters to solve structural model. Here we are considered all fuzzy parameters as a generalized fuzzy number i.e. generalized triangular fuzzy number and generalized trapezoidal fuzzy number. Here material density of the bar, permissible stress of each bar and applied load are fuzzy numbers. We use geometric programmi...