in this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. afterwards, the a...

An algebraic presentation of Martin-Löf’s intuitionistic type theory is given which is based on the notion of a category with families with extra structure. We then present a type-checking algorithm for the normal forms of this theory, and sketch how it gives rise to an initial category with families with extra structure. In this way we obtain a purely algebraic formulation of the correctness o...

In this paper, the concept of intuitionistic fuzzy mapping as a generalization of fuzzy mapping is presented, and its' relationship with intuitionistic fuzzy relations is derived. Moreover, some basicoperations of intuitionistic fuzzy mappings are defined, hence we can conclude that all of intuitionistic fuzzy mappings constitute a soft algebrawith respect to these operations. Afterwards, the A...

Trapezoidal intuitionistic fuzzy numbers (TrIFNs) express abundant and flexible information in a suitable manner and  are very useful to depict the decision information in the procedure of decision making. In this paper, some new aggregation operators, such as, trapezoidal intuitionistic fuzzy weighted power harmonic mean (TrIFWPHM) operator, trapezoidal intuitionistic fuzzy ordered weighted po...

We introduce the bimodal logic S4.Grzu, which is the extension of Bennett’s bimodal logic S4u by Grzegorczyk’s axiom ( (p→ p)→ p)→ p and show that the lattice of normal extensions of the intuitionistic modal logic WS5 is isomorphic to the lattice of normal extensions of S4.Grzu, thus generalizing the Blok–Esakia theorem. We also introduce the intuitionistic modal logicWS5.C, which is the extens...

in this paper, we introduce a new class of implicit functions and also common property (e.a) in modified intuitionistic fuzzy metric spaces and utilize the same to prove some common fixed point theorems in modified intuitionistic fuzzy metric spaces besides discussing related results and illustrative examples. we are not aware of any paper dealing with such implicit functions in modified intuit...

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitio...

Taking into account the notion of BL-general fuzzy automaton, in the present study we define the notation of BL-intuitionistic general L-fuzzy automaton and I-bisimulation for BL-intuitionistic general L-fuzzy automaton.Then for a given BL-intuitionistic general L-fuzzy automaton, we obtain the greatest I-bisimulation. According to this notion, we give the structure of quotient BL-intuiti...

In this paper we define intuitionistic fuzzy metric and normedspaces. We first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. In section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. Finally,we consider some properties of...

in some multi-attribute decision making (madm) problems, various relationships among the decision attributes should be considered. this paper investigates the prioritization relationship of attributes in madm with trapezoidal intuitionistic fuzzy numbers (trifns). trifns are a special intuitionistic fuzzy set on a real number set and have the better capability to model ill-known quantities. fir...